A tableau - based decision procedure for afragment of set theory involving a restrictedform of quanti cation ? Domenico Cantone 1 and Calogero

A Tableau-Based Decision Procedure for a Fragment of Set Theory Involving a Restricted Form of Quantification

We extend the unquantiied set-theoretic fragment discussed in 1] with a restricted form of quantiication, we prove decidability of the resulting fragment by means of a tableau calculus and we address the eeciency problem of the underlying decision procedure, by showing that the model-checking steps used in 1] are not necessary.

A New Fast Tableau - Based Decision Procedurefor an Unquanti ed Fragment of Set Theory ?

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.

A New Fast Tableau-Based Decision Procedure for an Unquantified Fragment of Set Theory

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.

A Tableau-Based Decision Procedure for a Fragment of Graph Theory Involving Reachability and Acyclicity

We study the decision problem for the language DGRA (directed graphs with reachability and acyclicity), a quantifier-free fragment of graph theory involving the notions of reachability and acyclicity. We prove that the language DGRA is decidable, and that its decidability problem is NP -complete. We do so by showing that the language enjoys a small model property : If a formula is satisfiable, ...

A Tableau Calculus for Integrating First-Order and Elementary Set Theory Reasoning