Related papers: On the Satisfiability of Local First-Order Logics …

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

Exactly solving first-order constraints (i.e., first-order formulas over a certain predefined structure) can be a very hard, or even undecidable problem. In continuous structures like the real numbers it is promising to compute approximate…

Solving the algebraic dichotomy conjecture for constraint satisfaction problems over structures first-order definable in countably infinite finitely bounded homogeneous structures requires understanding the applicability of…

Higher-order unification has been shown to be undecidable. Miller discovered the pattern fragment and subsequently showed that higher-order pattern unification is decidable and has most general unifiers. We extend the algorithm to…

Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…

We study the complexity of evaluating positive equality-free sentences of first-order (FO) logic over a fixed, finite structure B. This may be seen as a natural generalisation of the non-uniform quantified constraint satisfaction problem…

We provide decidability and undecidability results on the model-checking problem for infinite tree structures. These tree structures are built from sequences of elements of infinite relational structures. More precisely, we deal with the…

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…

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…

The \emph{Entscheidungsproblem}, or the classical decision problem, asks whether a given formula of first-order logic is satisfiable. In this work, we consider an extension of this problem to regular first-order \emph{theories}, i.e.,…

We give an algebraic characterisation of first-order logic with the neighbour relation, on finite words. For this, we consider languages of finite words over alphabets with an involution on them. The natural algebras for such languages are…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

We investigate the decidability and computational complexity of (deductive) conservative extensions in fragments of first-order logic (FO), with a focus on the two-variable fragment FO$^2$ and the guarded fragment GF. We prove that…

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…

In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…

We introduce tree-width for first order formulae \phi, fotw(\phi). We show that computing fotw is fixed-parameter tractable with parameter fotw. Moreover, we show that on classes of formulae of bounded fotw, model checking is fixed…

The question of 'what can be computed locally?' lies at the heart of distributed computing in networks. As established in Naor and Stockmeyer's seminal paper (STOC 1993), this question is undecidable, even for graph problems whose solutions…

Recent technological advances have led to unprecedented amounts of generated data that originate from the Web, sensor networks and social media. Analytics in terms of defeasible reasoning - for example for decision making - could provide…

We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…