In this paper we present a new fast tableau-based decision procedure for the ground set-theoretic fragment Multi-Level Syllogistic with Singleton (in short MLSS) which avoids the interleaving of model checking steps. The underlying tableau calculus is based upon the system KE.

In this paper we present a new fast tableau-based decision procedure for the ground set-theoretic fragment Multi-Level Syllogistic with Singleton (in short MLSS) which avoids the interleaving of model checking steps. The underlying tableau calculus is based upon the system KE.

We give an overview over three serious attempts to devise an effective decision method for CTL∗, namely Emerson and Jutla’s automata-theoretic decision procedure, Reynolds’ tableau search method and our recent approach based on an infinite tableau system with natural rules and with global conditions on the branches.

The goal of the article is twofold. first one to provide logics based on positional semantics which will be suitable for analysis epistemic modalities such as ‘agent ... knows/beliefs that ...’. second define tableau systemsfor logics. Firstly, we present minimal logic MR. Then, change notion formulas and in order consider iterations operator realization “free” classical formulas. After that, m...