Related papers: A sufficient condition for first order non-definab…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

We study multimodal logics over universally first-order definable classes of frames. We show that even for bimodal logics, there are universal Horn formulas that define set of frames such that the satisfiability problem is undecidable, even…

We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…

We provide simple necessary and sufficient conditions under which a path constitutes a solution to an infinite-horizon, continuous-time optimal control problem. We prove transversality conditions under standard assumptions. We also present…

We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…

We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…

The first-order theory of the automorphism group of an infinite resplendent model in a finite language is undecidable.

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.,…

While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…

We introduce some notions of invariant elementary definability which extend the notions of first-order order-invariant definability, and, more generally, definability invariant with respect to arbitrary numerical relations. In particular,…

Definite descriptions, such as 'the General Chair of KR 2024', are a semantically transparent device for object identification in knowledge representation. In first-order modal logic, definite descriptions have been widely investigated for…

We provide a sufficient condition for a polynomial ring, not necessarily commutative, to have a first-order definition for the rational integers.

This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…

We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…

First order algebraic differential equations are considered. An necessary condition for a first order algebraic differential equation to have a rational general solution is given: the algebraic genus of the equation should be zero.…

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…

We address the problem of characterizing $H$-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give several characterizations of a homomorphism dualities arising in a class of…

A pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V=HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are…