2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献_第4页

First-Order Reasoning and Efficient Semi-Algebraic Proofs 一阶推理和有效的半代数证明

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-16 DOI: 10.1109/LICS52264.2021.9470546

Fedor Part, Neil Thapen, Iddo Tzameret

{"title":"First-Order Reasoning and Efficient Semi-Algebraic Proofs","authors":"Fedor Part, Neil Thapen, Iddo Tzameret","doi":"10.1109/LICS52264.2021.9470546","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470546","url":null,"abstract":"Semi-algebraic proof systems such as sum-of-squares (SoS) have attracted a lot of attention recently due to their relation to approximation algorithms [3]: constant degree semi-algebraic proofs lead to conjecturally optimal polynomial-time approximation algorithms for important NP-hard optimization problems (cf. [4]). Motivated by the need to allow a more streamlined and uniform framework for working with SoS proofs than the restrictive propositional level, we initiate a systematic first-order logical investigation into the kinds of reasoning possible in algebraic and semi-algebraic proof systems. Specifically, we develop first-order theories that capture in a precise manner constant degree algebraic and semi-algebraic proof systems: every statement of a certain form that is provable in our theories translates into a family of constant degree polynomial calculus or SoS refutations, respectively; and using a reflection principle, the converse also holds.This places algebraic and semi-algebraic proof systems in the established framework of bounded arithmetic, while providing theories corresponding to systems that vary quite substantially from the usual propositional-logic ones.We give examples of how our semi-algebraic theory proves statements such as the pigeonhole principle, we provide a separation between algebraic and semi-algebraic theories, and we describe initial attempts to go beyond these theories by introducing extensions that use the inequality symbol, identifying along the way which extensions lead outside the scope of constant degree SoS. Moreover, we prove new results for propositional proofs, and specifically extend Berkholz’s [7] dynamic-by-static simulation of polynomial calculus (PC) by SoS to PC with the radical rule.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116649403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

The Laplace Mechanism has optimal utility for differential privacy over continuous queries 拉普拉斯机制对于连续查询的差分隐私具有最佳效用

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-15 DOI: 10.1109/LICS52264.2021.9470718

Natasha Fernandes, Annabelle McIver, Carroll Morgan

引用次数: 13

Demonic Lattices and Semilattices in Relational Semigroups with Ordinary Composition 具有普通复合的关系半群中的魔鬼格和半格

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-14 DOI: 10.1109/LICS52264.2021.9470509

R. Hirsch, Jas Semrl

引用次数: 2

From Multisets over Distributions to Distributions over Multisets 从分布上的多集到分布上的多集

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-14 DOI: 10.1109/LICS52264.2021.9470678

B. Jacobs

{"title":"From Multisets over Distributions to Distributions over Multisets","authors":"B. Jacobs","doi":"10.1109/LICS52264.2021.9470678","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470678","url":null,"abstract":"A well-known challenge in the semantics of programming languages is how to combine non-determinism and probability. At a technical level, the problem arises from the fact that there is a no distributive law between the powerset monad and the distribution monad — as noticed some twenty years ago by Plotkin. More recently, it has become clear that there is a distributive law of the multiset monad over the distribution monad. This article elaborates the details of this distributivity and shows that there is a rich underlying theory relating multisets and probability distributions. It is shown that the new distributive law, called parallel multinomial law, can be defined in (at least) four equivalent ways. It involves putting multinomial distributions in parallel and commutes with hypergeometric distributions. Further, it is shown that this distributive law commutes with a new form of zipping for multisets. Abstractly, this can be described in terms of monoidal structure for a fixed-size multiset functor, when lifted to the Kleisli category of the distribution monad. Concretely, an application of the theory to sampling semantics is included.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"307 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122728903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 18

Asynchronous Template Games and the Gray Tensor Product of 2-Categories 异步模板游戏与两类灰色张量积

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-11 DOI: 10.1109/LICS52264.2021.9470758

Paul-André Melliès

{"title":"Asynchronous Template Games and the Gray Tensor Product of 2-Categories","authors":"Paul-André Melliès","doi":"10.1109/LICS52264.2021.9470758","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470758","url":null,"abstract":"In his recent and exploratory work on template games and linear logic, Melliès defines sequential and concurrent games as categories with positions as objects and trajectories as morphisms, labelled by a specific synchronization template. In the present paper, we bring the idea one dimension higher and advocate that template games should not be just defined as 1-dimensional categories but as 2-dimensional categories of positions, trajectories and reshufflings (or reschedulings) as 2-cells. In order to achieve the purpose, we take seriously the parallel between asynchrony in concurrency and the Gray tensor product of 2-categories. One technical difficulty on the way is that the category $mathbb{S} = 2$-Cat of small 2-categories equipped with the Gray tensor product is monoidal, and not cartesian. This prompts us to extend the framework of template games originally formulated by Melliès in a category $mathbb{S}$ with finite limits, and to upgrade it in the style of Aguiar’s work on quantum groups to the more general situation of a monoidal category $mathbb{S}$ with coreflexive equalizers, preserved by the tensor product componentwise. We construct in this way an asynchronous template game semantics of multiplicative additive linear logic (MALL) where every formula and every proof is interpreted as a labelled 2-category equipped, respectively, with the structure of Gray comonoid for asynchronous template games, and of Gray bicomodule for asynchronous strategies.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114202044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Lovász-Type Theorems and Game Comonads Lovász-Type定理和游戏共性

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-07 DOI: 10.1109/LICS52264.2021.9470609

A. Dawar, Tomás Jakl, Luca Reggio

引用次数: 25

Gödel-McKinsey-Tarski and Blok-Esakia for Heyting-Lewis Implication

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-05 DOI: 10.1109/LICS52264.2021.9470508

Jim de Groot, Tadeusz Litak, D. Pattinson

{"title":"Gödel-McKinsey-Tarski and Blok-Esakia for Heyting-Lewis Implication","authors":"Jim de Groot, Tadeusz Litak, D. Pattinson","doi":"10.1109/LICS52264.2021.9470508","DOIUrl":"https://doi.org/10.1109/LICS52264.2021.9470508","url":null,"abstract":"Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict implication connective that satisfies the constructive counterparts of axioms for strict implication provable in classical modal logics. Variants of this logic are surprisingly widespread: they appear as Curry-Howard correspondents of (simple type theory extended with) Haskell-style arrows, in preservativity logic of Heyting arithmetic, in the proof theory of guarded (co)recursion, and in the generalization of intuitionistic epistemic logic.Heyting-Lewis Logic can be interpreted in intuitionistic Kripke frames extended with a binary relation to account for strict implication. We use this semantics to define descriptive frames (generalisations of Esakia spaces), and establish a categorical duality between the algebraic interpretation and the frame semantics. We then adapt a transformation by Wolter and Zakharyaschev to translate Heyting-Lewis Logic to classical modal logic with two unary operators. This allows us to prove a Blok-Esakia theorem that we then use to obtain both known and new canonicity and correspondence theorems, and the finite model property and decidability for a large family of Heyting-Lewis logics.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123826014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

In search of lost time: Axiomatising parallel composition in process algebras 寻找失去的时间:过程代数中平行组合的公理化

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-05-03 DOI: 10.1109/LICS52264.2021.9470526

L. Aceto, Elli Anastasiadi, Valentina Castiglioni, A. Ingólfsdóttir, B. Luttik

引用次数: 2

Multi-Structural Games and Number of Quantifiers 多结构博弈与量词数量

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-04-30 DOI: 10.1109/LICS52264.2021.9470756

Ronald Fagin, J. Lenchner, Kenneth W. Regan, Nikhil Vyas

引用次数: 5

Some constructive variants of S4 with the finite model property 具有有限模型性质的S4的构造型

2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2021-04-30 DOI: 10.1109/LICS52264.2021.9470643

P. Balbiani, Martín Diéguez, David Fern'andez-Duque

引用次数: 8