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Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

Logic in Computer Science · Computer Science 2017-03-08 Lidia Tendera

We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an…

Logic · Mathematics 2012-11-28 Mohammad Assem

We investigate a generalization of the {\L}o\'s-Tarski preservation theorem via the semantic notion of \emph{preservation under substructures modulo $k$-sized cores}. It was shown earlier that over arbitrary structures, this semantic notion…

Logic in Computer Science · Computer Science 2014-01-24 Abhisekh Sankaran , Bharat Adsul , Supratik Chakraborty

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…

Formal Languages and Automata Theory · Computer Science 2019-01-09 Dietrich Kuske , Georg Zetzsche

We consider two orthogonal points of view on finite permutations, seen as pairs of linear orders (corresponding to the usual one line representation of permutations as words) or seen as bijections (corresponding to the algebraic point of…

Combinatorics · Mathematics 2019-09-20 Michael Albert , Mathilde Bouvel , Valentin Féray

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…

Logic · Mathematics 2016-09-07 Carsten Butz , Ieke Moerdijk

We consider fragments of first-order logic and as models we allow finite and infinite words simultaneously. The only binary relations apart from equality are order comparison < and the successor predicate +1. We give characterizations of…

Formal Languages and Automata Theory · Computer Science 2015-03-17 Jakub Kallas , Manfred Kufleitner , Alexander Lauser

The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…

Logic in Computer Science · Computer Science 2023-10-03 Emanuel Kieroński

We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical…

Logic in Computer Science · Computer Science 2012-05-07 Andreas Krebs , A. V. Sreejith

Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…

Formal Languages and Automata Theory · Computer Science 2017-01-11 Thomas Place , Marc Zeitoun

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of…

Logic in Computer Science · Computer Science 2019-03-14 Witold Charatonik , Piotr Witkowski

We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…

Logic in Computer Science · Computer Science 2021-05-14 Dominik D. Freydenberger , Liat Peterfreund

A first-order theory has the Schroder-Bernstein property if any two of its models that are elementarily bi-embeddable are isomorphic. We prove that if a countable theory T has the Schroder-Bernstein property then it is classifiable (it is…

Logic · Mathematics 2007-05-23 John Goodrick

Lindstr\"om's Theorem characterizes first order logic as the maximal logic satisfying the Compactness Theorem and the Downward L\"owenheim-Skolem Theorem. If we do not assume that logics are closed under negation, there is an obvious…

Logic · Mathematics 2023-04-17 Saharon Shelah , Jouko Väänänen

Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…

Logic in Computer Science · Computer Science 2010-11-23 Facundo Carreiro

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…

Programming Languages · Computer Science 2020-02-21 Gilles Barthe , Raphaëlle Crubillé , Ugo Dal Lago , Francesco Gavazzo

Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary…

Logic · Mathematics 2016-05-02 Silvio Ghilardi , Samuel J. van Gool

We prove that the expressive power of first-order logic with team semantics plus contradictory negation does not rise beyond that of first-order logic (with respect to sentences), and that the totality atoms of arity k +1 are not definable…

Logic · Mathematics 2014-03-18 Pietro Galliani

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…

Logic in Computer Science · Computer Science 2021-04-27 Melissa Antonelli , Ugo Dal Lago , Paolo Pistone

We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…

Formal Languages and Automata Theory · Computer Science 2024-02-14 Denis Kuperberg