Relevance terminological logics towards logic-based information retrieval

Information Retrieval (IR) is presented as the task of retrieving the documents that are relevant to a given query. In the context of a Terminological Logic (TL) based approach to IR, this amounts to embodying a notion of relevance in the logical implication relation of the chosen TL. Among the many possible readings of the term ``relevance'', the one captured by relevance logic, and in particular by first-order tautological entailment, can be viewed as a promising source of inspiration, to the end of incorporating a logic-based form of relevance in the inference mechanism of TLs. In semantical terms, this amounts to adopting a four-valued semantics for TLs, thus obtaining Relevant Terminological Logics. Logics of this kind have already been used in Knowledge Representation in order to avoid the so-called paradoxes of logical implication and to improve the computational complexity when reasoning on concepts and individuals. Unfortunately, we have observed that the adoption of the, by now classical, four-valued semantics results in a too drastic loss of inferential capabilities. The aim of this paper is to present a less restrictive four-valued semantics for TLs, which could be considered as a suitable core for IR purposes, while maintaining the desired ``relevance'' flavour of relevance logics. In order to perform automated reasoning on this logic, we will also present a new, general and modular inference algorithm based on Gentzen-style calculus and a four-valued version of Craig's interpolation theorem. This theorem states that the defined entailment relation captures a close (structural) relationship between a knowledge base and a query. Therefore, the defined entailment relation could arguably be a good theoretical and practical bases for a logic-based approach to I