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检索条件"任意字段=Proceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science"

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Forbidden Induced Subgraphs and the Łoś-Tarski theorem 36

Forbidden Induced Subgraphs and the Łoś-Tarski Theorem

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36th annual acm/ieee symposium on logic in computer science, LICS 2021

作者： Chen, Yijia Flum, Jorg Shanghai Jiao Tong University Department of Computer Science China Mathematisches Institut Albert-Ludwigs-Universität Freiburg Germany

ISBN: (纸本)9781665448956

Let \mathcal C be a class of finite and infinite graphs that is closed under induced subgraphs. the well-known Łoś-Tarski theorem from classical model theory implies that \mathcal C is definable in first-order logic (FO) by a sentence if and only if \mathcal C has a finite set of forbidden induced finite subgraphs. It provides a powerful tool to show nontrivial characterizations of graphs of small vertex cover, of bounded tree-depth, of bounded shrub-depth, etc. in terms of forbidden induced finite subgraphs. Furthermore, by the Completeness theorem, we can compute from the corresponding forbidden induced subgraphs. Our results (a) and (b) show that this machinery fails on finite graphs.(a)there is a class of finite graphs that is definable in FO and closed under induced subgraphs but has no finite set of forbidden induced subgraphs.(b)Even if we only consider classes \mathcal C of finite graphs that can be characterized by a finite set of forbidden induced subgraphs such a characterization cannot be computed from an FO-sentence that defines \mathcal C and the size of the characterization cannot be bounded by f(||) for any computable function *** their importance in graph theory, our results also significantly strengthen similar known theorems for arbitrary structures. © 2021 ieee.

关键词： Forbidden induced subgraphs universal first-order sentences

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HoCHC: a refutationally complete and semantically invariant system of higher-order logic modulo theories 19

HoCHC: a refutationally complete and semantically invariant ...

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proceedings of the 34th annual acm/ieee symposium on logic in computer science

作者： C.-H. Luke Ong Dominik Wagner University of Oxford

We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC)---a system of higher-order logic modulo theories---and prove its soundness and refutational completeness w.r.t. both standard and Henkin semantics. As corollaries, we obtain the compactness theorem and semi-decidability of HoCHC for semi-decidable background theories, and we prove that HoCHC satisfies a canonical model property. Moreover a variant of the well-known translation from higher-order to 1st-order logic is shown to be sound and complete for HoCHC in both semantics. We illustrate how to transfer decidability results for (fragments of) 1st-order logic modulo theories to our higher-order setting, using as example the Bernays-Schönfinkel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic.

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the logic of Action Lattices is Undecidable 34

The Logic of Action Lattices is Undecidable

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Kuznetsov, Stepan RAS Steklov Math Inst 8 Gubkina St Moscow Russia Natl Res Univ Higher Sch Econ 3 Kochnovsky Pr Moscow Russia

We prove algorithmic undecidability of the (in)equational theory of residuated Kleene lattices (action lattices), thus solving a problem left open by D. Kozen, P. Jipsen, W. Buszkowski.

ISBN: (纸本)9781728136080

We prove algorithmic undecidability of the (in)equational theory of residuated Kleene lattices (action lattices), thus solving a problem left open by D. Kozen, P. Jipsen, W. Buszkowski.

关键词： Algebra Lattices Turing machines Standards Grammar computer science Cognition

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Learning Concepts Definable in First-Order logic with Counting 34

Learning Concepts Definable in First-Order Logic with Counti...

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： van Bergerem, Steffen Rhein Westfal TH Aachen Aachen Germany

ISBN: (纸本)9781728136080

We study classification problems over relational background structures for hypotheses that are defined using logics with counting. the aim of this paper is to find learning algorithms running in time sublinear in the size of the background structure. We show that hypotheses defined by FOCN(P)-formulas over structures of polylogarithmic degree can be learned in sublinear time. Furthermore, we prove that for structures of unbounded degree there is no sublinear learning algorithm for first-order formulas.

关键词： Training Approximation algorithms Encyclopedias Relational databases Hypertext systems Length measurement Size measurement

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logical Foundations of Quantitative Equality 22

Logical Foundations of Quantitative Equality

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proceedings of the 37th annual acm/ieee symposium on logic in computer science

作者： Francesco Dagnino Fabio Pasquali Università degli Studi di Genova Italy

ISBN: (纸本)9781450393515

In quantitative reasoning one compares objects by distances, instead of equivalence relations, so that one can measure how much they are similar, rather than just saying whether they are equivalent or not. In this paper we aim at providing a logical ground to quantitative reasoning with distances in Linear logic, using the categorical language of Lawvere’s doctrines. the key idea is to see distances as equality predicates in Linear logic. We use graded modalities to write a resource sensitive substitution rule for equality, which allows us to give it a quantitative meaning by distances. We introduce a deductive calculus for (Graded) Linear logic with quantitative equality and the notion of Lipschitz doctrine to give it a sound and complete categorical semantics. We also describe a universal construction of Lipschitz doctrines, which generates examples based for instance on metric spaces and quantitative realisability.

关键词： graded modalities linear logic quantitative reasoning hyperdoctrines

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Lambda Calculus and Probabilistic Computation 34

Lambda Calculus and Probabilistic Computation

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Faggian, Claudia della Rocca, Simona Ronchi CNRS Paris France Univ Torino Turin Italy

ISBN: (纸本)9781728136080

We introduce two extensions of the A -calculus with a probabilistic choice operator, A"ar and g'n, modeling respectively call -by -value and call-by-name probabilistic computation. We prove that both enjoys confluence and standardization, in an extended way: we revisit these two fundamental notions to take into account the asymptotic behaviour of terms. the common root of the two calculi is a further calculus based on Linear logic, A',D, which allows us to develop a unified, modular approach.

关键词： Calculus Probabilistic logic Standards Computational modeling computer languages Programming

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the Geometry of Bayesian Programming 34

The Geometry of Bayesian Programming

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Dal Lago, Ugo Hoshino, Naohiko Univ Bologna Bologna Italy INRIA Sophia Antipolis Biot France Kyoto Univ Kyoto Japan

ISBN: (纸本)9781728136080

We give a geometry of interaction model for a typed gimel-calculus endowed with operators for sampling from a continuous uniform distribution and soft conditioning, namely a paradigmatic calculus for higher-order Bayesian programming. the model is based on the category of measurable spaces and partial measurable functions, and is proved adequate with respect to both a distribution-based and a sampling-based operational semantics.

关键词： Semantics Extraterrestrial measurements Probabilistic logic Algebra Calculus Kernel Bayes methods

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Template games and differential linear logic 34

Template games and differential linear logic

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Mallies, Paul-Andre CNRS Paris France Univ Paris Diderot Paris France

ISBN: (纸本)9781728136080

We extend our recent template game model of multiplicative additive linear logic (MALL) with an exponential modality of linear logic (LL) derived from the standard categorical construction Sym of the free symmetric monoidal category. We obtain in this way the first game semantics of differential linear logic (DiLL) in its classical form. the construction of the model relies on a careful and healthy comparison with the model of generalised species designed ten years ago by Fiore, Gambino, Hyland and Winskel. Besides the resolution of an old open problem of game semantics, the study reveals an unexpected and promising convergence between linear logic and homotopy theory.

关键词： Games Cats Semantics Mathematical model Additives Turning

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Block products for algebras over countable words and applications to logic 34

Block products for algebras over countable words and applica...

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34th annual acm/ieee symposium on logic in computer science (LICS)

作者： Adsul, Bharat Sarkar, Saptarshi Sreejith, A. V. Indian Inst Technol Mumbai Maharashtra India IIT Goa Veling India

ISBN: (纸本)9781728136080

We propose a seamless integration of the block product operation to the recently developed algebraic framework for regular languages of countable words. A simple but subtle accompanying block product principle has been established. Building on this, we generalize the well-known algebraic characterizations of first-order logic (resp. first-order logic with two variables) in terms of strongly (resp. weakly) iterated block products. We use this to arrive at a complete analogue of Schutzenberger-McNaughton-Papert theorem for countable words. We also explicate the role of block products for linear temporal logic by formulating a novel algebraic characterization of a natural fragment.

关键词： Algebra Automata Standards Buildings Syntactics Tools Complexity theory

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Completeness for game logic 19

Completeness for game logic

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proceedings of the 34th annual acm/ieee symposium on logic in computer science

作者： Sebastian Enqvist Helle Hvid Hansen Clemens Kupke Johannes Marti Yde Venema Stockholm University Delft University of Technology University of Strathclyde Universität Bremen University of Amsterdam

Game logic was introduced by Rohit Parikh in the 1980s as a generalisation of propositional dynamic logic (PDL) for reasoning about outcomes that players can force in determined 2-player games. Semantically, the generalisation from programs to games is mirrored by moving from Kripke models to monotone neighbourhood models. Parikh proposed a natural PDL-style Hilbert system which was easily proved to be sound, but its completeness has thus far remained an open *** this paper, we introduce a cut-free sequent calculus for game logic, and two cut-free sequent calculi that manipulate annotated formulas, one for game logic and one for the monotone μ-calculus, the variant of the polymodal μ-calculus where the semantics is given by monotone neighbourhood models instead of Kripke structures. We show these systems are sound and complete, and that completeness of Parikh's axiomatization follows. Our approach builds on recent ideas and results by Afshari & Leigh (LICS 2017) in that we obtain completeness via a sequence of proof transformations between the systems. A crucial ingredient is a validity-preserving translation from game logic to the monotone μ-calculus.

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