A Framework for Reasoning about Probabilistic Spatio-Temporal Logic

Abstract

In previous research, frameworks have been constructed that can reason about the probabilistic locations of objects through different time instances. With these frameworks, certain work has been done on belief revision and consistency checking. The expressivity of these frameworks was very limited; they only contained these so-called ‘Probabilistic Spatio- Temporal atoms’ (PST atoms). In this thesis, a new framework that can reason more extensively with PST atoms is proposed. This is done in 3 different steps. In the first step, a framework is proposed that can only reason about the locations of objects. This is done by combining simplified PST atoms with propositional logic. In the second step, temporal operators are added to the first framework. For this framework, axiomatization has been done and soundness and completeness of the axioms have been proven. In the final step, probabilities were added to the temporal framework. For each framework, syntax, semantics and the satisfiability relation have been defined in a clear way. With these frameworks, more extensive reasoning is possible about PST atoms than in any of the frameworks that were defined in earlier research.