A Tableau-Based Decision Procedure for a Fragment of Set Theory Involving a Restricted Form of Quantification
نویسندگان
چکیده
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.
منابع مشابه
A tableau - based decision procedure for afragment of set theory involving a restrictedform of quanti cation ? Domenico Cantone 1 and Calogero
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.
متن کاملA 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, ...
متن کاملA 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.
متن کاملConjunctive Query Answering via a Fragment of Set Theory
We address the problem of Conjunctive Query Answering (CQA) for the description logic DL〈4LQS〉(D) (DL D , for short) which extends the logic DL〈4LQS〉(D) with Boolean operations on concrete roles and with the product of concepts. The result is obtained by formalizing DL D -knowledge bases and DL D conjunctive queries in terms of formulae of the four-level set-theoretic fragment 4LQS, which admit...
متن کاملA 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.
متن کامل