Automated Reasoning in Quantified Modal and Temporal Logics
This thesis is about automated reasoning in quantified modal and temporal logics, with an application to formal methods. Quantified modal and temporal logics are extensions of classical first-order logic in which the notion of truth is extended to take into account its necessity or equivalently, in the temporal setting, its persistence through time. Due to their high complexity, these logics are less widely known and studied than their propositional counterparts. Moreover, little so far is known about their mechanisability and usefulness for formal methods. The relevant contributions of this thesis are threefold: firstly, we devise a sound and complete set of sequent calculi for quantified modal logics; secondly, we extend the approach to the quantified temporal logic of linear, discrete time and develop a framework for doing automated reasoning via Proof Planning in it; thirdly, we show a set of experimental results obtained by applying the framework to the problem of Feature Interactions in telecommunication systems. These results indicate that (a) the problem can be concisely and effectively modeled in the aforementioned logic, (b) proof planning actually captures common structures in the related proofs, and (c) the approach is viable also from the point of view of efficiency.