One of the main issues in proof certification is that different theorem provers, even when designed for the same logic, tend to use different proof formalisms and produce outputs in different formats. The project ProofCert promotes the usage of a common specification language and of a small and trusted kernel in order to check proofs coming from different sources and for different logics. By relying on that idea and by using a classical focused sequent calculus as a kernel, we propose here a general framework for checking modal proofs. We present the implementation of the framework in a Prolog-like language and show how it is possible to specialize it in a simple and modular way in order to cover different proof formalisms, such as labelled systems, tableaux, sequent calculi and nested sequent calculi. We illustrate the method for the logicKby providing several examples and discuss how to further extend the approach.

Interpolation has been successfully applied in formal methods for model checking and test-case generation for sequential programs. Security protocols, however, exhibit idiosyncrasies that make them unsuitable for the direct application of interpolation. We address this problem and present an interp olation-based method for security protocol verification. Our method starts from a protocol specification and combines Craig interpolation, symbolic execution and the standard Dolev–Yao intruder model to search for possible attacks on the protocol. Interpolants are generated as a response to search failure in order to prune possible useless traces and speed up the exploration. We illustrate our method by means of concrete examples and discuss the results obtained by using a prototype implementation.

We propose an approach for defining labeled natural deduction systems for the class of Peircean branching temporal logics, seen as logics in their own right rather than as sub logics of Ockhamist systems. In particular, we give a system for the logic UB, i.e., the until-free fragment of CTL, and show that it is sound and complete. We also study normalization and discuss how derivations may reduce to a normal form using an appropriate management of proof contexts. Finally, we briefly discuss how to extend our system in order to capture full CTL.

We give a sound and complete labelled natural deduction system for a bundled branching temporal logic, namely the until-free version of BCTL*. The logic BCTL* is obtained by referring to a more general semantics than that of CTL*, where we only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting together a finite prefix of one path with the suffix of any other path beginning at the same state where the prefix ends (i.e. is fusion-closed). In other words, this logic does not enjoy the so-called limit-closure property of the standard CTL* validity semantics. We give both a classical and an intuitionistic version of our labelled natural deduction system for the until-free version of BCTL*, and carry out a proof-theoretical analysis of the intuitionistic system: we prove that derivations reduce to a normal form, which allows us to give a purely syntactical proof of consistency (for both the intuitionistic and classical versions) of the deduction system.

We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl. We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of useful normalization properties (in particular, derivations reduce to a normal form that enjoys a subformula property). We also discuss how to extend our systems to capture richer logics like (fragments of) LTL.