The fluted fragment with transitive relations

The Two-Variable Guarded Fragment with Transitive Relations

Quine's Fluted Fragment is Non-Elementary

We study the fluted fragment, a decidable fragment of first-order logic with an unbounded number of variables, originally identified by W.V. Quine. We show that the satisfiability problem for this fragment has non-elementary complexity, thus refuting an earlier published claim by W.C. Purdy that it is in NExpTime. More precisely, we consider, for all m greater than 1, the intersection of the fl...

The guarded fragment with transitive guards

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 2...

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-

Downward-directed transitive frames with universal relations

In this paper we identify modal logics of some bimodal Kripke frames corresponding to geometrical structures. Each of these frames is a set of ‘geometrical’ objects with some natural accessibility relation plus the universal relation. For these logics we present finite axiom systems and prove completeness. We also show that all these logics have the finite model property and are PSPACE-complete...