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We investigate (quantifier-free) spatial constraint languages with equality, contact and connectedness predicates as well as Boolean operations on regions, interpreted over low-dimensional Euclidean spaces. We show that the complexity of…
Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
This article fits in the area of research that investigates the application of topological duality methods to problems that appear in theoretical computer science. One of the eventual goals of this approach is to derive results in…
We consider quantifier-free spatial logics, designed for qualitative spatial representation and reasoning in AI, and extend them with the means to represent topological connectedness of regions and restrict the number of their connected…
It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete.…
Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all…
We consider the satisfiability problem for the two-variable fragment of first-order logic over finite unranked trees. We work with signatures consisting of some unary predicates and the binary navigational predicates child, right sibling,…
For Boolean satisfiability problems, the structure of the solution space is characterized by the solution graph, where the vertices are the solutions, and two solutions are connected iff they differ in exactly one variable. For this…
The $\epsilon$-logic (which is called $\epsilon$E-logic in this paper) of Kuyper and Terwijn is a variant of first order logic with the same syntax, in which the models are equipped with probability measures and in which the $\forall x$…
We classify the complexity of the satisfiability problem for extensions of CTL and UB. The extensions we consider are Boolean combinations of path formulas, fairness properties, past modalities, and forgettable past. Our main result shows…
A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…
A complete classification of the complexity of the local and global satisfiability problems for graded modal language over traditional classes of frames have already been established. By "traditional" classes of frames, we mean those…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Polyhedral semantics is a recently introduced branch of spatial modal logic, in which modal formulas are interpreted as piecewise linear subsets of an Euclidean space. Polyhedral semantics for the basic modal language has already been well…
We consider logics derived from Euclidean spaces $\mathbb{R}^n$. Each Euclidean space carries relations consisting of those pairs that are, respectively, distance more than 1 apart, distance less than 1 apart, and distance 1 apart. Each…
The choice of the right trade-off between expressiveness and complexity is the main issue in interval temporal logic. In their seminal paper, Halpern and Shoham showed that the satisfiability problem for HS (the temporal logic of Allen's…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…