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We identify a number of decidable and undecidable fragments of first-order concatenation theory. We also give a purely universal axiomatization which is complete for the fragments we identify. Furthermore, we prove some normal-form results.

Logic · Mathematics 2018-04-18 Lars Kristiansen , Juvenal Murwanashyaka

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…

Logic in Computer Science · Computer Science 2017-05-30 Jean Christoph Jung , Carsten Lutz , Mauricio Martel , Thomas Schneider , Frank Wolter

We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…

Databases · Computer Science 2019-03-21 Antoine Amarilli , Michael Benedikt , Pierre Bourhis , Michael Vanden Boom

Building on ideas of Gurevich and Shelah for the G\"odel Class, we present a new probabilistic proof of the finite model property for the Guarded Fragment of First-Order Logic. Our proof is conceptually simple and yields the optimal…

Logic in Computer Science · Computer Science 2026-05-29 Oskar Fiuk

With the methodological support of probing (or diagnostic classification), recent studies have demonstrated that Transformers encode syntactic and semantic information to some extent. Following this line of research, this paper aims at…

Computation and Language · Computer Science 2022-01-26 Mael Jullien , Marco Valentino , Andre Freitas

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification…

Logic in Computer Science · Computer Science 2024-05-31 Luca Geatti , Alessandro Gianola , Nicola Gigante

In this paper we discuss various problems, associated to temporal phenomena. These problems include persistence and change, the integration of objects and processes, and truth-makers for temporal propositions. We propose an approach which…

Artificial Intelligence · Computer Science 2013-12-09 Heinrich Herre

Constraint propagation is one of the basic forms of inference in many logic-based reasoning systems. In this paper, we investigate constraint propagation for first-order logic (FO), a suitable language to express a wide variety of…

Logic in Computer Science · Computer Science 2011-07-11 Johan Wittocx , Marc Denecker , Maurice Bruynooghe

Evaluating a Boolean conjunctive query Q against a guarded first-order theory F is equivalent to checking whether "F and not Q" is unsatisfiable. This problem is relevant to the areas of database theory and description logic. Since Q may…

Logic in Computer Science · Computer Science 2019-03-14 Vince Bárány , Georg Gottlob , Martin Otto

With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability…

Computation and Language · Computer Science 2013-06-11 Karl Moritz Hermann , Edward Grefenstette , Phil Blunsom

A number of model-comparison games central to (finite) model theory, such as pebble and Ehrenfeucht-Fra\"{i}ss\'{e} games, can be captured as comonads on categories of relational structures. In particular, the coalgebras for these comonads…

Logic in Computer Science · Computer Science 2025-05-07 Samson Abramsky , Thomas Laure , Luca Reggio

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…

Logic · Mathematics 2023-02-07 Jim de Groot

Recently, symbolic structures were proposed as finite representations of potentially infinite first-order structures, where Linear Integer Arithmetic terms and formulas define the domain and interpretations of a structure. We generalize…

Logic in Computer Science · Computer Science 2026-05-14 Neta Elad , Sharon Shoham

Existential rules are an expressive knowledge representation language mainly developed to query data. In the literature, they are often supposed to be in some normal form that simplifies technical developments. For instance, a common…

Artificial Intelligence · Computer Science 2022-06-08 David Carral , Lucas Larroque , Marie-Laure Mugnier , Michaël Thomazo

Finding a logical formula that separates positive and negative examples given in the form of labeled data items is fundamental in applications such as concept learning, reverse engineering of database queries, generating referring…

Logic in Computer Science · Computer Science 2022-08-18 Jean Christoph Jung , Carsten Lutz , Hadrien Pulcini , Frank Wolter

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…

cmp-lg · Computer Science 2008-02-03 Rolf Backofen , Gert Smolka

We study the expressive power and succinctness of order-invariant sentences of first-order (FO) and monadic second-order (MSO) logic on structures of bounded tree-depth. Order- invariance is undecidable in general and, thus, one strives for…

Logic in Computer Science · Computer Science 2016-03-31 Kord Eickmeyer , Michael Elberfeld , Frederik Harwath

Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon…

Logic in Computer Science · Computer Science 2021-12-22 Stefan Ellmauthaler , Markus Krötzsch , Stephan Mennicke

We consider the family of guarded and unguarded ordered logics, that constitute a recently rediscovered family of decidable fragments of first-order logic (FO), in which the order of quantification of variables coincides with the order in…

Logic in Computer Science · Computer Science 2022-06-24 Bartosz Bednarczyk , Reijo Jaakkola

Knowledge compilation transforms logical theories into circuit representations that support efficient reasoning. We study this problem for propositional groundings of FO2, the two-variable fragment of first-order logic over finite domains.…

Logic in Computer Science · Computer Science 2026-05-13 Qiaolan Meng , Juhua Pu , Hongting Niu , Yuyi Wang , Yuanhong Wang , Ondřej Kuželka