The guarded fragment with transitive guards

نویسندگان

Wieslaw Szwast

Lidia Tendera

چکیده

The guarded fragment with transitive guards, [GF+TG], is an extension of the guarded fragment of 9rst-order logic, GF, in which certain predicates are required to be transitive, transitive predicate letters appear only in guards of the quanti9ers and the equality symbol may appear everywhere. We prove that the decision problem for [GF+TG] is decidable. Moreover, we show that the problem is in 2EXPTIME. This result is optimal since the satis9ability problem for GF is 2EXPTIME-complete (J. Symbolic Logic 64 (1999) 1719–1742). We also show that the satis9ability problem for two-variable [GF+TG] is NEXPTIME-hard in contrast to GF with bounded number of variables for which the satis9ability problem is EXPTIME-complete. c © 2004 Elsevier B.V. All rights reserved. MSC: 03D15; 68Q17; 03B10; 03B25

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On the complexity of the two-variable guarded fragment with transitive guards

We investigate the complexity of the satisfiability problem for the two-variable guarded fragment with transitive guards.We prove that the satisfiability problem for the monadic version of this logic without equality is 2EXPTIME-hard. It is in fact 2EXPTIME-complete, since as shown by Szwast and Tendera, the whole guarded fragment with transitive guards is in 2EXPTIME.We also introduce a new lo...

متن کامل

The Two-Variable Guarded Fragment with Transitive Guards Is 2EXPTIME-Hard

We prove that the satisfiability problem for the two-variable guarded fragment with transitive guards GF +TG is 2EXPTIME-hard. This result closes the open questions left in [4], [17]. In fact, we show 2EXPTIME-hardness of minGF + TG, a fragment of GF + TG without equality and with just one transitive relation ≺, which is the only non-unary symbol allowed. Our lower bound for minGF + TG matches ...

متن کامل

Decidability of the Guarded Fragment with the Transitive Closure

We consider an extension of the guarded fragment in which one can guard quanti ers using the transitive closure of some binary relations. The obtained logic captures the guarded fragment with transitive guards, and in fact extends its expressive power non-trivially, preserving the complexity: we prove that its satis ability problem is 2Exptime-

متن کامل

Resolution Decision Procedures for the Guarded Fragment with Transitive Guards

We show how well-known refinements of ordered resolution, in particular redundancy elimination and ordering constraints in combination with a selection function, can be used to obtain a decision procedure for the guarded fragment with transitive guards. Another contribution of the paper is a special scheme notation, that allows to describe saturation strategies and show their correctness in a c...

متن کامل