Action Theory Contraction and Minimal Change

Proceedings of the 11th Conference on Principles of Knowledge Representation and Reasoning (KR'08)This work is about changing action domain descriptions in dynamic logic. We here revisit the semantics of action theory contraction, giving more robust operators that express minimal change based on a notion of distance between models. We then define syntactical contraction operators and establish their correctness w.r.t. our semantics. Finally we show that our operators satisfy the PDL-counterpart of the standard postulates for theory change adopted in the literature

Action Theory Revision in Dynamic Logic

!2th Workshop on Nonmonotonic Reasoning (NMR'08)Like any other logical theory, action theories in reasoning about actions may evolve, and thus need revision methods to adequately accommodate new information about the behavior of actions. Here we give a semantics that complies with minimal change for revising action theories stated in a version of PDL. We give algorithms that are proven correct w.r.t. the semantics for those theories that are modular

What Is a Good Domain Description? Evaluating & Revising Action Theories in Dynamic Logic

Traditionally, consistency is the only criterion for the quality of a theory in logic-based approaches to reasoning about actions. This work goes beyond that and contributes to the meta-theory of actions by investigating what other properties a good domain description should satisfy. Having Propositional Dynamic Logic (PDL) as background, we state some meta-theoretical postulates concerning this sore spot. When all postulates are satisfied, we call the action theory modular. We point out the problems that arise when the postulates about modularity are violated, and propose algorithmic checks that can help the designer of an action theory to overcome them. Besides being easier to understand and more elaboration tolerant in McCarthy's sense, modular theorieshave interesting computational properties. Moreover, we also propose a framework for updating domain descriptions and show the importance modularity has in action theory change

Simple Conditionals with Constrained Right Weakening

In this paper we introduce and investigate a very basic semantics for conditionals that can be used to define a broad class of conditional reasoning systems. We show that it encompasses the most popular kinds of conditional reasoning developed in logic-based KR. It turns out that the semantics we propose is appropriate for a structural analysis of those conditionals that do not satisfy the property of Right Weakening. We show that it can be used for the further development of an analysis of the notion of relevance in conditional reasoning

A One-Pass Tree-Shaped Tableau for Defeasible LTL

Defeasible Linear Temporal Logic is a defeasible temporal formalism for representing and verifying exception-tolerant systems. It is based on Linear Temporal Logic (LTL) and builds on the preferential approach of Kraus et al. for non-monotonic reasoning, which allows us to formalize and reason with exceptions. In this paper, we tackle the satisfiability checking problem for defeasible LTL. One of the methods for satisfiability checking in LTL is the one-pass tree shaped analytic tableau proposed by Reynolds. We adapt his tableau to defeasible LTL by integrating the preferential semantics to the method. The novelty of this work is in showing how the preferential semantics works in a tableau method for defeasible linear temporal logic. We introduce a sound and complete tableau method for a fragment that can serve as the basis for further exploring tableau methods for this logic

On the Decidability of a Fragment of preferential LTL

Linear Temporal Logic (LTL) has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. Non-monotonic reasoning, on the other hand, allows us to formalize and reason with exceptions and the dynamics of information. The goal of this paper is therefore to enrich temporal formalisms with non-monotonic reasoning features. We do so by investigating a preferential semantics for defeasible LTL along the lines of that extensively studied by Kraus et al. in the propositional case and recently extended to modal and description logics. The main contribution of the paper is a decidability result for a meaningful fragment of preferential LTL that can serve as the basis for further exploration of defeasibility in temporal formalisms

Conditional Inference under disjunctive rationality

The question of conditional inference, i.e., of which conditional sentences of the form “if A then, normally, B” should follow from a set KB of such sentences, has been one of the classic questions of AI, with several well-known solutions proposed. Perhaps the most notable is the rational closure construction of Lehmann and Magidor, under which the set of inferred conditionals forms a rational consequence relation, i.e., satisfies all the rules of preferential reasoning, plus Rational Monotonicity. However, this last named rule is not universally accepted, and other researchers have advocated working within the larger class of disjunctive consequence relations, which satisfy the weaker requirement of Disjunctive Rationality. While there are convincing arguments that the rational closure forms the “simplest” rational consequence relation extending a given set of conditionals, the question of what is the simplest disjunctive consequence relation has not been explored. In this paper, we propose a solution to this question and explore some of its properties