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JTabWb: a Java Framework for Implementing Terminating Sequent and Tableau Calculi

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Ferrari M. , Fiorentini C. , Fiorino G.

Fundamenta Informaticae

2017

tom Vol. 150, nr 1

119--142

JTabWb is a Java framework for developing provers based on sequent or tableau calculi. It provides a generic engine which searches for proof of a given goal driven by a user-defined prover. The user is required to define the components of a prover by implementing suitable Java interfaces. In this paper we describe the structure of the framework and the role of its components through a running example. To show the generality of the framework we review some of the provers implemented in JTabWb. Finally, to corroborate the fact that the framework can be used to generate efficient provers, we compare the performances of one of the implemented provers with the state-of-the-art provers for Intuitionistic Propositional Logic.

From Constructivism to Logic Programming : an Homage to Mario Ornaghi

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Ferrari M. , Fiorentini C. , Momigliano A.

2018

tom Vol. 161, nr 1/2

1--7

In this brief note, we outline Mario Ornaghi’s contributions to the field of computational logic to celebrate his 70th birthday.

A Semantical Analysis of Focusing and Contraction in Intuitionistic Logic

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Avellone A. , Fiorentini C. , Momigliano A.

Fundamenta Informaticae

2015

tom Vol. 140, nr 3/4

247--262

Focusing is a proof-theoretic device to structure proof search in the sequent calculus: it provides a normal form to cut-free proofs in which the application of invertible and non-invertible inference rules is structured in two separate and disjoint phases. Although stemming from proofsearch considerations, focusing has not been thoroughly investigated in actual theorem proving, in particular w.r.t. termination. We present a contraction-free (and hence terminating) focused multisuccedent sequent calculus for propositional intuitionistic logic, which refines the G4ip calculus in the tradition of Vorob’ev, Hudelmeier and Dyckhoff. We prove completeness of the calculus semantically and argue that this offers a viable alternative to other more syntactical means.