ACM Transactions on Computational Logic最新文献_第9页

Logics for Temporal Information Systems in Rough Set Theory 粗糙集理论中时态信息系统的逻辑

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2022-07-19 DOI: 10.1145/3549075

Md. Aquil Khan, M. Banerjee, Sibsankar Panda

引用次数: 0

Unifying Operational Weak Memory Verification: An Axiomatic Approach 统一操作弱记忆验证：一种公理化方法

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2022-06-27 DOI: 10.1145/3545117

Simon Doherty, Sadegh Dalvandi, Brijesh Dongol, H. Wehrheim

引用次数: 6

A Category Theoretic View of Contextual Types: From Simple Types to Dependent Types 语境类型的范畴论视角：从简单类型到依赖类型

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2022-06-06 DOI: 10.1145/3545115

Jason Z. S. Hu, B. Pientka, Ulrich Schöpp

{"title":"A Category Theoretic View of Contextual Types: From Simple Types to Dependent Types","authors":"Jason Z. S. Hu, B. Pientka, Ulrich Schöpp","doi":"10.1145/3545115","DOIUrl":"https://doi.org/10.1145/3545115","url":null,"abstract":"We describe the categorical semantics for a simply typed variant and a simplified dependently typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent higher-order abstract syntax (HOAS) trees and the strong function space that describes (recursive) computations about them. What makes Cocon different from standard type theories is the presence of first-class contexts and contextual objects to describe syntax trees that are closed with respect to a given context of assumptions. Following M. Hofmann’s work, we use a presheaf model to characterise HOAS trees. Surprisingly, this model already provides the necessary structure to also model Cocon. In particular, we can capture the contextual objects of Cocon using a comonad ♭ that restricts presheaves to their closed elements. This gives a simple semantic characterisation of the invariants of contextual types (e.g. substitution invariance) and identifies Cocon as a type-theoretic syntax of presheaf models. We further extend this characterisation to dependent types using categories with families and show that we can model a fragment of Cocon without recursor in the Fitch-style dependent modal type theory presented by Birkedal et al.","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"23 1","pages":"1 - 36"},"PeriodicalIF":0.5,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45776127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

A Generalized Realizability and Intuitionistic Logic 广义可实现性与直觉逻辑

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2022-05-17 DOI: 10.1145/3565367

A. Y. Konovalov

引用次数: 1

First-order Logic with Connectivity Operators 带连通算子的一阶逻辑

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2021-07-13 DOI: 10.1145/3595922

Nicole Schirrmacher, S. Siebertz, Alexandre Vigny

{"title":"First-order Logic with Connectivity Operators","authors":"Nicole Schirrmacher, S. Siebertz, Alexandre Vigny","doi":"10.1145/3595922","DOIUrl":"https://doi.org/10.1145/3595922","url":null,"abstract":"First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem parameterized by solution size. However, FO cannot express the very simple algorithmic question whether two vertices are connected. We enrich FO with connectivity predicates that are tailored to express algorithmic graph problems that are commonly studied in parameterized algorithmics. By adding the atomic predicates connk(x,y,z_1,..., zk) that hold true in a graph if there exists a path between (the valuations of) x and y after (the valuations of) z1,..., zk have been deleted, we obtain separator logic FO + conn. We show that separator logic can express many interesting problems, such as the feedback vertex set problem and elimination distance problems to first-order definable classes. Denote by FO + connk the fragment of separator logic that is restricted to connectivity predicates with at most k + 2 variables (that is, at most k deletions), we show that FO + connk + 1 is strictly more expressive than FO + connk for all k ≥ 0. We then study the limitations of separator logic and prove that it cannot express planarity, and, in particular, not the disjoint paths problem. We obtain the stronger disjoint-paths logic FO + DP by adding the atomic predicates disjoint-pathsk[(x1, y1),..., (xk, yk) that evaluate to true if there are internally vertex-disjoint paths between (the valuations of) xi and yi for all 1 ≤ i ≤ k. Disjoint-paths logic can express the disjoint paths problem, the problem of (topological) minor containment, the problem of hitting (topological) minors, and many more. Again, we show that the fragments FO + DPk that use predicates for at most k disjoint paths form a strict hierarchy of expressiveness. Finally, we compare the expressive power of the new logics with that of transitive-closure logics and monadic second-order logic.","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"24 1","pages":"1 - 23"},"PeriodicalIF":0.5,"publicationDate":"2021-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48028297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

The Complexity of Quantified Constraints: Collapsibility, Switchability, and the Algebraic Formulation 量化约束的复杂性:可折叠性、可切换性和代数公式

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2021-06-24 DOI: 10.1145/3568397

C. Carvalho, Florent R. Madelaine, B. Martin, Dmitriy Zhuk

{"title":"The Complexity of Quantified Constraints: Collapsibility, Switchability, and the Algebraic Formulation","authors":"C. Carvalho, Florent R. Madelaine, B. Martin, Dmitriy Zhuk","doi":"10.1145/3568397","DOIUrl":"https://doi.org/10.1145/3568397","url":null,"abstract":"Let 𝔸 be an idempotent algebra on a finite domain. By mediating between results of Chen [1] and Zhuk [2], we argue that if 𝔸 satisfies the polynomially generated powers property (PGP) and ℬ is a constraint language invariant under 𝔸 (i.e., in Inv(𝔸)), then QCSP ℬ is in NP. In doing this, we study the special forms of PGP, switchability, and collapsibility, in detail, both algebraically and logically, addressing various questions such as decidability on the way. We then prove a complexity-theoretic converse in the case of infinite constraint languages encoded in propositional logic, that if Inv}(𝔸) satisfies the exponentially generated powers property (EGP), then QCSP (Inv(𝔸)) is co-NP-hard. Since Zhuk proved that only PGP and EGP are possible, we derive a full dichotomy for the QCSP, justifying what we term the Revised Chen Conjecture. This result becomes more significant now that the original Chen Conjecture (see [3]) is known to be false [4]. Switchability was introduced by Chen [1] as a generalization of the already-known collapsibility [5]. There, an algebra 𝔸 :=({ 0,1,2};r) was given that is switchable and not collapsible. We prove that, for all finite subsets Δ of Inv (𝔸 A), Pol (Δ) is collapsible. The significance of this is that, for QCSP on finite structures, it is still possible all QCSP tractability (in NP) explained by switchability is already explained by collapsibility. At least, no counterexample is known to this.","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"24 1","pages":"1 - 26"},"PeriodicalIF":0.5,"publicationDate":"2021-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46187472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Expressiveness and Nash Equilibrium in Iterated Boolean Games 迭代布尔对策中的表达性与纳什均衡

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2021-06-08 DOI: 10.1145/3439900

GutiérrezJulián, HarrensteinPaul, PerelliGiuseppe, WooldridgeMichael

引用次数: 3

A Subatomic Proof System for Decision Trees 决策树的亚原子证明系统

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2021-05-04 DOI: 10.1145/3545116

Chris Barrett, Alessio Guglielmi

{"title":"A Subatomic Proof System for Decision Trees","authors":"Chris Barrett, Alessio Guglielmi","doi":"10.1145/3545116","DOIUrl":"https://doi.org/10.1145/3545116","url":null,"abstract":"We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is proof-theoretical naturalness: The system consists of all and only the inference rules generated by the single, simple, linear scheme of the recently introduced subatomic logic. Thanks to this regularity, cuts are eliminated via a natural construction. The second reason is that the system generates efficient proofs. Indeed, we show that a certain class of tautologies due to Statman, which cannot have better than exponential cut-free proofs in the sequent calculus, have polynomial cut-free proofs in our system. We achieve this by using the same construction that we use for cut elimination. In summary, by expanding the language of propositional logic, we make its proof theory more regular and generate more proofs, some of which are very efficient. That design is made possible by considering atoms as superpositions of their truth values, which are connected by self-dual, non-commutative connectives. A proof can then be projected via each atom into two proofs, one for each truth value, without a need for cuts. Those projections are semantically natural and are at the heart of the constructions in this article. To accommodate self-dual non-commutativity, we compose proofs in deep inference.","PeriodicalId":50916,"journal":{"name":"ACM Transactions on Computational Logic","volume":"23 1","pages":"1 - 25"},"PeriodicalIF":0.5,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45735718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Good-for-Game QPTL: An Alternating Hodges Semantics 适合游戏的QPTL:一个交替的Hodges语义

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2021-04-13 DOI: 10.1145/3565365

Dylan Bellier, M. Benerecetti, Dario Della Monica, F. Mogavero

引用次数: 3

The Intersection of Algorithmically Random Closed Sets and Effective Dimension 算法随机闭集与有效维数的交集

IF 0.5 4区数学

ACM Transactions on Computational Logic Pub Date : 2021-03-05 DOI: 10.1145/3545114

Adam Case, Christopher P. Porter

引用次数: 0