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Defining algorithmically presented structures in first-order logic 24

Defining algorithmically presented structures in first-order...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Khoussainov, Bakh Kasymov, Nadim Karimova, Nodira UESTC Chengdu Peoples R China Natl Univ Uzbekistan Tashkent Uzbekistan

ISBN: (纸本)9798400706608

We aim to describe the isomorphism types of infinite structures in the language of first-order logic. this pursuit holds importance in logic in computer science, encompassing model theory, descriptional complexity, and the foundations of computability. We introduce the notion of quasi-axiomatizability aimed at describing the isomorphism types of structures. Our focus centers on two classes of algorithmically presented structures. the first is the class of structures for which the positive atomic diagrams are computably enumerable. We call these structures positive structures. the second is the class of structures for which the negative atomic diagrams are computably enumerable. We call these structures negative structures. We study quasi-axiomatizability of structures from these classes by there exists, for all, there exists for all, for all there exists-sentences in expansions of languages. Our work is a contribution to the interplay between expressive power of first-order logic, computability, and model theory.

关键词： Isomorphisms expressive power of first-order logic for all, there exists, for all there exists, there exists for all sentences expansions positive structures negative structures computable enumeration

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Uniformisation of Regular Relations in First-Order logic with Two Variables 24

Uniformisation of Regular Relations in First-Order Logic wit...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Lhote, Nathan Michielini, Vincent Skrzypczak, Michal Aix Marseille Univ Lab Informat & Syst Marseille France Univ Warsaw Inst Informat Warsaw Poland

ISBN: (纸本)9798400706608

A uniformisation of a binary relation is a functional relation contained in it, with the same domain. the uniformisation problem asks whether such a uniformisation can be defined in a given formalism. We solve this problem in the context of regular relations over finite words, for the fragment FO2[<] of First-Order logic with two variables: we provide an algorithm that decides if a given regular relation over finite words admits a uniformisation definable in FO2[<]. the paper provides a new representation of languages definable in FO2[<], which can be used for the decidability of other problems involving this formalism, e.g. the problem of separability of two regular languages by a language definable in FO2[<].

关键词： Uniformisation Question Two-Variable Fragment Synthesis

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First order complexity of finite random structures 24

First order complexity of finite random structures

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Demin, Danila Zhukovskii, Maksim Moscow Inst Phys & Technol Dolgoprudnyi Russia St Petersburg Univ St Petersburg Russia Univ Sheffield Sheffield S Yorkshire England

ISBN: (纸本)9798400706608

For a sequence of random structures with n-element domains over a relational signature, we define its FO complexity as a certain subset in the Banach space l infinity/c(0). the well-known FO zero-one law and FO convergence law correspond to FO complexities equal to {0, 1} and a subset of R, respectively. We present a hierarchy of FO complexity classes, introduce a stochastic FO reduction that allows to transfer complexity results between different random structures, and deduce using this tool several new logical limit laws for binomial random structures. Finally, we introduce a conditional distribution on graphs, subject to a FO sentence f, that generalises certain well-known random graph models, show instances of this distribution for every complexity class, and prove that the set of all f validating 0-1 law is not recursively enumerable.

关键词： random structures first order logic logical limit laws zero-one laws random graphs logical complexity recursively enumerable languages

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A Nominal Approach to Probabilistic Separation logic 24

A Nominal Approach to Probabilistic Separation Logic

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Li, John M. Aytac, Jon Johnson-Freyd, Philip Ahmed, Amal Holtzen, Steven Northeastern Univ Boston MA 02115 USA Sandia Natl Labs Livermore CA USA

ISBN: (纸本)9798400706608

Currently, there is a gap between the tools used by probability theorists and those used in formal reasoning about probabilistic programs. On the one hand, a probability theorist decomposes probabilistic state along the simple and natural product of probability spaces. On the other hand, recently developed probabilistic separation logics decompose state via relatively unfamiliar measure-theoretic constructions for computing unions of sigma-algebras and probability measures. We bridge the gap between these two perspectives by showing that these two methods of decomposition are equivalent up to a suitable equivalence of categories. Our main result is a probabilistic analog of the classic equivalence between the category of nominal sets and the Schanuel topos. through this equivalence, we validate design decisions in prior work on probabilistic separation logic and create new connections to nominal-setlike models of probability.

关键词： computer circuits

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A Characterisation theorem for Two-Way Bisimulation-Invariant Monadic Least Fixpoint logic Over Finite Structures 24

A Characterisation Theorem for Two-Way Bisimulation-Invarian...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Pflueger, Maximilian Marti, Johannes Kostylev, Egor V. Univ Oxford Oxford England Univ Zurich Zurich Switzerland Univ Oslo Oslo Norway

ISBN: (纸本)9798400706608

A seminal theorem by van Benthem characterises the bisimulation-invariant fragment of First Order logic (FOL) in terms of Modal logic. Similarly, Janin and Walukiewicz have shown that the bisimulation-invariant fragment of Monadic Second Order logic (MSO) corresponds precisely to the (modal) mu-calculus. Notably, neither argument immediately carries over when only considering finite structures. In the case of FOL, Rosen provided an alternative proof, which also works over finite structures. However, such characterisations for any logic more expressive than FOL over finite structures have remained long-standing open problems. In this paper, we prove such a characterisation for parameter-free Monadic Least Fixpoint logic, a well-known logic in between FOL and MSO. In particular, we show that, over finite structures, every two-way bisimulation-invariant formula in this logic is equivalent to a formula in the two-way mu-calculus and vice versa.

关键词： monadic least fixpoint logic bisimulation mu-calculus

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Decidability of Quasi-Dense Modal logics 24

Decidability of Quasi-Dense Modal Logics

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Ostropolski-Nalewaja, Piotr Lyon, Tim S. Tech Univ Dresden Dresden Germany Univ Wroclaw Wroclaw Poland

ISBN: (纸本)9798400706608

the decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form lozenge(k)p -> lozenge(n)p, has remained a long-standing open problem. In this paper, we make significant progress toward solving this problem and show that decidability holds for a large subclass of these logics, namely, for quasi-dense logics. Such logics are extensions of K with modal reduction axioms such that 0 logics consisting of disjunctive existential rules, which are first-order formulae typically used to specify ontologies in the context of database theory. We show that such proof systems can be used to generate proofs and models of modal formulae, and provide an intricate model-theoretic argument showing that such generated models can be encoded as finite objects called templates. By enumerating templates of bound size, we obtain an EXPSPACE decision procedure as a consequence.

关键词： Chase Decidability Existential rule Kripke model Modal logic Modal reduction principle Model theory Quasi-density axiom

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An expressively complete local past propositional dynamic logic over Mazurkiewicz traces and its applications 39

An expressively complete local past propositional dynamic lo...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Adsul, Bharat Gastin, Paul Kulkarni, Shantanu Weil, Pascal Indian Inst Technol Mumbai India Univ Paris Saclay ENS Paris Saclay CNRS LMF F-91190 Gif Sur Yvette France CNRS ReLaX IRL 2000 Siruseri India Univ Bordeaux LaBRI CNRS UMR 5800 F-33400 Talence France

ISBN: (纸本)9798400706608

We propose a local, past-oriented fragment of propositional dynamic logic to reason about concurrent scenarios modelled as Mazurkiewicz traces, and prove it to be expressively complete with respect to regular trace languages. Because of locality, specifications in this logic are efficiently translated into asynchronous automata, in a way that reflects the structure of formulas. In particular, we obtain a new proof of Zielonka's fundamental theorem and we prove that any regular trace language can be implemented by a cascade product of localized asynchronous automata, which essentially operate on a single process. these results refine earlier results by Adsul et al. which involved a larger fragment of past propositional dynamic logic and used Mukund and Sohoni's gossip automaton. Our new results avoid using this automaton, or Zielonka's timestamping mechanism and, in particular, they show how to implement a gossip automaton as a cascade product.

关键词： Mazurkiewicz traces propositional dynamic logic regular trace languages expressive completeness asynchronous automata cascade product Krohn Rhodes theorem Zielonka's theorem Gossip automaton

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Non-Elementary Compression of First-Order Proofs in Deep Inference Using Epsilon-Terms 39

Non-Elementary Compression of First-Order Proofs in Deep Inf...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Allett, Cameron Univ Bath Bath England

ISBN: (纸本)9798400706608

I introduce the falsifier calculus, a new deep-inference proof system for first-order predicate logic in the language of Hilbert's epsilon-calculus. It uses a new inference rule, the falsifier rule, to introduce epsilon-terms into a proof, distinct from the critical axioms of the traditional epsilon-calculus. the falsifier rule is a generalisation of one of the quantifier-shifts, inference rules for shifting quantifiers inside and outside of formulae. Like the epsilon-calculus and proof systems which include quantifier-shifts, the falsifier calculus admits non-elementarily shorter cut-free proofs of certain first-order theorems than the sequent calculus. Analogous to the way in which Herbrand's theorem decomposes a proof into a first-order and a propositional part, connected by a Herbrand disjunction as an intermediate formula, I prove a decomposition theorem for the falsifier calculus which gives rise to a new notion of intermediate formula in the epsilon-calculus, falsifier disjunctions. I then prove that certain first-order theorems admit non-elementarily smaller falsifier disjunctions than Herbrand disjunctions.

关键词： deep inference epsilon-calculus Herbrand's theorem first-order logic

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Model Checking Disjoint-Paths logic on Topological-Minor-Free Graph Classes 24

Model Checking Disjoint-Paths Logic on Topological-Minor-Fre...

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Schirrmacher, Nicole Siebertz, Sebastian Stamoulis, Giannos thilikos, Dimitrios M. Vigny, Alexandre Bremen Univ Bremen Germany Univ Warsaw Warsaw Poland Univ Montpellier LIRMM CNRS Montpellier France Univ Clermont Auvergne Clermont Ferrand France

ISBN: (纸本)9798400706608

Disjoint-paths logic, denoted FO+ DP, extends first-order logic (FO) with atomic predicates dp(k) [(x(1),y(1)),..., (s(k),y(k))], expressing the existence of internally vertex-disjoint paths between x(i) and y(i), for 1 <= i <= k. We prove that for every graph class excluding some fixed graph as a topological minor, the model checking problem for FO+DP is fixed-parameter tractable. this extends the model checking algorithm of Golovach et al. [SODA 2023] for FO+DP for minor-closed graph classes. It also essentially settles the question of tractable model checking for this logic on subgraph-closed classes, since the problem is hard on subgraph-closed classes not excluding a topological minor (assuming a further mild condition on efficiency of encoding).

关键词： Model checking Topological-minor-free graphs First-order logic Disjoint paths Parameterized algorithms

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the Relational Machine Calculus 39

The Relational Machine Calculus

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39th annual acm/ieee symposium on logic in computer science (LICS)

作者： Barrett, Chris Castle, Daniel Heijltjes, Willem Univ Oxford Oxford England Univ Bath Bath England

ISBN: (纸本)9798400706608

this paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. the RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its standard call-byname stack machine in two directions. One, "locations", introduces multiple stacks, which enable effect operators to be encoded into the abstraction and application constructs. the second, "sequencing", introduces the imperative notions of "skip" and "sequence", similar to kappa-calculus and concatenative programming languages. the key observation of the RMC is that the first-order fragment of the FMC exhibits a latent duality which, given a simple decomposition of the relevant constructors, can be concretely expressed as an involution on syntax. Semantically, this gives rise to a sound and complete calculus for string diagrams of Frobenius monoids. We consider unification as the corresponding symmetric generalization of beta-reduction. By further including standard operators of Kleene algebra, the RMC embeds a range of computational models: the kappa-calculus, logic programming, automata, Interaction Nets, and Petri Nets, among others. these embeddings preserve operational semantics, which for the RMC is again given by a generalization of the standard stack machine for the lambda-calculus. the equational theory of the RMC (which supports reasoning about its operational semantics) is conservative over both the first-order lambda-calculus and Kleene algebra, and can be oriented to give a confluent reduction relation.

关键词： lambda-calculus Kleene algebra logic programming reversible programming non-determinism hypergraph category Krivine abstract machine categorical semantics operational semantics

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