All files are .pdf, unless said otherwise (and draft versions).
Most new articles are accessible via arXiv.org, under the same title,
in preliminary versions.
(February 7, 2011)
[GS10] Dov Gabbay, Karl Schlechta:
"Conditionals and modularity in
general logics"
Springer, Heidelberg, August 2011,
ISBN 978-3-642-19067-4,
a preliminary version is accessible via
arXiv.org, same title
1 Introduction
1.1 The main subjects of this book
1.1.1 An example
1.1.1.1 An abstract description of both cases in
above example
1.1.2 Connections
1.2 Main definitions and results
1.2.1 The monotone case
1.2.2 The non-monotonic case
1.3 Overview of this introduction
1.4 Basic definitions
1.5 Towards a uniform picture of conditionals
1.5.1 Discussion and classification
1.5.2 Additional structure on language and truth
values
1.5.3 Representation for general revision, update,
and counterfactuals
1.6 Interpolation
1.6.1 Introduction
1.6.2 Problem and Method
1.6.3 Monotone and antitone semantic and syntactic
interpolation
1.6.4 Laws about size and interpolation in
non-monotonic logics
1.6.5 Summary
1.7 Neighbourhood semantics
1.7.1 Defining neighbourhoods
1.7.2 Additional requirements
1.7.3 Connections between the various properties
1.7.4 Various uses of neighbourhood semantics
1.8 An abstract view on modularity and
independence
1.8.1 Introduction
1.8.2 Abstract definition of independence
1.8.3 Other aspects of independence
1.9 Conclusion and outlook
1.10 Previously published material,
acknowledgements
2 Basic definitions
2.1 Introduction
2.1.1 Overview of this chapter
2.2 Basic algebraic and logical definitions
2.2.1 Countably many disjoint sets
2.2.2 Introduction to many-valued logics
2.3 Preferential structures
2.3.1 The minimal variant
2.3.2 The limit variant
2.3.3 Preferential structures for many-valued
logics
2.4 IBRS and higher preferential structures
2.4.1 General IBRS
2.4.2 Higher preferential structures
2.5 Theory revision
2.5.0.8A remark on intuition
2.5.1 Theory revision for many-valued logics
3 Towards a uniform picture of conditionals
3.1 Introduction
3.1.1 Overview of this chapter
3.2 An abstract view on conditionals
3.2.1 A general definition as arbitrary operator
3.2.2 Properties of choice functions
3.2.3 Evaluation of systems of sets
3.2.4 Conditionals based on binary relations
3.2.4.1 Short discussion of above examples
3.3 Conditionals and additional structure on
language and truth values
3.3.1 Introduction
3.3.2 Operations on language and truth values
3.3.3 Operations on language elements and truth
values within one language
3.3.4 Operations on several languages
3.3.5 Operations on definable model sets
3.3.6 Softening concepts
3.3.7 Aspects of modularity and independence in
defeasible inheritance
3.4 Representation for general revision, update,
and counterfactuals
3.4.1 Importance of theory revision for general
structures, reactivity, and its solution
3.4.2 Introduction
3.4.3 Semantic representation for generalized
distance based theory revision
3.4.4 Semantic representation for generalized
update and counterfactuals
3.4.5 Syntactic representation for generalized
revision, update, counterfactuals
4 Monotone and antitone semantic and syntactic
interpolation
4.1 Introduction
4.1.1 Overview
4.1.2 Problem and Method
4.1.3 Monotone and antitone semantic and syntactic
interpolation
4.2 Monotone and antitone semantic interpolation
4.2.1 The two-valued case
4.2.2 The many-valued case
4.3 The interval of interpolants in monotonic or
antitonic logics
4.3.1 Introduction
4.3.2 Examples and a simple fact
4.3.3 + and - as new semantic and syntactic
operators
4.4 Monotone and antitone syntactic interpolation
4.4.1 Introduction
4.4.2 The classical propositional case
4.4.3 Finite (intuitionistic) Goedel logics
5 Laws about size and interpolation in
non-monotonic logics
5.1 Introduction
5.1.1 A succinct description of our main ideas
and results in this chapter
5.1.2 Various concepts of size and non-monotonic
logics
5.1.3 Additive and multiplicative laws about size
5.1.4 Interpolation and size
5.1.5 Hamming relations and size
5.1.6 Equilibrium logic
5.1.7 Interpolation for revision and argumentation
5.1.8 Language change to obtain products
5.2 Laws about size
5.2.1 Additive laws about size
5.2.2 Multiplicative laws about size
5.2.3 Hamming relations and distances
5.2.4 Summary of properties
5.2.5 Language change in classical and
non-monotonic logic
5.3 Semantic interpolation for non-monotonic logic
5.3.1 Discussion
5.3.2 Interpolation of the form AÝ~BÝ-C
5.3.3 Interpolation of the form AÝ-BÝ~C
5.3.4 Interpolation of the form AÝ~BÝ~C
5.3.5 Interpolation for distance based revision
5.3.6 The equilibrium logic EQ
5.4 Context and structure
5.5 Interpolation for argumentation
6 Neighbourhood semantics
6.1 Introduction
6.1.1 Defining neighbourhoods
6.1.2 Additional requirements
6.1.3 Connections between the various properties
6.1.4 Various uses of neighbourhood semantics
6.2 Detailed overview
6.2.1 Motivation
6.2.2 Tools to define neighbourhoods
6.2.3 Additional requirements
6.2.4 Interpretation of the neighbourhoods
6.2.5 Overview of the different lines of reasoning
6.2.6 Extensions
6.3 Tools and requirements for neighbourhoods
and how to obtain them
6.3.1 Tools to define neighbourhoods
6.3.2 Obtaining such tools
6.3.3 Additional requirements for neighbourhoods
6.3.4 Connections between the various concepts
6.4 Neighbourhoods in deontic and default logic
6.4.1 Introduction
6.4.2 Two important examples for deontic logic
6.4.3 Neighbourhoods for deontic systems
7 Conclusion and outlook
7.1 Conclusion
7.1.1 Semantic and syntactic interpolation
7.1.2 Independence and interpolation for
monotonic logic
7.1.3 Independence and interpolation for
non-monotonic logic
7.1.4 Neighbourhood semantics
7.2 Outlook
7.2.1 The dynamics of reasoning
7.2.2 A revision of basic concepts of logic:
justification
[GS09f] Dov Gabbay, Karl Schlechta:
"Logical tools for handling change in
agent-based systems"
Springer, ISBN 978-3642044069
a (condensed) preliminary version is accessible via
arXiv.org, same title
1 Introduction and Motivation
1.1 Program
1.2 Short overview of the different logics
1.2.1 Nonmonotonic logics
1.2.2 Theory revision
1.2.3 Theory update
1.2.4 Deontic logic
1.2.5 Counterfactual conditionals
1.2.6 Modal logic
1.2.7 Intuitionistic logic
1.2.8 Inheritance systems
1.2.9 A summarizing table for the semantics
1.3 A discussion of concepts
1.3.1 Basic semantic entities, truth values, and
operators
1.3.2 Algebraic and structural semantics
1.3.3 Restricted operators and relations
1.3.4 Copies in preferential models
1.3.5 Further remarks on universality of
representation proofs
1.3.6 Ý~ in the object language?
1.3.7 Various considerations on abstract semantics
1.3.8 A comparison with Reiter defaults
1.4 IBRS
1.4.1 Definition and comments
1.4.2 The power of IBRS
1.4.3 Abstract semantics for IBRS and its
engineering realization
2 Basic definitions and results
2.1 Algebraic definitions
2.2 Basic logical definitions
2.3 Basic definitions and results for nonmonotonic
logics
3 Abstract semantics by size
3.1 The first order setting
3.2 General size semantics
3.2.1 Introduction
3.2.2 Main table
3.2.3 Coherent systems
4 Preferential structures - Part I
4.1 Introduction
4.1.1 Remarks on nonmonotonic logics and
preferential semantics
4.1.2 Basic definitions
4.2 Preferential structures without domain
conditions
4.2.1 General discussion
4.2.2 Detailed discussion
5 Preferential structures - Part II
5.1 Simplifications by domain conditions, logical
properties
5.1.1 Introduction
5.1.2 Smooth structures
5.1.3 Ranked structures
5.1.4 The logical properties with definability
preservation
5.2 A-ranked structures
5.2.1 Representation results for A-ranked
structures
5.3 Two sequent calculi
5.3.1 Introduction
5.3.2 Plausibility Logic
5.3.3 A comment on the work by Arieli and Avron
5.4 Blurred observation - absence of definability
preservation
5.4.1 Introduction
5.4.2 General and smooth structures without
definability preservation
5.4.3 Ranked structures
5.5 The limit variant
5.5.1 Introduction
5.5.2 The algebraic limit
5.5.3 The logical limit
6 Higher preferential structures
6.1 Introduction
6.2 The general case
6.3 Discussion of the totally smooth case
6.4 The essentially smooth case
6.5 Translation to logic
7 Deontic logic and hierarchical conditionals
7.1 Semantics of deontic logic
7.1.1 Introductory remarks
7.1.2 Basic definitions
7.1.3 Philosophical discussion of obligations
7.1.4 Examination of the various cases
7.1.5 What is an obligation?
7.1.6 Conclusion
7.2 A comment on work by Aqvist
7.2.1 Introduction
7.2.2 There are (at least) two solutions
7.2.3 Outline
7.3 Hierarchical conditionals
7.3.1 Introduction
7.3.2 Formal modelling and summary of results
7.3.3 Overview
7.3.4 Connections with other concepts
7.3.5 Formal results and representation for
hierarchical conditionals
8 Theory update and theory revision
8.1 Update
8.1.1 Introduction
8.1.2 Hidden dimensions
8.2 Theory revision
8.2.1 Introduction to theory revision
8.2.2 Booth revision
8.2.3 Revision and independence
8.2.4 Preferential modelling of defaults
8.2.5 Remarks on independence
9 An analysis of defeasible inheritance systems
9.1 Introduction
9.1.1 Terminology
9.1.2 Inheritance and reactive diagrams
9.1.3 Conceptual analysis
9.2 Introduction to nonmonotonic inheritance
9.2.1 Basic discussion
9.2.2 Directly sceptical split validity upward
chaining off-path inheritance
9.2.3 Review of other approaches and problems
9.3 Defeasible inheritance and reactive diagrams
9.3.1 Summary of our algorithm
9.3.2 Overview
9.3.3 Compilation and memorization
9.3.4 Executing the algorithm
9.3.5 Signposts
9.3.6 Beyond inheritance
9.4 Interpretations
9.4.1 Introduction
9.4.2 Informal comparison of inheritance with the
systems P and R
9.4.3 Inheritance as information transfer
9.4.4 Inheritance as reasoning with prototypes
9.5 Detailed translation of inheritance to
modified systems of small sets
9.5.1 Normality
9.5.2 Small sets
Preliminary version:
[GS09f]
see also
[Sch06-t1]
[Sch04] Karl Schlechta: Coherent systems
Vol. 2 of the Series:
Studies in Logic and Practical Reasoning,
Elsevier, Amsterdam,
Sept. 2004,
pp. 468,
ISBN 0-444-51789-8
see also: LIF TR 14-2003 for a preliminary version
Abstract:
We discuss several types of common sense
reasoning, reduce them to a small number of
basic semantical concepts, and show several
(in-)completeness results for such logics.
TABLE OF CONTENTS
=================
Foreword (by David Makinson)
Summary
Acknowledgements
Chapter 1 : Introduction
Chapter 2 : Concepts
Chapter 3 : Preferences
Chapter 4 : Distances
Chapter 5 : Definability preservation
Chapter 6 : Sums
Chapter 7 : Size
Chapter 8 : Integration
Chapter 9 : Conclusion and outlook
Bibliography
Index
CHAPTER 1 : INTRODUCTION
========================
1.1 The main topics of the book
1.1.1 Conceptual analysis
1.1.2 Generalized modal logic and integration
1.1.3 Formal results
1.1.4 Various remarks
1.2 Historical remarks
1.3 Organisation of the book
1.4 Overview of the chapters
1.4.1 The conceptual part (Chapter 2)
1.4.2 The formal part (Chapters 3-7)
1.4.3 Integration (Chapter 8)
1.4.4 Problems, ideas and techniques
1.5 Specific remarks on propositional logic
1.6 Basic definitions
1.6.1 The algebraic part
1.6.2 The logical part
1.6.2.1 Results on the absence of representation
CHAPTER 2 : CONCEPTS
====================
2.1 Introduction
2.2 Reasoning types
2.2.1 Traditional non-monotonic logics
2.2.1.1 Normal, important, or interesting cases
2.2.1.2 The majority of cases
2.2.1.3 As many as possible (Reiter defaults)
2.2.2 Prototypical and ideal cases
2.2.3 Extreme cases and interpolation
2.2.4 Clustering
2.2.5 Certainty
2.2.6 Quality of an answer, approximation, and
complexity
2.2.7 Useful reasoning
2.2.8 Inheritance and argumentation
2.2.9 Dynamic systems
2.2.10 Theory revision
2.2.10.1 General discussion
2.2.10.2 The AGM approach
2.2.11 Update
2.2.12 Counterfactual conditionals
2.3 Basic semantical concepts
2.3.1 Preference
2.3.2 Distance
2.3.3 Size
2.3.3.1 Sums and products
2.4 Coherence
CHAPTER 3 : PREFERENCES
=======================
3.1 Introduction
3.1.1 General discussion
3.1.2 The basic definitions and results
3.2 General preferential structures
3.2.1 General minimal preferential structures
3.2.2 Transitive minimal preferential structures
3.2.3 One copy version
3.2.4 A (very) short remark on X-logics
3.3 Smooth minimal preferential structures
3.3.1 Smooth minimal preferential structures with
arbitrarily many copies
3.3.2 Smooth and transitive minimal preferential
structures
3.4 The logical characterization of general and smooth
preferential models
3.4.1 Simplifications of the general transitive limit case
3.5 A counterexample to the KLM-system
3.5.1 The formal results
3.6 A non-smooth model of cumulativity
3.6.1 The formal results
3.6.1.1 A non-smooth injective structure validating
P, (WD), -(NR)
3.7 Plausibility logic - problems without closure
under finite union
3.7.1 Introduction
3.7.2 Completeness and incompleteness results for
plausibility logic
3.7.2.1 (PlI)+(PlRM)+(PlCC) is complete (and sound)
for preferential models
3.7.2.2 Incompleteness of full plausibility logic for
smooth structures
3.7.2.3 Discussion and remedy
3.8 The role of copies in preferential structures
3.9 A new approach to preferential structures
3.9.1 Introduction
3.9.1.1 Main concepts and results
3.9.1.2 Motivation and overview
3.9.1.3 Basic definitions and facts
3.9.1.4 Outline of our representation results and technique
3.9.2 Validity in traditional and in our preferential
structures
3.9.3 The disjoint union of models and the problem of
multiple copies
3.9.3.1 Disjoint unions and preservation of validity in
disjoint unions
3.9.3.2 Multiple copies
3.9.4 Representation in the finite case
3.10 Ranked preferential structures
3.10.1 Introduction
3.10.1.1 Detailed discussion of this section
3.10.1.2 Introductory facts and definitions
3.10.2 The minimal variant
3.10.2.1 Some introductory results
3.10.2.2 Characterizations
3.10.3 The limit variant without copies
3.10.3.1 Representation
3.10.3.2 Partial equivalence of limit and minimal ranked
structures
CHAPTER 4 : DISTANCES
=====================
4.1 Introduction
4.1.1 Theory Revision
4.1.2 Counterfactuals
4.1.3 Summary
4.2 Revision by symmetrical and not necessarily
symmetric distance
4.2.1 Introduction
4.2.2 The algebraic results
4.2.2.1 Introduction and pseudo-distances
4.2.2.2 The representation results for the symmetric case
4.2.2.3 The representation result for the finite not
necessarily symmetric case
4.2.3 The logical results
4.2.3.1 Introduction
4.2.3.2 The symmetric case
4.2.3.3 The finite not necessarily symmetric case
4.2.4 There is no finite characterization
4.2.5 The limit case
4.2.5.1 Introduction
4.2.5.2 Remarks on the logics of the revision limit
case
4.2.5.3 Equivalence of the minimal and the limit case
for formulas
4.3 Local and global metrics for the semantics of
counterfactuals
4.3.1 Introduction
4.3.1.1 Basic definitions
4.3.2 The results
4.3.2.1 Outline of the construction for Proposition 4.3.1
4.3.2.2 Detailed proof of Proposition 4.3.1
4.3.2.3 The limit variant
CHAPTER 5 : DEFINABILITY PRESERVATION
=====================================
5.1 Introduction
5.1.1 The problem
5.1.2 The remedy
5.1.2.1 Preferential structures
5.1.2.2 Theory revision
5.1.2.3 Summary
5.1.3 Basic definitions and results
5.1.3.1 General part
5.1.3.2 Results for the definability preserving case
and counterfactuals
5.1.3.3 Discussion of the technical development
5.1.4 A remark on definability preservation and
modal logic
5.2 Preferential structures
5.2.1 The algebraic results
5.2.1.1 The conditions
5.2.1.2 The general case
5.2.1.3 The smooth case
5.2.2 The logical results
5.2.3 The general case and the limit version
cannot be characterized
5.3 Revision
5.3.1 The algebraic result
5.3.2 The logical result
CHAPTER 6 : SUMS
================
6.1 Introduction
6.1.1 The general situation and the Farkas
algorithm
6.1.2 Update by minimal sums
6.1.3 Comments on "Belief revision with unreliable
observations"
6.1.4 "Between" and "behind"
6.1.5 Summary
6.2 The Farkas algorithm
6.3 A representation result for update by minimal
sums
6.3.1 Introduction
6.3.2 An abstract result
6.3.3 Representation
6.3.3.1 Introduction
6.3.3.2 The result
6.3.4 There is no finite representation for our type
of update possible
6.3.4.1 Outline
6.3.4.2 The details
6.4 Comments on "Belief revision with unreliable
observations"
6.4.1 Introduction
6.4.1.1 The situation
6.4.1.2 Basic definitions and results
6.4.2 A characterization of Markov systems (in the
finite case)
6.4.2.1 Outline and introduction
6.4.2.2 The representation result for the finite case
6.4.3 There is no finite representation possible
6.5 "Between" and "Behind"
6.5.1 There is no finite representation for "between"
and "behind"
CHAPTER 7 : SIZE
================
7.1 Introduction
7.1.1 The details
7.2 Generalized quantifiers
7.2.1 Introduction
7.2.2 Results
7.3 Comparison of three abstract coherent systems
based on size
7.3.1 Introduction
7.3.2 Presentation of the three systems
7.3.2.1 The system of Ben-David/Ben-Eliyahu
7.3.2.2 The system of the author
7.3.2.3 The system of Friedman/Halpern
7.3.3 Comparison of the systems of Ben-David/Ben-Eliyahu
and the author
7.3.3.1 Equivalence of both systems
7.3.4 Comparison of the systems of Ben-David/Ben-Eliyahu
and of
Friedman/Halpern
7.4 Theory revision based on model size
7.4.1 Introduction
7.4.2 Results
7.4.2.1 Pre-EE relations and epistemic entrenchment
relations
7.4.2.2 Stable sets
7.4.2.3 Revision based on model size
CHAPTER 8 : INTEGRATION
=======================
8.1 Introduction
8.1.1 Rules or object language?
8.1.2 Various levels of reasoning
8.2 Reasoning types and concepts
8.3 Formal aspects
8.3.1 Classical modal logic
8.3.2 Classical propositional operators have no unique
interpretation
8.3.3 Combining individual completeness results
CHAPTER 9 : CONCLUSION AND OUTLOOK
==================================
Preliminary version:
[Sch04]
[Sch97-2] K.Schlechta : "Nonmonotonic logics - Basic Concepts,
Results, and Techniques"
Springer Lecture Notes series, LNAI 1187, Jan. 1997,
243pp
Table of contents:
1 Introduction
1.1 Preliminaries
1.2 Our philosophical position
1.2.1 Logic as a tool
1.2.2 Basic semantical notions
1.2.3 Abstract semantics
1.2.4 Restricted monotony and irrelevance
1.2.5 Logic and structural information
1.2.6 Summary and program
1.3 Introduction to nonmonotonic logics and
its problems
1.3.1 History and an example
1.3.2 Some basic differences
1.3.3 A (simplified) introduction to Reiter's
theory of defaults
1.3.4 Static and dynamic aspects of defaults
1.3.5 Introduction to preferential structures
1.3.6 Introduction to defaults as generalized
quantifiers
1.3.7 A two stage approach
1.3.8 Introduction to logic and analysis
1.3.9 Introduction to theory revision
1.3.10 Introduction to structured reasoning in
diagrams
1.3.11 The problem of irrelevant information
1.4 Basic definitions and notation
1.5 Acknowledgements
2 Preferential structures and related logics
2.1 Preferential structures
2.1.1 Introduction and basic definitions
2.1.2 Orderings on &L and completeness results
2.1.3 Defaults and preferential models
2.1.4 Supraclassicality + cumulativity +
distributivity does not entail classical
representability
2.1.5 A representation theorem for preferential
models
2.1.6 General smoothness
2.1.7 Limit preferential models
2.2 Local and global metrics for the
semantics of counterfactual conditionals
2.3 Extension by finite approximation from
below
3 Defaults as generalized quantifiers
3.1 Introduction
3.2 Defaults as generalized quantifiers
3.3 Sceptical revision of partially ordered
defaults
4 Logic and analysis
4.1 Overview, motivation, and basic definitions
4.2 Technical development
5 Theory revision and probability
5.1 Introduction
5.2 Epistemic preference relations
5.3 Measuring theories, and an outlook for a
different treatment of theory revision
6 Structured reasoning
6.1 Inheritance diagrams
6.1.1 Introduction
6.1.2 A detailed survey of inheritance … la
Thomason et al.
6.1.3 Review of other approaches and problems
6.1.4 A parallel definition for the sceptical
and the extension-based approach
6.1.5 Directly sceptical inheritance cannot
capture the intersection of extensions
6.1.6 A semantics for defeasible inheritance
6.2 Networks of inference : J. Pearl's book
7 References
Preliminary version:
[Sch97-2]
[GS09c] D.Gabbay, K.Schlechta: "Semantic Interpolation"
Journal of Applied Non-classical Logics,
Vol 20/4, 2010, pp. 345-371
Abstract:
We define semantic interpolation and show
that it always exists for monotone or antitone
(propositional) logics. We show that it sometimes,
but not always, carries over to syntactic
interpolation. Finally, we investigate several
forms of semantic interpolation for non-monotonic
logic.
[GS09a] D.Gabbay, K.Schlechta: "Size and Logic"
Review of Symbolic Logic,
Vol. 2, No. 2, pp. 396-413, 2009
Abstract:
We show how to develop a multitude of rules of
nonmonotonic logic from very simple and natural
notions of size, using them as building blocks.
[GS09b] D.Gabbay, K.Schlechta: "Independence - revision and defaults",
Studia Logica (2009) 92, pp. 381-394,
Abstract:
We investigate different aspects of independence here,
in the context of theory revision, generalizing slightly
work by Chopra, Parikh, and Rodrigues, and in the
context of preferential reasoning.
[GS08b] D.Gabbay, K.Schlechta: "Reactive preferential
structures and nonmonotonic consequence",
Review of Symbolic Logic,
Vol. 2, No. 2, pp. 414-450, 2009
Abstract:
We introduce Information Bearing
Relation Systems (IBRS) as an abstraction
of many logical systems. We then define
a general semantics for IBRS, and
show that a special case of IBRS
generalizes in a very natural way
preferential semantics and solves open
representation problems for weak
logical systems. This is possible, as
we can "break" the strong coherence
properties of preferential structures
by higher arrows, i.e. arrows, which do
not go to points, but to arrows
themselves.
[GS08h] D.Gabbay, K.Schlechta: "A comment on work by
Booth and co-authors",
Studia Logica, 2010, 94:403-432
Abstract:
We solve a representation problem left open in an article
by Booth and co-authors.
see also in
[GS08h]
[GS08a] D.Gabbay, K.Schlechta: "Cumulativity without
closure of the domain under finite unions",
Review of Symbolic Logic,
1 (3): 372-392, 2008
Abstract:
For nonmonotonic logics, Cumulativity
is an important logical rule.
We show here that Cumulativity fans out
into an infinity of different
conditions, if the domain is not closed
under finite unions.
[GS08d] D.Gabbay, K.Schlechta: "A theory of hierarchical
consequence and conditionals",
Journal of Logic, Language and Information,
19:1, 3-32, 2010
Abstract:
We introduce A-ranked preferential
structures and combine them with an
accessibility relation. A-ranked
preferential structures are intermediate
between simple preferential structures
and ranked structures. The additional
accessibilty relation allows us to
consider only parts of the overall
A-ranked structure. This framework
allows us to formalize contrary to duty
obligations, and other pictures where
we have a hierarchy of situations,
and maybe not all are accessible to all
possible worlds. Representation
results are proved.
[GS08e] D.Gabbay, K.Schlechta: "Defeasible inheritance
systems and reactive diagrams",
Logic Journal of the IGPL,
17:1-54, 2009
Abstract:
We give a conceptual analysis of
(defeasible or nonmonotonic) inheritance
diagrams, and compare our analysis to
the "small" and "big sets" of preferential
and related reasoning.
In our analysis, we consider nodes as
information sources and truth values,
direct links as information, and valid
paths as information channels and
comparisons of truth values. This
results in an upward chaining, split validity,
off-path preclusion inheritance
formalism of a particularly simple type.
We show that the small and big sets of
preferential reasoning have to be
relativized if we want them to conform
to inheritance theory, resulting in a
more cautious approach, perhaps closer
to actual human reasoning.
Finally, we interpret inheritance
diagrams as theories of prototypical
reasoning, based on two distances: set
difference, and information difference.
We will also see that some of the major
distinctions between inheritance
formalisms are consequences of deeper
and more general problems of treating
conflicting information.
[GS08c] D.Gabbay, K.Schlechta: "Roadmap for preferential
logics",
Journal of applied nonclassical logics,
Vol. 19/1, pp. 43-95, 2009,
Abstract:
We give a systematic overview of
semantical and logical rules in nonmonotonic
and related logics. We show connections
and sometimes subtle differences, and
also compare such rules to uses of the
notion of size.
[LMS01] D.Lehmann, M.Magidor, K.Schlechta: "Distance
Semantics for Belief Revision",
Journal of Symbolic Logic, Vol.66, No. 1, March 2001,
p. 295-317
Abstract:
A vast and interesting family of natural
semantics for belief revision is defined. Suppose
one is given a distance d between any two models.
One may then define the revision of a theory K by
a formula alpha as the theory defined by the set
of all those models of alpha that are closest, by
d, to the set of models of K. This family is
characterized by a set of rationality postulates
that extends the AGM postulates. The new
postulates describe properties of iterated
revisions.
[SD01] K.Schlechta, J.Dix: "Explaining updates by minimal
sums",
Theoretical Computer Science, 266 (2001), pp. 819-838
Abstract:
Human reasoning about developments of the world
involves always an assumption of inertia. We
discuss two approaches for formalizing such an
assumption, based on the concept of an
explanation: (1) there is a general preference
relation given on the set of all explanations,
(2) there is a notion of a distance between
models and explanations are preferred if their
sum of distances is minimal. We show exactly
under which conditions the converse is true as
well and therefore both approaches are equivalent
modulo these conditions. Our main result is a
general representation theorem in the spirit of
Kraus, Lehmann and Magidor.
[Sch00-1] K.Schlechta: "New techniques and completeness results
for preferential structures"
Journal of Symbolic Logic, Vol. 65, No. 2, pp. 719-746,
June 2000
Abstract :
Preferential structures are probably the best
examined semantics for nonmonotonic and deontic
logics, but also provide semantical approaches to
theory revision and update, and other fields
where a preference relation between models is
a natural interpretation. They have been widely
used to differentiate the various systems of such
logics, and their construction is one of the main
subjects in the formal investigation of these
logics. We introduce new techniques to construct
preferential structures for completeness proofs.
Since our main interest is to provide general
techniques, which can be applied in various
situations and for various base logics
(propositional and other), we take a purely
algebraic approach, which can be translated into
logics by easy lemmata. In particular, we give a
clean construction via indexing by trees for
transitive structures, this allows to simplify
the proofs of [Sch92] and in particular of
[Sch96-1], and to extend the results given there.
[SGMRT00] K.Schlechta, L.Gourmelen, S.Motre, O.Rolland,
B.Tahar: "A new approach to preferential
structures", Fundamenta Informaticae, Vol. 42,
No. 3-4, pp. 391-410, April-May 2000
Abstract:
This paper deals with some fundamental concepts
and questions of preferential structures. A model
for preferential reasoning will, in this article,
be a total order on the models of the underlying
classical language. Instead of working in
completeness proofs with a canonical preferential
structure as done traditionally, we work with
sets of such total orders. We thus stay close to
the way completeness proofs are done in classical
logic. Our new approach will also justify
multiple copies (or labelling functions) present
in most work on preferential structures. A
representation result for the finite case is given.
[Sch00-2] K.Schlechta: "Unrestricted preferential structures",
Journal of Logic and Computation,
Vol.10, No.4, pp.573-581, 2000
Abstract:
We solve in this short, technical paper one of the
perhaps major open problems of preferential
structures, and give an unrestricted representation
result. Up to now - to the author's knowledge - all
representation results for preferential structures
were subject to some restriction: definability
preservation (the author's terminology, fullness in
Lehmann's terminology) or some kind of finiteness.
The results presented here are valid without any
restrictions.
[BLS99] S.Berger, D.Lehmann, K.Schlechta: "Preferred
History Semantics for Iterated Updates",
Journal of Logic and Computation,
Vol.9, No.6, pp.817-833, 1999
Abstract:
We give a semantics to iterated update by a
preference relation on possible developments. An
iterated update is a sequence of formulas, giving
(incomplete) information about successive states
of the world. A development is a sequence of
models, describing a possible trajectory through
time. We assume a principle of inertia and prefer
those developments, which are compatible with the
information, and avoid unnecessary changes. The
logical properties of the updates defined in this
way are considered, and a representation result
is proved.
[Sch99] K.Schlechta: "A topological construction of a
non-smooth model of cumulativity"
Journal of Logic and Computation,
Vol.9, No.4, pp.457-462, 1999
Abstract :
To solve a problem posed by Bezzazi, Makinson,
Perez (Bezzazi, Makinson, Perez: "Beyond Rational
Monotony: Some Strong Non-Horn Rules for
Nonmonotonic Inference Relations", JLC Vol. 7, No.5,
p.605, 1997), we construct an injective, non-smooth
preferential model of Cumulativity and Weak
Determinacy, in which Negation Rationality fails.
We make essential use of infinite sequences of
models approaching sets of models. To our knowledge,
this is the first time that such topological
constructions are used in the context of
preferential models.
[ALS99] L.Audibert, C.Lhoussaine, K.Schlechta: "Distance
based revision of preferential logics"
Logic Journal of the Interest Group
in Pure and Applied Logics (1999), Vol. 7, No. 4, July 1999,
pp. 429-446
Abstract :
We first analyze AGM revision as conditions on
choice functions for sets of models. This
abstraction seems to us to capture the essentials
of classical revision, it also immediately
reveals the connection between revision and
ranked preferential models, and gives further
insight into the distance semantics for revision
as developped by Lehmann, Magidor, and Schlechta.
Our analysis shows how to apply the essential
ideas of revision to other situations than
classical theories and formulas, we exemplify
this by examining preferential databases.
We revise one preferential logic or database, L,
with another one, L'. The basic idea is to describe
such a logic as a partial order, either as the
order of a preferential model which defines the
logic, or as the order between formulas defined
by the logic. A partial order can be seen as the
set of total orders which extend it, and, given a
distance on the set of total orders, we can
define a revision as follows: L*L' will be the
logic corresponding to the partial order
generated by those total orders extending (the
order of) L', which are closest to the set of
total orders extending (the order of) L. We thus
give a semantical approach to the problem. A
representation result is proven.
[Sch97-1] K.Schlechta : "A Reduction of the Theory of Confirmation
to the Notions of Distance and Measure",
Logic Journal of the Interest Group in Pure and Applied
Logics, Vol.5, No.1, pp.49-64, 1997
Abstract :
We present an analysis and formalization of
confirmation of a theory through observation. The
basic ideas are, first, to carry the results of
single observations over to neighbouring cases by
analogy, using an abstract distance relation as
in the Stalnaker/Lewis semantics for
counterfactual conditionals. A theory is then, in
a second step, considered confirmed iff we have
thus concluded positively for a "large" part of
the universe - where "large" is interpreted by a
weak filter. Formal semantics as well as sound
and complete axiomatizations for the (trivial)
first order and the propositional case are given.
[Sch97-3] K.Schlechta : "Symmetrical Theory Revision",
(Non-prioritized belief revision based on
distances between models),
Theoria, Vol. 63, Part 1-2, pp. 34-53, 1997
(appeared in 1999)
Abstract :
We base Theory Revision on a notion of distance
between the models of the underlying logic.
Revisions constructed from such distances have
nice properties: The AGM postulates are (with a
minor exception) satisfied, and additional
properties, e.g. for iterated revision, hold. The
present article adapts this idea to
non-prioritized Theory Revision. Some motivation
and comparison to other, similar approaches are
given, and so is a representation result.
[BGHPSW97] D.Bellot, C.Godefroid, P.Han, J.P.Prost, K.Schlechta,
E.Wurbel:
"A semantical approach to the concept of screened
revision",
Theoria, Vol. 63, Part 1-2, pp. 24-33, 1997
(appeared in 1999)
Abstract :
We interpret Makinson's concept of screened
revision as a special form of iterated revision,
and give it a formal definition based on a
distance semantics. Differences between
Makinson's and our approach are discussed, and a
representation result is given.
[Sch97-4] K.Schlechta: "Filters and Partial Orders",
Journal of the Interest Group in Pure and Applied
Logics, Vol. 5, No. 5, p. 753-772, 1997
Abstract :
We discuss several abstract semantics for
nonmonotonic logics. We present their
motivations, their development and some
historical origins, and show that the
three systems considered are essentially
equivalent:
(a) the coherent systems of filters of
S.Ben-David and R.Ben-Eliahu,
(b) the coherent systems of filters developed by
the author,
(c) the partial order semantics of N.Friedman and
J.Halpern.
[Sch96-1] K.Schlechta : "Some Completeness Results for Stoppered
and Ranked Classical Preferential Models",
Journal of Logic and Computation, Oxford,
Vol. 6, No. 4, pp. 599-622, 1996
Abstract :
We extend the work begun in [Sch92] to stoppered
(or smooth) and ranked classical preferential
models, giving several soundness and completeness
results for these structures. In addition, we
discuss the number of copies of models needed to
represent arbitrary logics defined by
preferential structures.
[Sch96-3] K.Schlechta : "Completeness and Incompleteness for
Plausibility Logic",
Journal of Logic, Language and Information, 5:2, 1996,
p.177-192, Kluwer, Dordrecht
Abstract :
Plausibility Logic was introduced by Daniel
Lehmann. We show - among some other results -
completeness of a subset of Plausibility Logic
for Preferential Models, and incompleteness of
full Plausibility Logic for smooth Preferential
Models.
[Sch96-2] K.Schlechta : "A Two-Stage Approach to First Order
Default Reasoning",
Fundamenta Informaticae, Vol. 28, No. 3-4, pp. 377-402,
1996
Abstract :
Our subject is the representation and analysis of
simple first-order default statements of ordinary
language, such as "normally, birds fly". There
are, among other approaches, two kinds of
analysis, both semantic in style. One interprets
"normally, birds fly" along the lines of "for
every item x in the domain of discourse, the most
normal models of "x is a bird" are models of
"x flies"". This is the preferential models
approach, first outlined by Bossu/Siegel and
Shoham, and studied by Kraus, Lehmann, Magidor
and others. The other interprets "normally, birds
fly" along the lines of "there is an important
subset of the birds, all of whose elements fly".
This is the generalized quantifier approach,
formulated and developed by the author. The
purpose of the present paper is to show how the
two approaches may usefully be combined into a
single two-stage approach, and how such a
combination provides an elegant account of
certain problematic examples.
[Sch95-1] K.Schlechta : "Defaults as Generalized Quantifiers",
Journal of Logic and Computation, Oxford,
Vol.5, No.4, p.473-494, 1995
Abstract :
We interpret (open normal) defaults as
generalized FOL-quantifiers, give a semantics and
a corresponding sound and complete axiom system.
Nested and negated defaults are admissible and
have a clear meaning. Moreover, the logic
provides a notion of consistency for default
theories, which is used for a theory revision
approach in an order sorted language.
[Sch95-2] K.Schlechta : "Logic, Topology, and Integration",
Journal of Automated Reasoning, 14:353-381, 1995, Kluwer
Abstract :
The central notion will be that of closeness of
(or difference between) two theories. In the
first part, we give intuitive arguments in favour
of considering topologies on the set of theories,
continuous logics, and the average difference
between two logics, i.e. the integral of their
difference. We continue by arguing for the
importance of the difference between theories
in a wide range of applications and problems. In
the second part, we give some basic definitions
and results for one such type of topology. In
particular, separation properties and compactness
will be discussed, and examples given. The
techniques employed for constructing the topology
will also be used for defining a sigma-algebra of
measurable sets on the set of theories, leading to
the usual definition of the Lebesgue integral,
and a precise definition of the average
difference of two logics.
[Sch95-3] K.Schlechta : "Preferential Choice Representation
Theorems for Branching Time Structures"
Journal of Logic and Computation, Oxford,
Vol.5, pp.783-800, 1995
Abstract :
The idea of preferential choice is applied here
to dynamic structures in two directions :
1. We show that a deontic choice function of
"good" developments can be represented by a
ranked, stoppered preferential relation on all
developments.
2. We generalize the Katsuno/Mendelzon Update
Semantics to preferences between developments and
obtain a representation theorem for arbitrarily
many time points.
[Sch95-5] K.Schlechta : "Some Completeness Results for
Propositional Conditional Logics",
Bulletin of the IGPL, Vol.3, No.1, March 1995,
p.111-115
Abstract :
We consider three different measures of distance
between classical propositional models, and
provide sound and complete axiomatisations for
the ensuing conditional semantics, by translating
conditional formulas into equivalent classical
ones.
[SM94] K.Schlechta, D.Makinson : "Local and Global Metrics
for the Semantics of Counterfactual Conditionals",
Journal of Applied Non-Classical Logics, Vol.4, No.2,
pp.129-140, Hermes, Paris, 1994
Abstract :
The semantics for counterfactual conditionals
employs indexed relations <[a] between possible
worlds, with x<[a]y read intuitively as "x is
closer to a than is y". This paper considers the
question how far these different "closeness"
relations of a model may be derived from a common
source. Despite some well-known negative
observations, we show that there is also quite a
strong positive answer. Our main result is that
for any model equipped with modular relations
derived from multiple metrics d[a] via the
equation x<[a]y iff d[a](a,x)
1993
[Sch93] K.Schlechta : "Directly Sceptical Inheritance Cannot
Capture the Intersection of Extensions",
Journal of Logic and Computation, Oxford,
Vol.3, No.5 (1993), p. 455-467
Abstract :
We show that, under some very weak assumptions
about the definitions of sceptical and
extension-based defeasible inheritance, directly
sceptical inheritance cannot capture the
intersection of extensions.
1992
[Sch92] K.Schlechta : "Some Results on Classical Preferential
Models",
Journal of Logic and Computation, Oxford,
Vol.2, No.6 (1992), p. 675-686
Abstract :
We first show that a result of Kraus, Lehmann,
Magidor on classical preferential models does not
carry over to the general infinite case. We
further show that - in the absence of all
restrictions on finiteness - "logically nice"
(definability preserving) classical preferential
models correspond essentially to infinite
conditionalisation.
1991
[MS91] D.Makinson, K.Schlechta : "Floating Conclusions and
Zombie Paths",
(On principles and problems of defeasible inheritance),
Artificial Intelligence 48 (1991), p. 199-209
Abstract :
We discuss two difficulties in the "directly
sceptical" approach to inference in defeasible
inheritance nets, as developed by Horty, Thomason
and Touretzky. We suggest that as a result of the
general architecture of the approach, it is
intrinsically unable to deal with a phenomenon of
"floating conclusions", and has great difficulty
in accommodating a phenomenon of "zombie paths".
The conclusion drawn is that the directly
sceptical approach cannot hope to do the work of
an approach via the family of all extensions.
[Sch91-1] K.Schlechta : "Theory Revision and Probability",
Notre Dame Journal of Formal Logic 32, No.2 (1991),
p. 307-319
Abstract :
The problem of Theory Revision is to "add" a
formula to a theory, while preserving
consistency, or to "subtract" a formula from a
theory. In the process, only - in some sense -
minimal changes are to be made to the given
theory and certain plausible conditions to be
satisfied. In general, however, logic,
minimality, and those conditions do not uniquely
determine the process. Uniqueness can be achieved
in a natural way by imposing an order on the
formulae, as done by Gardenfors and Makinson :
Given such a suitable order of "epistemic
entrenchment", dependant on the theory
considered, it is easy to define a unique
revision process for that theory. We improve
their results in the following way : We show how
to define orders, which give rise to unique
revision processes too, but in addition, 1) are
well compatible with logic and thus have nice
logical properties, 2) do not depend on the
theory considered, so it suffices to fix one
order for iterated revision, and are thus
especially well suited for computational
purposes, 3) have a natural probabilistic
construction. In conclusion, we show that the
completeness problems of Theory Revision,
discussed by Alchourron, Gardenfors and Makinson,
carry over to a certain extent to an approach of
Theory Revision based on revising axiom systems.
WARNING: Proposition 2.4 is wrong. This was
pointed out by Hans Rott. (The proof of (K-1) is
wrong.)
(This is my only published sin I am aware of - but
perhaps you find more of them.)
[Sch91-2] K.Schlechta : "Results on Infinite Extensions",
Journal of Applied Non-Classical Logics, Hermes,
Paris, Vol. 1, No. 1 (1991), p. 65-72
Abstract :
In a joint paper M.Freund, D.Lehmann, D.Makinson
(M.Freund, D.Lehmann, D.Makinson : Canonical
Extensions to the Infinite Case of Finitary
Nonmonotonic Inference Relations. in :
Proceedings, 1. German Workshop on Non-Monotonic
Reasoning, GMD St.Augustin 1989, G.Brewka,
H.Freitag Eds., [FLM]) have examined a natural
extension of finitary inference rules to the
infinite case. We present here some results
related to this problem. The first shows that the
extension does not preserve cautious monotony.
This was formulated as a question in the original
version of [FLM] , the new version cites our
result, though without proof. The second shows
that two versions of distributivity are
equivalent - as shown in [FLM], distributivity
plus cautious monotony is strong enough to carry
cautious monotony through to the extension. The
third result gives a partial (induction through
regular cardinals) answer to a natural question
concerning a parallel problem in the infinite.
The fourth result cautions against one kind of
weakening of the basic construction. Basically,
the weakened approach corresponds to convergent
partial sequences, the original one to totally
converging sequences. It is not surprising that
the former can give funny logics. The fifth
presents another technique for constructing still
quite well-behaved non-monotonic logics.
1990
[JS90] R.B.Jensen, K.Schlechta : "Results on the Generic Kurepa
Hypothesis",
Archive for Mathematical Logic, Vol. 30 (1990), p. 13-27
Abstract :
K.J.Devlin has extended Jensen's construction of
a model of ZFC and CH without Souslin trees to a
model without Kurepa trees either. We modify the
construction again to obtain a model with these
properties, but in addition, without Kurepa trees
in ccc-generic extensions. We use a partially
defined box-sequence, given by a fine structure
lemma. We also show that the usual collapse of
kappa Mahlo to omega_2 will give a model without
Kurepa trees not only in the model itself, but
also in ccc-extensions.
Articles submitted to international journals and submitted books
2009
Articles submitted to international conferences, proceedings etc.:
------------------------------------------------------------------
Articles submitted to international conferences, proceedings etc.:
Manuscripts (to be submitted):
In preparation:
Articles in refereed books with international participation
2006
[Sch07] K.Schlechta: "Nonmonotonic logics - a preferential
approach",
in: "Handbook of the history of logic", vol.8:
"The many-valued and non-monotonic turn in logic",
D.Gabbay, J.Woods eds., Elsevier, 2007, pp. 451-516
2002
[Sch02-1] K.Schlechta : "Consid‚rations subjectives sur la
s‚mantique de la r‚vision des th‚ories" (trad.
P.Livet),
in "R‚vision des croyances", P.Livet ed.,
HermŠs/Lavoisier, Paris, 2002,
p. 167-180
Abstract :
Nous allons nous contrer sur un mode de pens‚e que l'on
pourrait peut-ˆtre nommer "philosophie de la
formalisation" de la th‚orie de la r‚vision, en comparant
sans exigences trop strictes les diff‚rentes propri‚t‚s
et les structures s‚mantiques, et en ‚vitant autant que
possible de trop rentrer dans les d‚tails techniques.
1995
[Sch95-4] K.Schlechta : "Some Completeness Results for Classical
Preferential Models",
in "Logic, Action, and Information", A.Fuhrmann,
H.Rott eds., De Gruyter, Berlin/New York, 1995/96,
p. 229-237
Abstract :
After giving basic definitions, facts and
examples for preferential structures in Section
1, we present here without proof several
completeness results for such preferential
structures. In each case, our main technical
result is combinatorial in character, the
transfer to logic will always be more or less
straightforward.
Articles in refereed proceedings of international conferences
1999
[DS99] J.Dix, K.Schlechta: Explaining updates by minimal
sums,
19th. Intern. Conf. on Foundations of Software
Technology and Theoretical Computer Science,
13-15 Dec. 1999, IIT Campus, Chennai, India,
Springer LNCS 1738
Abstract:
Human reasoning about developments of the world
involves always an assumption of inertia. We
discuss two approaches for formalizing such an
assumption, based on the concept of an
explanation: (1) there is a general preference
relation given on the set of all explanations,
(2) there is a notion of a distance between
models and explanations are preferred if their
sum of distances is minimal. We show exactly
under which conditions the converse is true as
well and therefore both approaches are equivalent
modulo these conditions. Our main result is a
general representation theorem in the spirit of
Kraus, Lehmann and Magidor.
1998
[ALS99] L.Audibert, C.Lhoussaine, K.Schlechta: "Distance based
revision of preferential logics", in
Belief Revision Workshop of KR98 (Knowledge Representation),
Trento, Italy, 1998 (electronic proceedings)
See [ALS99] (above).
[AS98] L.Audibert, K.Schlechta: Defeasible inheritance and
reference classes, to appear in the Proceeding of the
Belief Revision Workshop of KR98 (Knowledge Representation),
Trento, Italy, 1998, Hans Rott, Maryanne Williams eds.
Abstract:
We formalize how information from a reference
class is used to augment the information of a
base class. While theory revision operates on
theories and formulas of the same language, the
languages of the base and the reference class
might be different.
The information we consider is defeasible, and we
examine two approaches, one working on
preferential models expressing this information,
the other working on the partial orders defined
by the information. We show that our two
approaches are equivalent.
We finally apply these ideas to elucidate
defeasible inheritance, choosing the reference
classes via valid paths, and, conversely, we
motivate the definition of valid paths with the
reference class concept.
1996
[SLM96] K.Schlechta, D.Lehmann, M.Magidor : "Distance Semantics
for Belief Revision", in
Proceedings of: Theoretical Aspects of Rationality and
Knowledge, Tark VI, 1996, ed. Y.Shoham, Morgan Kaufmann,
San Francisco, 1996, p. 137-145
Abstract :
A vast and interesting family of natural
semantics for Belief Revision is defined. Suppose
one is given a distance d between any two models.
One may define the revision of a theory K by a
formula a as the theory defined by the set of all
those models of a that are closest, by d, to the
set of models of K. This family is characterized
by a set of rationality postulates that extends
the AGM postulates. The new postulates describe
properties of iterated revisions.
1995
[Sch95-6] K.Schlechta : "A Two-Stage Approach to First Order Default
Reasoning", in
"Symbolic and Quantitative Approaches to Reasoning and
Uncertainty" (Proceedings of ECSQARU-95, Fribourg, Suisse,
July 1995), C.Froidevaux, J.Kohlas eds., p. 379-386,
Springer Lecture Notes in AI, 1995
See [Sch96-2].
[Sch95-7] K.Schlechta : "A Reduction of the Theory of Confirmation
to the Notions of Distance and Measure", in
"Symbolic and Quantitative Approaches to Reasoning and
Uncertainty" (Proceedings of ECSQARU-95, Fribourg, Suisse,
July 1995), C.Froidevaux, J.Kohlas eds., p. 387-394,
Springer Lecture Notes in AI, 1995
See [Sch97-1].
[Sch95-8] K.Schlechta : "A Reduction of the Theory of Confirmation to
the Notions of Distance and Measure",
10th International Congress of Logic, Methodology and
Philosophy of Science, Firenze (Italy), August 1995
See [Sch97-1].
1993
[BS93] F.Baader, K.Schlechta : "A Semantics for Open Normal
Defaults via a Modified Preferential Approach", in
"Symbolic and Quantitative Approaches to Reasoning and
Uncertainty" (Proceedings of ECSQARU-93, Granada, Spain,
November 1993), M.Clarke, R.Kruse, S.Moral eds., p. 9-16,
Springer Lecture Notes in AI, 1993
1991
[Sch91-3] K.Schlechta : "Some Results on Theory Revision",
"The Logic of Theory Change", A. Fuhrmann, M. Morreau
eds., Springer Verlag 1991, p.72-92
[BMS91-1] G.Brewka, D.Makinson, K.Schlechta : "JTMS and Logic
Programming",
"Proceedings International Workshop on Non-Monotonic
Reasoning and Logic Programming",
Washington, Juli 1991
Abstract :
This paper makes three main points. We observe
first that the inference relation induced by a
set of JTMS justification rules (or equivalently,
by a logic program with negation under the
Gelfond-Lifschitz semantics) is not in general
cumulative: the addition to a set of assumptions
of some of the derivable conclusions may lead to
a loss of others.
We then show how cumulativity may be restored by
adapting a technique recently applied by Brewka
to default logic. The basic idea is to upgrade
the universe of discourse: replace the elementary
propositions, between which inference customarily
takes place, by more complex items consisting of
elementary propositions indexed by certain of the
"reasons" that lead to their acceptance.
However, as we finally show, the indexed JTMS
still has a shortcoming: it does not give an
adequate treatment of the phenomenon of "floating
conclusions". The problem of finding an
alternative aproach that handles floating
conclusions adequately without losing
cumulativity again, remains open.
[BMS91-2] G.Brewka, D.Makinson, K.Schlechta : "Cumulative Inference
Relations for JTMS and Logic Programming",
"Nonmonotonic and Inductive Logic", J.Dix, K.P.Jantke,
P.Schmitt eds., Springer Verlag 1991, p.1-12
Abstract :
This paper makes three main points. We observe
first that the inference relation induced by a
set of JTMS justification rules under the
grounded model semantics (or equivalently, by a
logic program with negation under the
Gelfond-Lifschitz semantics) is not in general
cumulative: the addition to a set of assumptions
of some of the derivable conclusions may lead to
a loss of others.
We then show how cumulativity may be restored by
adapting a technique recently applied by Brewka
to default logic. The basic idea is to upgrade
the universe of discourse: replace the elementary
propositions, between which inference customarily
takes place, by more complex items consisting of
elementary propositions indexed by certain of the
"reasons" that lead to their acceptance.
However, as we finally show, the indexed JTMS
still has a shortcoming: it does not give an
adequate treatment of the phenomenon of "floating
conclusions". The problem of finding an
alternative aproach that handles floating
conclusions adequately without losing
cumulativity again, remains open.
1990
[Sch90] K.Schlechta : "Semantics for Defeasible Inheritance",
Proceedings ECAI 90, L.G.Aiello ed., London 1990,
p.594-597
Abstract :
We will propose a semantics for non-monotonic
inheritance which can handle preclusion. Our
approach is based on formalizing the notion of a
"normal" subset, allowing us to state e.g.
"normally, all p are q". Since for preclusion,
direct links are in a stronger way true than
valid paths, we express this by different degrees
of "normality", resulting in a many-valued
semantics. Primarily, our semantics is intended
for the directly sceptical approach; for
extensions, we suggest a combination with
possible worlds.
1989
[Sch89-1] K.Schlechta : "Defeasible Inheritance : Coherence
Properties and Semantics",
"Proceedings of Tubingen Workshop on Semantic Networks
and Non-Monotonic Reasoning", M.Morreau ed.,
SNS-Report 89-48, Seminar fur naturlichsprachliche
Systeme, Universitaet Tubingen, (1989)
Abstract :
In Makinson, Schlechta: "Floating Conclusions and
Zombie Paths", Artificial Intelligence 48 (1991),
p.199-209 ([MS91]), we discussed problems of both
the directly sceptical and the extensions
approach to reasoning in defeasible inheritance
systems. Here, we present and examine solutions
to some of these problems, giving stability
special attention. In addition, we present a
(class of) semantics for defeasible inheritance,
based on "normal" subsets.
[Sch89-2] K.Schlechta : "Directly Sceptical Inheritance cannot
Capture the Intersection of Extensions",
"Proceedings Workshop Non-Monotonic Reasoning 1989",
G.Brewka, H.Freitag eds.,
GMD-Report 443, Arbeitspapiere der Gesellschaft fur
Mathematik und Datenverarbeitung (1989)
See [Sch93].
Articles in refereed proccedings of national conferences
1988
[Sch88-1] K.Schlechta : "Remarks on Shoham's Temporal Logic",
Proceedings der GWAI 88, W.Hoeppner ed.,
Springer Verlag 1988 (Informatik Fachberichte Nr. 181)
Abstract :
We describe a problem in Shoham's system of
temporal logic and present a solution.
[Sch88-2] K.Schlechta : "Remarks on Consistency and Completeness of
Circumscription"
Proceedings der GWAI 88, W.Hoeppner ed.,
Springer Verlag 1988 (Informatik Fachberichte Nr. 181)
Abstract :
We discuss definable minimal models, the
semantical counterpart of first order
circumscription, examine the adequacy of Mott's
system of circumscription and show that some
completeness results of Perlis and Minker fail in
Mott's system.
Technical reports and archive submissions
Note : 1. Some Technical Reports have also been submitted for
publication elsewhere or appeared as such meanwhile.
2. "LIM" stands for:
Laboratoire d'Informatique de Marseille, CNRS ESA 6077,
Universite de Provence, CMI, 39, Rue Joliot-Curie,
F-13453 Marseille Cedex 13, France
3. "LIF" stands for:
Laboratoire d'Informatique Fondamentale de Marseille,
CNRS UMR, Universite de Provence, CMI,
39, Rue Joliot-Curie, F-13453 Marseille Cedex 13,
France
www.lif.univ-mrs.fr
2006
[Sch06-t1] Karl Schlechta: Domain closure conditions and
definability preservation
HAL ccsd-00084398,
arXiv.org math.LO/0607189,
73 p.,
(submitted July 7, 2006)
Abstract:
We show the importance of closure of the
domain under finite unions, in particular for
Cumulativity, and representation results. We
see that in the absence of this closure,
Cumulativity fans out to an infinity of
different conditions.
We introduce the concept of an algebraic
limit, and discuss its importance. We then
present a representation result for a new
concept of revision, introduced by Booth et
al., using approximation by formulas.
We analyse definability preservation
problems, and show that intersection is the
crucial step. We simplify older proofs for
the non-definability cases, and add a new
result for ranked structures.
AMS Classification: 03B42, 03B65, 03B70,
68T27, 68T30
[Sch06-t2] Karl Schlechta: Remarks on inheritance systems
HAL hal-00117112,
arXiv.org math.LO/0611937
11 p.,
(submitted November 30, 2006)
Abstract:
We try a conceptual analysis of inheritance
diagrams, first in abstract terms, and then
compare to "normality" and the "small/big
sets" of preferential and related reasoning.
The main ideas are about nodes as truth
values and information sources, truth
comparison by paths, accessibility or
relevance of information by paths, relative
normality, and prototypical reasoning.
AMS Classification: 68T27, 68T30
2003
[Sch03-t1] Karl Schlechta: Coherent systems
LIF TR 14-2003
(Preliminary version of [Sch04])
Abstract:
We discuss several types of common sense
reasoning, reduce them to a small number of
basic semantical concepts, and show several
(in-)completeness results for such logics.
2000
[SFBMS00] Karl Schlechta, Enrico Formenti, Jean-Marc Batty,
Jean Francois Morcillot, Sophie Sadok:
"Comments on 'Belief revision with unreliable
observations' ",
LIM Research Report 2000-362
Abstract:
We discuss the article "Belief Revision with
Unreliable Observations" by C.Boutilier, N.Friedman,
and J.Halpern, and give a characterization of (a
finite variant) of Markov systems, using an old
algorithm, due to Farkas.
[Sch00-m1] K.Schlechta: "Representation results for limit
preferential structures",
Research Report, 2000-8,
Institut des Sciences Cognitives, 67 blvd. Pinel,
F-69675 Bron Cedex, France
1999
[Sch00-1] K.Schlechta: New techniques and completeness results
for preferential structures
Research Report, 1999-5,
Institut des Sciences Cognitives, 67 blvd. Pinel,
F-69675 Bron Cedex, France
See [Sch00-1] (above).
[Sch97-t2] K.Schlechta: Representation results for revision and
update (in cooperation with D.Lehmann and M.Magidor)
Research Report, 1999-4,
Institut des Sciences Cognitives, 67 blvd. Pinel,
F-69675 Bron Cedex, France
Abstract :
These notes are based on joint work with
D.Lehmann and M.Magidor, Hebrew University,
Jerusalem. Thus, they are coauthors in substance.
We show a number of representation results for
revision and update, all based on distances
between models, or on ranked orders between
sequences of models.
Section 2:
We first show an abstract representation result.
It will be used for update (Proposition 5.4), and
a close analogue will be used for one proof for
the asymmetric revision case (Proposition 4.7).
We can apply it to the symmetric revision case
too, but there it does not seem to simplify the
situation. Its main value is perhaps more
psychological than mathematical: It gives a
direction how to build the completeness proof, by
pointing out which Lemmas to prove (Facts 4.5,
4.6, 4.10, 4.11, 5.2, 5.3).
Section 3:
We treat revision determined by a symmetric
distance between models. As usual, we first
(Section 3.1) work on (sets of) models, and turn
then to logic (Section 3.2).
Section 4:
We treat revision determined by a not necessarily
symmetric distance between models. We work in the
finite case (finiteness is used repeatedly in the
proofs), and only with sets of models.
Translation to logic will be straightforward.
After some initial remarks (Section 4.1), we give
two proofs with slightly different conditions.
The latter one (Section 4.3) is based on Daniel
Lehmann's conditions.
Section 5:
We treat update determined by a ranked order
between sequences of developments, again we work
in the finite case, and only with models. We
first (Section 5.2) treat the case where
subsequences are supposed to be better
explanations. We give two representation results,
with two somewhat different sets of conditions
(Section 5.2.1, Section 5.2.2). Finally (Section
5.3), we treat the case where sequences are
ordered by the sum of their differences - a
distance between individual models being given.
[Sch99-t1] K.Schlechta, "A new approach to preferential
structures",
in "DGNMR99, Proceedings of the fourth
Dutch-German workshop on nonmonotonic reasoning
techniques and their applications",
H.Rott, C.Albert, G.Brewka, C.Witteveen eds.,
Research Report,
Institute for Logic, Language, and Computation,
Amsterdam, The Netherlands
See [SGMRT00] (above).
1998
[ALS98-t] L.Audibert, C.Lhoussaine, K.Schlechta: "Distance based
revision of preferential logics"
LIM Research Report RR 262, 3/98
See [ALS99] (above).
[LMS01] D.Lehmann, M.Magidor, K.Schlechta: "Distance
Semantics for Belief Revision",
Leibniz Center for Research in Computer Science,
Technical Report TR-98-10,
Institute of Computer Science, Hebrew University,
Givat Ram, Jerusalem 91904, Israel
See [LMS01] (above).
[BLS99] S.Berger, D.Lehmann, K.Schlechta: "Preferred
History Semantics for Iterated Updates",
Leibniz Center for Research in Computer Science,
Technical Report TR-98-11,
Institute of Computer Science, Hebrew University,
Givat Ram, Jerusalem 91904, Israel
See [BLS99] (above).
[AS98] L.Audibert, K.Schlechta: "Defeasible inheritance and
reference classes"
LIM Research Report RR 281, 9/98
See [AS98] (above).
1997
[BGHPSW97-t] D.Bellot, C.Godefroid, P.Han, J.P.Prost, K.Schlechta,
E.Wurbel:
"A semantical approach to the concept of screened revision",
LIM Research Report RR 217, 3/97
See [BGHPSW97].
1996
[Sch96-t1] K.Schlechta: Filters and Partial Orders
LIM Research Report RR 140, 1/96
See [Sch97-4].
[Sch96-t2] K.Schlechta : "On basic concepts and ideas of nonmonotonic
logics",
LIM Research Report RR 192, 10/96
See [Sch97-2].
1995
[LMS95-t1] D.Lehmann, M.Magidor, K.Schlechta : "A Semantics for Theory
Revision",
LIM Research Report 1995 - 126
[Sch95-t1] K.Schlechta : "Inheritance - Language or Structure ?",
LIM Research Report RR 138, 12/95
Abstract :
We argue that logic and the structural
information of inheritance diagrams might be
quite different. We show how a seemingly
reasonable attempt to give a semantics to
inheritance diagrams via a coherent system of
filters fails. We further argue that structural
information should perhaps be considered as
primitive. Given then such structural
information, and theories valid for single nodes,
structure can determine inheritance of these
theories. Conflicts can be solved in a theory
revision approach. Conflicts between theories of
equal weight necessitate a modified (symmetric)
revision operation. We give a possible solution
of symmetric revision based on a distance
semantics.
1994
[Sch94-t1] K.Schlechta : "Limit Preferential Models",
LIM Research Report RR 6, 03/94
Abstract :
We show a representation theorem for a subclass
of limit preferential models.
[Sch94-t2] K.Schlechta : "Completeness and Incompleteness for
Plausibility Logic",
LIM Research Report RR 7, 04/94
See [Sch96-3].
[Sch92-n4] K.Schlechta : "Some Completeness Results for Stoppered and
Ranked Classical Preferential Models",
LIM Research Report RR 15, 05/94
See [Sch96-1].
[Sch89-n1] K.Schlechta : "Defaults as Generalized Quantifiers",
LIM Research Report RR 16, 05/94
See [Sch95-1].
[Sch92-n9] K.Schlechta : "Preferences in Dynamic Structures",
LIM Research Report RR 17, 05/94
See [Sch95-3].
[Sch94-t3] K.Schlechta : "Some Completeness Results for Propositional
Conditional Logics",
LIM Research Report RR 23, 06/94
See [Sch95-5].
[Sch94-t4] K.Schlechta : "A Two-Stage Approach to First Order Default
Reasoning",
LIM Research Report RR 36, 09/94
See [Sch96-2].
[SM94] K.Schlechta, D.Makinson : "Local and Global Metrics for the
Semantics of Counterfactual Conditionals",
LIM Research Report RR 37, 09/94
See [SM94].
[Sch94-t5] K.Schlechta : "A Reduction of the Theory of Confirmation
to the Notions of Distance and Measure",
LIM Research Report RR 64, 12/94
See [Sch97-1].
1993
[BS93-t1] F.Baader, K.Schlechta : "A Semantics for Open Normal
Defaults via a Modified Preferential Approach",
Internal Report RR-93-13,
Deutsches Forschungszentrum fur Kunstliche Intelligenz
(DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken,
Germany, 1993
[Sch92-n1] K.Schlechta : "Logic, Topology, and Integration",
Tech. Rept. of Gesellschaft fur Mathematik und
Datenverarbeitung, (GMD), POB 1240, D-53757 St.Augustin,
Germany, 1993
See [Sch95-2].
1992
[Sch92-t1] K.Schlechta : "Results on Non-Monotonic Logics",
IWBS Report 204, IBM Germany, IWBS, POB 80 08 80,
D-7000 Stuttgart 80, Germany, 1992
(Habilitation Thesis, University of Hamburg)
[SM89] K.Schlechta, D.Makinson : "On Principles and Problems of
Defeasible Inheritance",
Internal Report RR-92-59,
Deutsches Forschungszentrum fur Kunstliche Intelligenz
(DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken,
Germany, 1992
Abstract :
We have two aims here: First, to discuss some
basic principles underlying different approaches
to Defeasible Inheritance; second, to examine
problems of these approaches as they already
appear in quite simple diagrams. We build upon,
but go beyond, the discussion in the joint paper
of Touretzky, Horty, and Thomason: A Clash of
Intuitions (D.S.Touretzky, J.F.Horty,
R.H.Thomason : A Clash of Intuitions : The
Current State of Nonmonotonic Multiple
Inheritance Systems, IJCAI 1987).
[Sch88-n1] K.Schlechta : "Defaults, Preorder Semantics and
Circumscription",
Internal Report RR-92-60,
Deutsches Forschungszentrum fur Kunstliche Intelligenz
(DFKI), Stuhlsatzenhausweg 3, D-66123 Saarbrucken,
Germany, 1992
Abstract :
We examine questions related to translating
defaults into circumscription. Imielinski has
examined the concept of preorder semantics as an
abstraction from specific systems of
circumscription. We give precise definitions,
characterize preorder semantics syntactically and
examine the translatability of one default into
preorder semantics. Finally, we give a rather
bleak outlook on the translation of defaults into
circumscription.
Talks at international conferences without proceedings
(but with programm committee or on invitation)
December 1989, Conference on defeasible inheritance, Tubingen
on "Defeasible Inheritance"
June 1990, Nonmonotonic Reasoning Workshop, Lake Tahoe
on "Defaults as Generalized Quantifiers"
September 1990, Conference on non-monotonic logics, Konstanz
on "Preferential Models"
Fall 1990, Deduktionstreffen, Lautenbach
on "Defaults as Generalized Quantifiers"
December 1990, NIL90, Karlsruhe
on "Homogenousness in Defeasible Reasoning"
December 1991, NIL91, Schloss Reinhardsbrunn
on "Some Results for Preferential Structures"
August 1992, Workshop Logic and Change, GWAI, Bonn
on "New Results on Preferential Structures"
October 1992, LogIn, Konstanz
on "Preferential Structures"
August 95, "Logic Colloquium 95", Haifa, Israel, invited talk
August 95, "Seventh European Summer School in Logic", invited talk
March 99, "Fourth Dutch-German Workshop on Nonmonotonic Reasoning
Techniques and Their Applications", Amsterdam, invited talk
Various activities
Organization:
August 95, "Seventh European Summer School in Logic",
co-organizer of Workshop (with F.Baader)
June 00, LiCS-Workshop, "Nonmonotonicity and Belief Revision",
co-organizer (with D.Lehmann)
I have invited (dates are approximate):
Yuri Gurevich, University of Michigan, USA, December 1994
Shai Ben-David, Technion, Haifa, Israel, February 1996
Menachem Magidor, Hebrew University, Jerusalem, Israel, June 1996
Daniel Lehmann, Hebrew University, Jerusalem, Israel, June 1997
Aron Avron, Tel Aviv, Israel, June 2005
David Makinson, London, May 2006
I was invited:
Hebrew University, Jerusalem, Israel, April 1995, by Daniel
Lehmann and Menachem Magidor
Editor:
I was Associate editor of the journal Studia Logica
Reviewing:
I have reviewed for various journals and conferences.