Logical tools for handling change in agent-based systems
We give a unified approach to various results and problems of nonclassical logics
math.LO↗
arXiv subjects
Karl Schlechta
Publications and source records attributed to Karl Schlechta.
A semantics for obligations
We analyze a number of properties obligations have or should have.
math.LO↗
Size and Logic
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.
math.LO↗
Defeasible inheritance systems and reactive diagrams
We give an analysis of defeasible inheritance diagrams, also from the perspective of reactive diagrams.
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A theory of hierarchical consequence and conditionals
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
math.LO↗
Roadmap for preferential logics
We give an overview of logical and semantical rules for nonmonotonic and related logics.
math.LO↗
Reactive preferential structures and nonmonotonic consequence
We introduce information bearing systems (IBRS) as an abstraction of many logical systems. We define a general semantics for IBRS, and show that IBRS generalize in a natural way preferential semantics and solve open representation problems.
math.LO↗
Cumulativity without closure of the domain under finite unions
For nonmonotonic logics, Cumulativity is an important rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.
math.LO↗
Factorization (Splitting)
We show some elementary facts about the semantical analogue of Parikh's Splitting, which we call Factorization.
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A remark on utility streams
We consider arbitrarily long, but finite utility streams, and some appropriate axioms.
math.LO↗
Remarks on Inheritance Systems
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.
math.LO↗
Domain closure conditions and definability preservation
We examine problems due to lack of domain closure and definability preservation
math.LO↗
Distance Semantics for Belief Revision
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 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.
cs.AI↗
Preferred History Semantics for Iterated Updates
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.
cs.AI↗