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

Abstract

Abstract. JTabWb is a Java framework for developing provers based on terminating sequent or tableau calculi. It provides a generic engine which performs proof-search driven by a user-defined specification. The user is required to define the components of a prover by implementing suitable Java interfaces. The implemented provers can be used as standalone applications or embedded in other Java applications. The framework also supports proof-trace generation, L A T E X rendering of proofs and counter-model generation.

A syntactic proof of decidability for the logic of bunched implication BI

“…General theorem provers based on terminating sequent calculi have been implemented e.g. see [5] and it would be interesting to extend such a system to LBI * r . Given that finding a syntactic proof of decidability has already proved so vexing, we defer the calculation of the complexity upper bound for derivability arising from this decision procedure as future work.…”

Duality between Unprovability and Provability in Forward Refutation-search for Intuitionistic Propositional Logic

“…The sequent σ (13) is essential to build the countermodel since it corresponds to a world where both ¬¬p ⊃ p and S are forced, while ¬p ∨ p is not; to get Γ = {¬¬p ⊃ p, S} in the left of σ (13) , we have to use premises σ such that Γ ⊆ Lhs(σ ) (see Lemma 1(i)). Sequents σ (8) and σ (2) are needed to obtain ¬p ∨ p in the right of σ (13) , while sequents σ (7) and σ (11) are needed to support ¬¬p ⊃ p and S respectively. One can easily check that the side conditions (J1) and (J2) hold, thus the displayed application of rule ∨ is sound.…”

“…To evaluate the potential of our approach, we have developed frj, a Java implementation of our proof-search procedure based on the full-fledged framework JTabWb [11]. So far we have implemented the plain forward strategy and the redundancy checks based on forward and backward subsumption.…”

“…To evaluate the potential of our approach we have implemented frj, a Java prototype of our proof-search procedure based on the JTabWb framework [11] 3 . frj implements term-indexing, forward and backward subsumption and it allows the user to generate the rendering of proofs and of the extracted countermodels.…”