Related papers: Finite-Degree Predicates and Two-Variable First-Or…
A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…
We give a simple new proof that regular languages defined by first-order sentences with no quantifier alteration can be defined by such sentences in which only regular atomic formulas appear. Earlier proofs of this fact relied on arguments…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of…
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all…
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 consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
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 analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that…
We study the expressive power of successor-invariant first-order logic, which is an extension of first-order logic where the usage of an additional successor relation on the structure is allowed, as long as the validity of formulas is…
We study the positive logic FO+ on finite words, and its fragments, pursuing and refining the work initiated in [Kuperberg 2023]. First, we transpose notorious logic equivalences into positive first-order logic: FO+ is equivalent to LTL+ ,…
Order-invariant first-order logic is an extension of first-order logic FO where formulae can make use of a linear order on the structures, under the proviso that they are order-invariant, i.e. that their truth value is the same for all…
We introduce a novel decidable fragment of first-order logic. The fragment is one-dimensional in the sense that quantification is limited to applications of blocks of existential (universal) quantifiers such that at most one variable…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…
We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…
We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi$ (in $\mathcal{L}_{\omega,\omega}$) is…
In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for…