Ágnes Kurucz

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We study the complexity of some fragments of firstorder temporal logic over natural numbers time. The onevariable fragment of linear first-order temporal logic even with sole temporal operator2 is EXPSPACE-complete (this solves an open problem of [10]). So are the one-variable, two-variable and monadic monodic fragments with Until and Since. If we add the(More)
In this paper, we construct and investigate a hierarchy of spatio-temporal formalisms that result from various combinations of propositional spatial and temporal logics such as the propositional temporal logic PT L, the spatial logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a clear picture of the trade-off between expressiveness(More)
We show that—unlike products of ‘transitive’ modal logics which are usually undecidable— their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one(More)
One may think of many ways of combining modal logics representing various aspects of an application domain. Two ‘canonical’ constructions, supported by a well-developed mathematical theory, are fusions [17, 6, 7] and products [8, 7]. The fusion L1⊗ · · ·⊗Ln of n ≥ 2 normal propositional unimodal logics Li with the boxes 2i is the smallest multimodal logic(More)
Connections between Algebraic Logic and (ordinary) Logic. Algebraic counterpart of model theoretic semantics, algebraic counterpart of proof theory, and their connections. The class Alg(L) of algebras associated to any logic L. Equivalence theorems stating that L has a certain logical property iff Alg(L) has a certain algebraic property. (E.g. L admits a(More)
The general methodology of “algebraizing” logics (cf. [2], [4]) is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order(More)
We show that all the complexities of a possible axiomatisation of S5, the n-modal logic of products of n equivalence frames, are already present in any axiomatisation of Kn. Then in particular, we show that if 3 ≤ n < ω then, for any set L of n-modal formulas between Kn and S5, the class of all frames for L is not closed under ultraproducts and is therefore(More)
We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the twovariable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in(More)