We propose a reformulation of quantiiers rules in sequent calculi which allows to replace blind existential instantiation with uniication, thereby reducing non-determinism and complexity in proof-search. Our method, based on some ideas underlying the proof of Herbrand theorem for classical logic, may be applied to any \reasonable" non-classical sequent calculus, but here we focus on sequent cal...

In spite of sequent calculus being an appealing tool for describing logical systems, its use along with nonmonotonic logics has been largely neglected. Reasons may be the hardness in implementing a context sensitive mechanism able to detect changes in the theory. This seems to brake the locality of context of sequent rules. Nevertheless, a nonmo-notonic sequent calculus may be helpful if result...

The sequent calculus admits many proofs of the same conclusion that differ only by trivial permutations of inference rules. In order to eliminate this “bureaucracy” from sequent proofs, deductive formalisms such as proof nets or natural deduction are usually used instead of the sequent calculus, for they identify proofs more abstractly and geometrically. In this paper we recover permutative can...

Many important results in proof theory for sequent calculus (cut-elimination, completeness and other properties of search strategies, etc) are proved using permutations of sequent rules. The focus of this paper is on the development of systematic and automated-oriented techniques for the analysis of permutability in some sequent calculi. A representation of sequent calculi rules is discussed, w...

Justification logics are modal-like logics that provide a framework for reasoning about epistemic justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the method due to Sara Negri, we internalize the Kripke-style semantics of justification logics, known as Fitting models, within the syntax of the sequent ...

We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the syntactic principles that need to be obeyed in constructing correct proofs. It does not provide any help in finding good proof strategies. Instead it aims a...