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Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are…

Artificial Intelligence · Computer Science 2014-05-01 Ringo Baumann , Wolfgang Dvorák , Thomas Linsbichler , Hannes Strass , Stefan Woltran

Lindstr\"om theorem obviously fails as a characterization of $\mathcal{L}_{\omega \omega}^{-} $, first-order logic without identity. In this note we provide a fix: we show that $\mathcal{L}_{\omega \omega}^{-} $ is \emph{maximal} among…

Logic · Mathematics 2022-12-07 Guillermo Badia , Xavier Caicedo , Carles Noguera

Let kappa be an uncountable regular cardinal. Call an equivalence relation on functions from kappa into 2 Sigma_1^1-definable over H(kappa) if there is a first order sentence F and a parameter R subseteq H(kappa) such that functions…

Logic · Mathematics 2007-05-23 Saharon Shelah , Pauli Väisänen

Fix a finite ordinal n>2. We show that there exists an atomic, simple and countable representable CA_n, such that its minimal completion is outside SNr_nCA_{n+3}. Hence, for any finite k\geq 3, the variety SNr_nCA_{n+k} is not…

Logic · Mathematics 2014-08-15 Tarek Sayed Ahmed

The fully enriched μ-calculus is the extension of the propositional μ-calculus with inverse programs, graded modalities, and nominals. While satisfiability in several expressive fragments of the fully enriched μ-calculus is known…

Logic in Computer Science · Computer Science 2015-07-01 Piero A. Bonatti , Carsten Lutz , Aniello Murano , Moshe Y. Vardi

The classes of slender and cotorsion-free abelian groups are axiomatizable in the infinitary logics L_{infty,omega_1} and L_{infty,omega}, respectively. The Baer-Specker group Z^omega is not L_{infty,omega_1}-equivalent to a slender group.

Logic · Mathematics 2007-05-23 Oren Kolman , Saharon Shelah

Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly…

Logic · Mathematics 2021-02-18 Filippo Calderoni , Heike Mildenberger , Luca Motto Ros

We extend to singular cardinals the model-theoretical relation $\lambda \stackrel{\kappa}{\Rightarrow} \mu$ introduced in P. Lipparini, The compactness spectrum of abstract logics, large cardinals and combinatorial principles, Boll. Unione…

Logic · Mathematics 2008-05-13 Paolo Lipparini

We prove an algebraic extension theorem for the computably enumerable sets, $\mathcal{E}$. Using this extension theorem and other work we then show if $A$ and $\hat{A}$ are automorphic via $\Psi$ then they are automorphic via $\Lambda$…

Logic · Mathematics 2007-05-23 Peter Cholak , Leo Harrington

This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic…

Logic in Computer Science · Computer Science 2023-02-13 Benedikt Pago

We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.

Logic in Computer Science · Computer Science 2024-06-19 Alejandro Díaz-Caro , Gilles Dowek , Malena Ivnisky , Octavio Malherbe

Logical frameworks are successful in modeling proof systems. Recently, CoLF extended the logical framework LF to support higher-order rational terms that enable adequate encoding of circular objects and derivations. In this paper, we…

Logic in Computer Science · Computer Science 2023-12-12 Zhibo Chen

Cartesian difference categories are a recent generalisation of Cartesian differential categories which introduce a notion of "infinitesimal" arrows satisfying an analogue of the Kock-Lawvere axiom, with the axioms of a Cartesian…

Logic in Computer Science · Computer Science 2020-12-01 Mario Alvarez-Picallo , C. -H. Luke Ong

A forcing extension may create new isomorphisms between two models of a first order theory. Certain model theoretic constraints on the theory and other constraints on the forcing can prevent this pathology. A countable first order theory is…

Logic · Mathematics 2016-09-06 John T. Baldwin , Michael C. Laskowski , Saharon Shelah

This is part I of a study on cardinals that are characterizable by Scott sentences. Building on [3], [6] and [1] we study which cardinals are characterizable by a Scott sentence $\phi$, in the sense that $\phi$ characterizes $\kappa$, if…

Logic · Mathematics 2016-02-10 Ioannis Souldatos

In this paper, we present a typed lambda calculus ${\bf SILL}(\lambda)_{\Sigma}$, a type-theoretic version of intuitionistic linear logic with subexponentials, that is, we have many resource comonadic modalities with some interconnections…

Logic · Mathematics 2025-10-03 Daniel Rogozin

A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic. We adapt this approach to abstract categorial grammars (ACG). Thus we define…

Logic · Mathematics 2020-05-21 Sergey Slavnov

We give a complete classification of the set of parameters $\kappa$ for which the singular value of $E_{\kappa}:z\mapsto \exp(z)+\kappa$ escapes to infinity under iteration. In particular, we show that every path-connected component of this…

Dynamical Systems · Mathematics 2007-12-11 Markus Förster , Lasse Rempe , Dierk Schleicher

We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…

Logic in Computer Science · Computer Science 2025-09-25 Alejandro Díaz-Caro , Gilles Dowek

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…

Logic in Computer Science · Computer Science 2022-10-17 Pablo Barenbaum , Teodoro Freund