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We give a sufficient condition under which every finite-satisfiable formula of a given PCTL fragment has a model with at most doubly exponential number of states (consequently, the finite satisfiability problem for the fragment is in…

Logic in Computer Science · Computer Science 2021-07-09 Miroslav Chodil , Antonín Kučera

It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete.…

Logic in Computer Science · Computer Science 2015-07-01 Thomas Schwentick , Thomas Zeume

One-dimensional fragment of first-order logic is obtained by restricting quantification to blocks of existential (universal) quantifiers that leave at most one variable free. We investigate this fragment over words and trees, presenting a…

Logic in Computer Science · Computer Science 2024-04-08 Emanuel Kieronski , Antti Kuusisto

We study the time complexity of the weighted first-order model counting (WFOMC) over the logical language with two variables and counting quantifiers. The problem is known to be solvable in time polynomial in the domain size. However, the…

Logic in Computer Science · Computer Science 2024-08-26 Jan Tóth , Ondřej Kuželka

We determine the complexity of second-order HyperLTL satisfiability, finite-state satisfiability, and model-checking: All three are equivalent to truth in third-order arithmetic. We also consider two fragments of second-order HyperLTL that…

Logic in Computer Science · Computer Science 2026-03-18 Hadar Frenkel , Gaëtan Regaud , Martin Zimmermann

In this short note we prove that the satisfiability problem of the Ackermann fragment with one leading existential quantifier is ExpTime-complete.

Logic in Computer Science · Computer Science 2022-02-01 Reijo Jaakkola

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…

Logic in Computer Science · Computer Science 2025-09-11 Alessandro Artale , Christopher Hampson , Roman Kontchakov , Andrea Mazzullo , Frank Wolter

We present new results on finite satisfiability of logics with counting and arithmetic. One result is a tight bound on the complexity of satisfiability of logics with so-called local Presburger quantifiers, which sum over neighbors of a…

Logic in Computer Science · Computer Science 2025-10-31 Michael Benedikt , Chia-Hsuan Lu , Tony Tan

We consider an extension of the unary negation fragment of first-order logic in which arbitrarily many binary symbols may be required to be interpreted as equivalence relations. We show that this extension has the finite model property.…

Logic in Computer Science · Computer Science 2018-09-14 Daniel Danielski , Emanuel Kieronski

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges…

Logic in Computer Science · Computer Science 2024-09-04 Chia-Hsuan Lu , Tony Tan

During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…

Logic in Computer Science · Computer Science 2021-10-05 Bartosz Bednarczyk , Maja Orłowska , Anna Pacanowska , Tony Tan

We study the satisfiability problem for the fluted fragment extended with transitive relations. We show that the logic enjoys the finite model property when only one transitive relation is available. On the other hand we show that the…

Logic in Computer Science · Computer Science 2019-06-24 Ian Pratt-Hartmann , Lidia Tendera

This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…

Logic in Computer Science · Computer Science 2025-12-30 Mikhail Rybakov

The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a…

Logic in Computer Science · Computer Science 2021-01-26 Emanuel Kieroński , Sebastian Rudolph

Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…

Logic in Computer Science · Computer Science 2021-03-16 Reijo Jaakkola

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain. Data values can be compared wrt.\ equality. As the satisfiability problem for this logic is undecidable in…

Logic in Computer Science · Computer Science 2024-08-07 Benedikt Bollig , Arnaud Sangnier , Olivier Stietel

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

Verification of properties of first order logic with two variables FO2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having…

Logic in Computer Science · Computer Science 2013-06-03 Saguy Benaim , Michael Benedikt , Rastislav Lenhardt , James Worrell

It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two…

Logic in Computer Science · Computer Science 2016-04-21 Thomas Zeume , Frederik Harwath

We study the satisfiability problem for the fluted fragment extended with transitive relations. The logic enjoys the finite model property when only one transitive relation is available and the finite model property is lost when…

Logic in Computer Science · Computer Science 2024-05-22 Ian Pratt-Hartmann , Lidia Tendera