A decidable fragment of the elementary theory of relations and some applications

Authors:
D. Cantone;V. Cutello
Affiliations:
Archimedes S.R.L., Catania, Viale Ulisse 12, 95126, Catania, Italy;Courant Institute New York University and Dipartimento di Matematica, Università di Catania, Italy
Venue:
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Year:
1990

Citing 11
Cited 3

Programming with sets; an introduction to SETL

Programming with sets; an introduction to SETL
Decision procedures for elementary sublanguages of set theory. V. Multilevel syllogistic extended by the general union operator

Journal of Computer and System Sciences
Principles of database and knowledge-base systems, Vol. I

Principles of database and knowledge-base systems, Vol. I
The automation of syllogistic. II. optimization and complexity issues

Journal of Automated Reasoning
Set-theoretic reduction of Hilbert's tenth problem

CSL '89 Proceedings of the third workshop on Computer science logic
Computable set theory

Computable set theory
Decision procedures for elementary sublanguages of set theory: XI. Multilevel syllogistic extended by some elementary map constructs

Journal of Automated Reasoning - Special issue on new trends in automated reasoning
Decision procedures for elementary sublanguages of set theory: XIII. Model graphs, reflection and decidability

Journal of Automated Reasoning - Special issue on new trends in automated reasoning
Learning Discrete Math with ISETL

Learning Discrete Math with ISETL
A Decision Procedure for Unquantified Formulas of Graph Theory

Proceedings of the 9th International Conference on Automated Deduction
Optimal implementation of conjunctive queries in relational data bases

STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing

Decision procedures for stratified set-theoretic syllogistics

ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
A tableau-based decision procedure for a fragment of graph theory involving reachability and acyclicity

TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
On the Satisfiability Problem for a 4-level Quantified Syllogistic and Some Applications to Modal Logic

Fundamenta Informaticae - Special Issue on the Italian Conference on Computational Logic: CILC 2011

Quantified Score

Hi-index	0.00

Visualization

Abstract

The class of purely universal formulae of the elementary theory of relations with equality is shown to have an NP-complete satisfiability problem, under the assumption that there is an a priori bound on the length of quantifier prefixes and the arities of relation variables. In the second part of the paper we discuss possible applications in the field of theorem proving in set and graph theory and of consistency checking for queries in relational databases.