Preferential Reasoning for Modal Logics

  • Authors:

  • Katarina Britz;Thomas Meyer;Ivan Varzinczak

  • Affiliations:

  • Centre for Artificial Intelligence Research, CSIR Meraka Institute and University of KwaZulu-Natal, South Africa;Centre for Artificial Intelligence Research, CSIR Meraka Institute and University of KwaZulu-Natal, South Africa;Centre for Artificial Intelligence Research, CSIR Meraka Institute and University of KwaZulu-Natal, South Africa

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

Modal logic is the foundation for a versatile and well-established class of knowledge representation formalisms in artificial intelligence. Enriching modal logics with non-monotonic reasoning capabilities such as preferential reasoning as developed by Lehmann and colleagues would therefore constitute a natural extension of such KR formalisms. Nevertheless, there is at present no generally accepted semantics, with corresponding syntactic characterization, for preferential consequence in modal logics. In this paper we fill this gap by providing a natural and intuitive semantics for preferential and rational modal consequence. We prove representation results for both preferential and rational consequence, which paves the way for effective decision procedures for modal preferential reasoning. We then illustrate applications of our constructions to modal logics widely used in AI, notably in the contexts of reasoning about actions, knowledge and beliefs. We argue that our semantics constitutes the foundation on which to explore preferential reasoning in modal logics in general.