This project deals with the study of mathematical foundations, and later development, of deduction and
programming in several types of non-classical logics, especially multiple-valued logics and intermediate
logics, with the aim of providing means for intelligent management of information. The classical problem
of deduction is, given explicit knowledge expressed in a given formalism together
with a set of inference rules, to deduce the implicit knowledge which could be relevant for applications.
Specifically, we are interested in those knowledge bases containing uncertain or incomplete information, to
develop mechanisms of analysis in which vague or imprecise queries are permitted.
A first formal framework chosen is fuzzy logic and different paradigms of fuzzy logic programming. In this project we propose the development of a theoretical framework which generalizes different existent approaches to logic programming in vague or imprecise contexts by considering different lattice-like generalized structures as the set of truth-values: bilattices, trilattices, multilattices, biresiduated lattices, etc. For this general goal, two additional specific problems will be addressed: firstly, unification in these general contexts, in which categorical techniques are expected to be useful and, secondly, automated deduction in these systems, in which we will use the TAS methodology.
From the programming point of view, extensions are sought of the paradigm of Answer Set Programming (ASP) which in turn is already a generalisation of classical logic programming. These extensions of ASP can be implemented either in existing implimentations of ASP, or by using systems based on quantified boolean formulas (e.g. QUIP), or by using TAS. The importance of basic research in these logical systems for Knowledge Technology is driven by the numerous potential applications they offer for modeling and solving problems in areas such as information management, cognitive robotics, Semantic Web, etc.