Ján Šefránek

Static and Dynamic Semantics: Preliminary Report

This paper is aiming at a contribution to the logic program updates research. A (dynamic) semantics of sequences of logic programs is presented. The semantics is closely connected to the answer set semantics. We follow the construction of answer sets proposed by Dimopoulos and Torres. Solutions of three kinds of conflicts are added to the construction. After that, some decisions aiming at a step from inconsistencies handling to updating, are presented and analyzed. We present also some postulates characterizing relations between static and dynamic semantics. Subsequently a comparison to other postulates for logic program updates is provided. Presented postulates are satisfied by our dynamic semantics.

A Kripkean semantics for dynamic logic programming

The main goal of the paper is to propose a tool for a semantic specification of program updates (in the context of dynamic logic programming paradigm). A notion of Kripke structure κP associated with a generalized logic program P is introduced. It is shown that some paths in κP specify stable models of P and vice versa, to each stable model of P corresponds a path in κP. An operation on Kripke structures is defined: for Kripke structures κP and κU associated with P (the original program) and U (the updating program), respectively, a Kripke structure κP⊕U is constructed. κP⊕U specifies (in a reasonable sense) a set of updates of P by U. There is a variety of possibilities for a selection of an updated program.

Resolving conflicts in knowledge for ambient intelligence

Ambient intelligence (AmI) proposes pervasive information systems composed of autonomous agents embedded within the environment who, in orchestration, complement human activity in an intelligent manner. As such, it is an interesting and challenging application area for many computer science fields and approaches. A critical issue in such application scenarios is that the agents must be able to acquire, exchange, and evaluate knowledge about the environment, its users, and their activities. Knowledge populated between the agents in such systems may be contextually dependent, ambiguous, and incomplete. Conflicts may thus naturally arise, that need to be dealt with by the agents in an autonomous way. In this survey, we relate AmI to the area of knowledge representation and reasoning (KR), where conflict resolution has been studied for a long time. We take a look at a number of KR approaches that may be applied: context modelling, multi-context systems, belief revision, ontology evolution and debugging, argumentation, preferences, and paraconsistent reasoning. Our main goal is to describe the state of the art in these fields, and to draw attention of researchers to important theoretical issues and practical challenges that still need to be resolved, in order to reuse the results from KR in AmI systems or similar complex and demanding applications.

A Descriptive Approach to Preferred Answer Sets

We are aiming at a semantics of logic programs with preferences defined on rules, which always selects a preferred answer set, if there is a non-empty set of (standard) answer sets of the given program.

Conflict Resolution in Assumption-Based Frameworks

We show how defeasible reasoning can be embedded into ABF. Differently from other proposals, we do not encode the conflict resolution mechanism for defeasible rules into the ABF’s deductive systems. Instead, we formalize the notions of conflict and conflict resolution and make them part of the extended ABF framework (XABF). This improves the control over the conflict resolution process, and allows to devise and compare different domain-dependent conflict resolution strategies. We also show, that no matter which conflict resolution strategy is used, our framework is able to guarantee certain desired properties.

Belief, Knowledge, Revisions, and a Semantics of Non-Monotonic Reasoning

Przymusinskis Autoepistemic Logic of Knowledge and Belief (AELKB) is a unifying framework for various non-monotonic formalisms. In this paper we present a semantic characterization of AELKB in terms of Dynamic Kripke Structures (DKS). A DKS is composed of two components - a static one (a Kripke structure) and a dynamic one (a set of transformations). Transformations between possible worlds correspond to hypotheses generation and to revisions. Therefore they enable to define a semantics of insertions to and revisions of AELKB-theories. A computation of the transformations (between possible worlds) is based on (an enhanced) model-checking. The transformations may be used as a method of computing static autoepistemic expansions.

Inconsistencies handling: nonmonotonic and paraconsistent reasoning

A characterization of non-monotonic reasoning is given. Not-sound inference operator using, consistency maintaining and belief revision as key features of non-monotonic reasoning are discussed. A problem of inconsistencies handling leads to another approach interesting in our context, it is based on paraconsistent inference.