Palestra do prof. Ivan Varzinczak: Reasoning about concept and role typicality in ontologies
"Reasoning about concept and role typicality in ontologies"
Abstract: Description Logics (DLs) are a family of logic-based knowledge representation formalisms with useful computational properties and a variety of applications in artificial intelligence and in databases. In particular, DLs are well-suited for representing and reasoning about terminological knowledge and constitute the formal foundations of semantic-web ontologies. Technically, DLs correspond to decidable fragments of first-order logic and are closely related to modal logics. Notwithstanding their good trade-off between expressive power and computational complexity, DLs remain fundamentally classical formalisms and therefore are not suitable for modelling and reasoning about aspects that are ubiquitous in human quotidian reasoning. Examples of these are exceptions to general rules, incomplete knowledge, and many others, characterising the type of reasoning usually known under the broad term defeasible reasoning. In this regard, endowing DLs and their associated reasoning services with the ability to cope with defeasibility is a natural step in their development. In this work, we propose a meaningful extension of description logics for non-monotonic reasoning. We introduce ALCH*, a logic allowing for the representation of and reasoning about both typical class-membership and typical instances of a relation. We propose a preferential semantics à la KLM for ALCH* in terms of partially-ordered DL interpretations which intuitively captures the notions of typicality we are interested in. We define a tableau-based algorithm for checking ALCH* knowledge-base consistency and show that it is sound and complete w.r.t. our preferential semantics. The general framework we here propose can serve as the foundation for further exploration of non-monotonic reasoning in description logics and similarly structured logics.
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