Ivan José Varzinczak

Regression in Modal Logic

In this work we propose an encoding of Reiters Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.

Semantic foundation for preferential description logics

Description logics are a well-established family of knowledge representation formalisms in Artificial Intelligence. Enriching description logics with non-monotonic reasoning capabilities, especially preferential reasoning as developed by Lehmann and colleagues in the 90s, 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 description logics. In this paper we fill this gap by providing a natural and intuitive semantics for defeasible subsumption in the description logic

Metatheory of actions: Beyond consistency

\mathcal{ALC}

PTL: a propositional typicality logic

. Our semantics replaces the propositional valuations used in the models of Lehmann et al.. with structures we refer to as concept models . We present representation results for the description logic

Editorial: Reasoning with Context in the Semantic Web

\mathcal{ALC}

Preferential Reasoning for Modal Logics

for both preferential and rational consequence relations. We argue that our semantics paves the way for extending preferential and rational consequence, and therefore also rational closure, to a whole class of logics that have a semantics defined in terms of first-order relational structures.

On action theory change

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 metatheory of actions by investigating what other properties a good domain description should have. We state some metatheoretical postulates concerning this sore spot. When all postulates are satisfied we call the action theory modular. Besides being easier to understand and more elaboration tolerant in McCarthys sense, modular theories have interesting properties. 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.

Introducing Defeasibility into OWL Ontologies

We introduce Propositional Typicality Logic (PTL), a logic for reasoning about typicality. We do so by enriching classical propositional logic with a typicality operator of which the intuition is to capture the most typical (or normal) situations in which a formula holds. The semantics is in terms of ranked models as studied in KLM-style preferential reasoning. This allows us to show that rational consequence relations can be embedded in our logic. Moreover we show that we can define consequence relations on the language of PTL itself, thereby moving beyond the propositional setting. Building on the existing link between propositional rational consequence and belief revision, we show that the same correspondence holds for rational consequence and belief revision on PTL. We investigate entailment for PTL, and propose two appropriate notions thereof.

Introducing Role Defeasibility in Description Logics

This Special Issue on Reasoning with Context in the Semantic Web collects ten articles that shed direct or indirect light on the role of context in Semantic Web theories and applications. Context has become a key-factor for the realization of the Semantic Web. There is a growing need for general and robust modeling and reasoning techniques that make it possible to handle the heterogeneity of knowledge, for instance, in situations where the same term has different meanings in different domains. Also the homogeneity of knowledge requires a context-based treatment, for instance, in situations where different terms have the same meaning in different domains, or where they may be seen as representing a coherent sub-domain. Research on these topics has mostly concentrated on the relationship between formal ontologies, which are the logical structures that encode the semantics of a software’s domain of application, and their context of use, or of development and maintenance, or of communication. This has resulted in

Horn Belief Change: A Contraction Core

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.