Related papers: A Uniform One-Dimensional Fragment with Alternatio…

In this thesis (modal) dependence logic is investigated. It was introduced in 2007 by Jouko V\"a\"aan\"anen as an extension of first-order (resp. modal) logic by the dependence operator =(). For first-order (resp. propositional) variables…

We study the two-variable fragments D^2 and IF^2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D^2, both problems are…

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…

We study the precise computational complexity of deciding satisfiability of first-order quantified formulas over the theory of fixed-size bit-vectors with binary-encoded bit-widths and constants. This problem is known to be in EXPSPACE and…

We consider the quantifier alternation hierarchy within two-variable first-order logic FO^2[<,suc] over finite words with linear order and binary successor predicate. We give a single identity of omega-terms for each level of this…

This work deals with the presence of topological structures in models of two real scalar fields in the two-dimensional spacetime. The subject concerns the presence of a geometric constriction, which appears with a modification of the…

Dependence logic provides an elegant approach for introducing dependencies between variables into the object language of first-order logic. In [1] generalized quantifiers were introduced in this context. However, a satisfactory account was…

We present a first-order theory of sequences with integer elements, Presburger arithmetic, and regular constraints, which can model significant properties of data structures such as arrays and lists. We give a decision procedure for the…

We study the satisfiability problem for the fluted fragment extended with transitive relations. We show that the logic enjoys the finite model property when only one transitive relation is available. On the other hand we show that the…

Hilbert's Entscheidungsproblem has given rise to a broad and productive line of research in mathematical logic, where the classification process of decidable classes of first-order sentences represent only one of the remarkable results.…

Nominal terms extend first-order terms with binding. They lack some properties of first- and higher-order terms: Terms must be reasoned about in a context of 'freshness assumptions'; it is not always possible to 'choose a fresh variable…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations…

We introduce a novel model-theoretic framework inspired from graph modification and based on the interplay between model theory and algorithmic graph minors. The core of our framework is a new compound logic operating with two types of…

This paper aims to incorporate the notion of quantifier-free formulas modulo a first-order theory and the stratification of formulas by quantifier alternation depth modulo a first-order theory into the algebraic treatment of classical…

We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…

Counting logics with a bounded number of variables form one of the central concepts in descriptive complexity theory. Although they restrict the number of variables that a formula can contain, the variables can be nested within scopes of…

Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…

We establish coNExpTime-completeness of the problem of deciding order-invariance of a given two variable first-order formula, improving and significantly simplifying coTwoNExpTime bound by Zeume and Harwath.

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…