Theory and Implementation of knowledge base systems for FO(.) (R-2080)

A Knowledge Base System (KBS) is a software system that manages a declarative Knowledge Base (KB) and is able to solve various tasks by applying different forms of inference on the KB. The goal of the project is to study a KBS for a rich extension FO(.) of first order logic (FO). In the past, we already studied finite model generation for extensions of FO with Inductive Definitions, aggregates and arithmetic. On the language level, we will study further extensions of FO(.) with nested induction/coinduction and with modal operators implementing an NP-oracle. We also want to study the expressivity of the resulting language and of certain interesting fragments. On the implementation level, we will extend the FO(.) model generation system IDP for the new language extensions and we will study other forms of inference such as deductive inference in the context of decidable fragments of FO(.), approximate reasoning, model revision and debugging. All tasks at this level involve study of complexity, and development of algorithms and implementation.

Keywords:Artificial intelligence, Databases, Knowledge bases, Knowledge representation, Logic

Disciplines:Mathematical sciences and statistics