The tableau method is widely used by logicians to give decision procedure for classical and non classical logics. But the move from proof-theoretic tool to an efficient automated theorem prover is often difficult for researchers with no technical background. The main “problem” is the non-determinism inherent in the tableau method. In this paper we give a functional algorithm to mechanize the ta...

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...

To overcome the inability of Description Logics (DLs) to represent vague or imprecise information, several fuzzy extensions have been proposed in the literature. In this context, an important family of reasoning algorithms for fuzzy DLs is based on a combination of tableau algorithms and Operational Research (OR) problems, specifically using Mixed Integer Linear Programming (MILP). In this pape...

In [12,16] we showed how to combine propositional BDI logics using Gabbay’s fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based decision procedure for the combined/fibred logics. To achieve this end we first outline with an example two types of tableau systems, (graph & path), and discuss why both are inadequate in the case of fibring. Having done...

This paper describes a generic tableau algorithm, which is the basis for a general customizable method for producing oracles from temporal logic speciications. A generic argument gives semantic rules with which to build the semantic tableau for a speciication. Parameterizing the tableau algorithm by semantic rules permits it to easily accommodate a variety of temporal operators and provides a c...

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filt...

The current rst-order automatic prover FAUST, embedded in HOL, is based on a sequent calculus which is quite slow and memory intensive. In this paper, an improved version of FAUST using a modiied form of tableau calculus called Tableau Graph Calculus is presented which overcomes the well-known ineeciencies of the traditional tableau calculus to a large extent. This calculus works on a compact r...

In [11,13] we showed how to combine propositional BDI logics using Gabbay’s fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based decision procedure for the combined/fibred logics. We show how to uniformly construct a tableau calculus for the combined logic using Governatori’s labelled tableau system KEM.

A tableau inversion is a pair of entries from the same column of a row-standard tableau that lack the relative ordering necessary to make the tableau columnstandard. An i-inverted Young tableau is a row-standard tableau with precisely i inversion pairs, and may be interpreted as a generalization of (column-standard) Young tableaux. Inverted Young tableaux that lack repeated entries were introdu...