Many verification problems reduce to proving the validity of formulas involving both propositional connectives and domain-specific functions and predicates. This paper presents an explicating theorem prover architecture that leverages recent advances in propositional SAT solving and the development of proof-generating domain-specific procedures. We describe the implementation of an explicating ...

Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise and proofs, where some parts have been omitted. Current theories gradual types, though, lack central feature type theory: propositional equality. Lennon-Bertrand et al. show that, when reflexive proof refl is only closed value an equality type, extension Cal...

Separation logic is a spatial logic for reasoning locally about heap structures. A decidable fragment of its assertion language was presented in [1], based on a bounded model property. We exploit this property to give an encoding of this fragment into a first-order logic containing only the propositional connectives, quantification over the natural numbers and equality. This result is the first...

The aim of the present paper is to prove that concept validity and positive satisfiability with an empty ontology in Fuzzy Description Logic IALE, under standard product semantics respect quasi-witnessed models, are decidable. In our framework we not considering reasoning tasks over ontologies. proof result consists reducing problem a finitary consequence propositional logic Monteiro-Baaz delta...

Modern processors have relatively simple specificationsbased on their instruction set architectures. Their implementations, however, are very complex, especially with the advent of performance-enhancing techniques such as pipelining, superscalar operation, and speculative execution. Formal techniques to verify that a processor implements its instruction set specification could yield more reliab...