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

Terminating tableau calculi for modal logic K with global counting operators

This paper presents the first systematic treatment of tableau calculi for modal logic K with global counting operators. Using a recently introduced tableau synthesis framework we establish two terminating tableau calculi for the logic. Whereas the first calculus is a prefix tableau calculus, the second is a refinement that internalises the semantics of the logic without using nominals. We prove...

How to Synthesize a Tableau

We synthesize a refutationally complete tableau calculus for propositional logic by a new method, using ordered resolution as a procedural framework at the meta level. Algebraically, the calculus solves the word problem for free distributive lattices. Goal-directedness of the construction is enforced by a ne-tuned well-founded ordering on terms, atoms and clauses. The synthesis is performed in ...

Dual Systems of Tableaux and Sequents for PLTL

On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph that must be checked and (possibly) pruned in a second phase of the refutation procedure. On the other hand, traditional sequent calculi for TL make use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automatization. A remarkable consequence of usi...

Using the TPTP Language for Representing Derivations in Tableau and Connection Calculi

The TPTP language, developed within the framework of the TPTP library, allows the representation of problems and solutions in first-order and higher-order logic. Whereas the writing of solutions in resolution calculi is well documented and used, an appropriate representation of solutions in tableau or connection calculi using the TPTP syntax has not yet been specified. This paper describes how ...

Duplication-Free Tableau Calculi Together With Cut-Free and Contraction-Free Sequent Calculi for the Interpolable . . .