Tableau vs. Sequent Calculi for Minimal Entailment

ar X iv : 1 40 5 . 15 65 v 1 [ cs . L O ] 7 M ay 2 01 4 Tableau vs . Sequent Calculi for Minimal Entailment

In this paper we compare two proof systems for minimal entailment: a tableau system OTAB and a sequent calculus MLK , both developed by Olivetti (1992). Our main result shows that OTAB-proofs can be efficiently translated into MLK -proofs, i.e.,MLK psimulates OTAB . The simulation is technically very involved and answers an open question posed by Olivetti (1992) on the relation between the two ...

Non-elementary Speed-ups in Proof Length by Different Variants of Classical Analytic Calculi

In this paper, diierent variants of classical analytic calculi for rst-order logic are compared with respect to the length of proofs possible in such calculi. A cut-free sequent calculus is used as a prototype for diierent other analytic calculi like analytic tableau or various connection calculi. With modiied branching rules ({rules), non-elementary shorter minimal proofs can be obtained for a...

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

A Tableau Calculus for Equilibrium Entailment

We apply tableau methods to the problem of computing entailment in the nonmonotonic system of equilibrium logic, a generalisation of the inference relation associated with the stable model and answer set semantics for logic programs. We describe tableau calculi for the nonclassical logics underyling equilibrium entailment, namely hereand-there with strong negation and its strengthening classica...

Binary Sequent Calculi for Truth-invariance Entailment of Finite Many-valued Logics

In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new binary sequent calculi (each sequent is a pair of formulae) for many valued logic with a finite set of truth values, and of Kripke-like semantics for it that is both sound and complete. We did not use the logic entailment based o...