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Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science最新文献

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Syntax and Semantics of Quantitative Type Theory 数量类型理论的句法和语义
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209189
R. Atkey
{"title":"Syntax and Semantics of Quantitative Type Theory","authors":"R. Atkey","doi":"10.1145/3209108.3209189","DOIUrl":"https://doi.org/10.1145/3209108.3209189","url":null,"abstract":"We present Quantitative Type Theory, a Type Theory that records usage information for each variable in a judgement, based on a previous system by McBride. The usage information is used to give a realizability semantics using a variant of Linear Combinatory Algebras, refining the usual realizability semantics of Type Theory by accurately tracking resource behaviour. We define the semantics in terms of Quantitative Categories with Families, a novel extension of Categories with Families for modelling resource sensitive type theories.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132099475","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: 86
Around Classical and Intuitionistic Linear Logics 围绕经典和直觉线性逻辑
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209132
Olivier Laurent
{"title":"Around Classical and Intuitionistic Linear Logics","authors":"Olivier Laurent","doi":"10.1145/3209108.3209132","DOIUrl":"https://doi.org/10.1145/3209108.3209132","url":null,"abstract":"We revisit many aspects of the syntactic relations between (variants of) classical linear logic (LL) and (variants of) intuitionistic linear logic (ILL) in the propositional setting. On the one hand, we study different (parametric) \"negative\" translations from LL to ILL: their expressiveness, the relations with extensions of LL and their use in the proof theory of LL (cut elimination and focusing). In particular, this bridges the intuitionistic restriction on sequents (at most one conclusion) and the focusing property of linear logic. On the other hand, we generalise the known partial results about conservativity of LL over ILL, leading for example to a conservativity proof for LL over tensor logic (TL).","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115548622","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: 7
Species, Profunctors and Taylor Expansion Weighted by SMCC: A Unified Framework for Modelling Nondeterministic, Probabilistic and Quantum Programs SMCC加权的种、泛函子和泰勒展开:非确定性、概率性和量子程序建模的统一框架
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209157
Takeshi Tsukada, Kazuyuki Asada, C. Ong
{"title":"Species, Profunctors and Taylor Expansion Weighted by SMCC: A Unified Framework for Modelling Nondeterministic, Probabilistic and Quantum Programs","authors":"Takeshi Tsukada, Kazuyuki Asada, C. Ong","doi":"10.1145/3209108.3209157","DOIUrl":"https://doi.org/10.1145/3209108.3209157","url":null,"abstract":"Motivated by a tight connection between Joyal's combinatorial species and quantitative models of linear logic, this paper introduces weighted generalised species (or weighted profunctors), where weights are morphisms of a given symmetric monoidal closed category (SMCC). For each SMCC W, we show that the category of W-weighted profunctors is a Lafont category, a categorical model of linear logic with exponential. As a model of programming languages, the construction of this paper gives a unified framework that induces adequate models of nondeterministic, probabilistic, algebraic and quantum programming languages by an appropriate choice of the weight SMCC.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124652583","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: 17
Computability Beyond Church-Turing via Choice Sequences 通过选择序列超越Church-Turing的可计算性
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209200
M. Bickford, L. Cohen, R. Constable, Vincent Rahli
{"title":"Computability Beyond Church-Turing via Choice Sequences","authors":"M. Bickford, L. Cohen, R. Constable, Vincent Rahli","doi":"10.1145/3209108.3209200","DOIUrl":"https://doi.org/10.1145/3209108.3209200","url":null,"abstract":"Church-Turing computability was extended by Brouwer who considered non-lawlike computability in the form of free choice sequences. Those are essentially unbounded sequences whose elements are chosen freely, i.e. not subject to any law. In this work we develop a new type theory BITT, which is an extension of the type theory of the Nuprl proof assistant, that embeds the notion of choice sequences. Supporting the evolving, non-deterministic nature of these objects required major modifications to the underlying type theory. Even though the construction of a choice sequence is non-deterministic, once certain choices were made, they must remain consistent. To ensure this, BITT uses the underlying library as state and store choices as they are created. Another salient feature of BITT is that it uses a Beth-like semantics to account for the dynamic nature of choice sequences. We formally define BITT and use it to interpret and validate essential axioms governing choice sequences. These results provide a foundation for a fully intuitionistic version of Nuprl.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122048770","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: 16
Allegories: decidability and graph homomorphisms 寓言:可决性与图同态
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209172
D. Pous, Valeria Vignudelli
{"title":"Allegories: decidability and graph homomorphisms","authors":"D. Pous, Valeria Vignudelli","doi":"10.1145/3209108.3209172","DOIUrl":"https://doi.org/10.1145/3209108.3209172","url":null,"abstract":"Allegories were introduced by Freyd and Scedrov; they form a fragment of Tarski's calculus of relations. We show that their equational theory is decidable by characterising it in terms of a specific class of graph homomorphisms. We actually do so for an extension of allegories which we prove to be conservative: allegories with top. This makes it possible to exploit a correspondence between terms and K4-free graphs, for which isomorphisms were known to be finitely axiomatisable.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124486507","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: 7
Continuous Reasoning: Scaling the impact of formal methods 连续推理:扩展形式化方法的影响
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209109
P. O'Hearn
{"title":"Continuous Reasoning: Scaling the impact of formal methods","authors":"P. O'Hearn","doi":"10.1145/3209108.3209109","DOIUrl":"https://doi.org/10.1145/3209108.3209109","url":null,"abstract":"This paper describes work in continuous reasoning, where formal reasoning about a (changing) codebase is done in a fashion which mirrors the iterative, continuous model of software development that is increasingly practiced in industry. We suggest that advances in continuous reasoning will allow formal reasoning to scale to more programs, and more programmers. The paper describes the rationale for continuous reasoning, outlines some success cases from within industry, and proposes directions for work by the scientific community.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123067742","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: 64
Ribbon Tensorial Logic 带状张量逻辑
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209129
Paul-André Melliès
{"title":"Ribbon Tensorial Logic","authors":"Paul-André Melliès","doi":"10.1145/3209108.3209129","DOIUrl":"https://doi.org/10.1145/3209108.3209129","url":null,"abstract":"We introduce a topologically-aware version of tensorial logic, called ribbon tensorial logic. To every proof of the logic, we associate a ribbon tangle which tracks the flow of tensorial negations inside the proof. The translation is functorial: it is performed by exhibiting a correspondence between the notion of dialogue category in proof theory and the notion of ribbon category in knot theory. Our main result is that the translation is also faithful: two proofs are equal modulo the equational theory of ribbon tensorial logic if and only if the associated ribbon tangles are equal up to topological deformation. This \"proof-as-tangle\" theorem may be understood as a coherence theorem for balanced dialogue categories, and as a mathematical foundation for topological game semantics.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115793028","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: 7
LMSO: A Curry-Howard Approach to Church's Synthesis via Linear Logic LMSO:柯瑞-霍华德线性逻辑下的丘奇综合
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209195
P. Pradic, Colin Riba
{"title":"LMSO: A Curry-Howard Approach to Church's Synthesis via Linear Logic","authors":"P. Pradic, Colin Riba","doi":"10.1145/3209108.3209195","DOIUrl":"https://doi.org/10.1145/3209108.3209195","url":null,"abstract":"We propose LMSO, a proof system inspired from Linear Logic, as a proof-theoretical framework to extract finite-state stream transducers from linear-constructive proofs of omega-regular specifications. We advocate LMSO as a stepping stone toward semi-automatic approaches to Church's synthesis combining computer assisted proofs with automatic decisions procedures. LMSO is correct in the sense that it comes with an automata-based realizability model in which proofs are interpreted as finite-state stream transducers. It is moreover complete, in the sense that every solvable instance of Church's synthesis problem leads to a linear-constructive proof of the formula specifying the synthesis problem.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129602413","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: 7
The State Complexity of Alternating Automata 交变自动机的状态复杂性
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209167
Nathanaël Fijalkow
{"title":"The State Complexity of Alternating Automata","authors":"Nathanaël Fijalkow","doi":"10.1145/3209108.3209167","DOIUrl":"https://doi.org/10.1145/3209108.3209167","url":null,"abstract":"This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. We look at alternating automata as introduced by Chandra, Kozen and Stockmeyer: such machines run independent computations on the word and gather their answers through boolean combinations. We devise a lower bound technique relying on boundedly generated lattices of languages, and give two applications of this technique. The first is a hierarchy theorem, stating that there are languages of arbitrarily high polynomial alternating state complexity, and the second is a linear lower bound on the alternating state complexity of the prime numbers written in binary. This second result strengthens a result of Hartmanis and Shank from 1968, which implies an exponentially worse lower bound for the same model.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117110091","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: 4
Inner Models of Univalence 一体性的内部模型
Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science Pub Date : 2018-07-09 DOI: 10.1145/3209108.3209112
T. Coquand
{"title":"Inner Models of Univalence","authors":"T. Coquand","doi":"10.1145/3209108.3209112","DOIUrl":"https://doi.org/10.1145/3209108.3209112","url":null,"abstract":"We present a simple inner model construction for dependent type theory, which preserves univalence.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129308894","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: 0
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