2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)最新文献_第2页

Equivalence of inductive definitions and cyclic proofs under arithmetic 归纳定义的等价性及算术下的循环证明

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005114

S. Berardi, M. Tatsuta

{"title":"Equivalence of inductive definitions and cyclic proofs under arithmetic","authors":"S. Berardi, M. Tatsuta","doi":"10.1109/LICS.2017.8005114","DOIUrl":"https://doi.org/10.1109/LICS.2017.8005114","url":null,"abstract":"A cyclic proof system, called CLKID-omega, gives us another way of representing inductive definitions and efficient proof search. The 2011 paper by Brotherston and Simpson showed that the provability of CLKID-omega includes the provability of the classical system of Martin-Lof's inductive definitions, called LKID, and conjectured the equivalence. By this year the equivalence has been left an open question. In general, the conjecture was proved to be false in FoSSaCS 2017 paper by Berardi and Tatsuta. However, if we restrict both systems to only the natural number inductive predicate and add Peano arithmetic to both systems, the conjecture was proved to be true in FoSSaCS 2017 paper by Simpson. This paper shows that if we add arithmetic to both systems, they become equivalent, namely, the conjecture holds. The result of this paper includes that of the paper by Simpson as a special case. In order to construct a proof of LKID for a given cyclic proof, this paper shows every bud in the cyclic proof is provable in LKID, by cutting the cyclic proof into subproofs such that in each subproof the conclusion is a companion and the assumptions are buds. The global trace condition gives some induction principle, by using an extension of Podelski-Rybalchenko termination theorem from well-foundedness to induction schema. In order to prove this extension, this paper also shows that infinite Ramsey theorem is formalizable in Peano arithmetic.","PeriodicalId":313950,"journal":{"name":"2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133722902","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: 29

Fully abstract encodings of λ-calculus in HOcore through abstract machines 利用抽象机实现HOcore中λ-微积分的全抽象编码

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005118

Małgorzata Biernacka, Dariusz Biernacki, Sergueï Lenglet, Piotr Polesiuk, D. Pous, Alan Schmitt

引用次数: 3

Foundational nonuniform (Co)datatypes for higher-order logic 高阶逻辑的基本非一致(Co)数据类型

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005071

J. Blanchette, Fabian Meier, A. Popescu, Dmitriy Traytel

引用次数: 15

Definability of summation problems for Abelian groups and semigroups 阿贝尔群与半群求和问题的可定义性

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005082

Faried Abu Zaid, A. Dawar, E. Grädel, Wied Pakusa

引用次数: 3

Bar induction: The good, the bad, and the ugly 酒吧归纳:好的，坏的和丑陋的

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005074

Vincent Rahli, M. Bickford, R. Constable

引用次数: 11

On shift-invariant maximal filters and hormonal cellular automata 移不变最大滤波器与激素元胞自动机

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005145

J. Cervelle, Grégory Lafitte

引用次数: 2

Foundation for a series of efficient simulation algorithms 为一系列高效的仿真算法奠定基础

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005069

Gérard Cécé

引用次数: 11

On the extension of computable real functions 关于可计算实函数的扩展

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005067

M. Hoyrup, W. Gomaa

引用次数: 0

Higher-order parity automata 高阶奇偶自动机

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005077

Paul-André Melliès

引用次数: 14

Differentiation in logical form 逻辑形式的微分

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) Pub Date : 2017-06-20 DOI: 10.1109/LICS.2017.8005143

A. Edalat, Mehrdad Maleki

{"title":"Differentiation in logical form","authors":"A. Edalat, Mehrdad Maleki","doi":"10.1109/LICS.2017.8005143","DOIUrl":"https://doi.org/10.1109/LICS.2017.8005143","url":null,"abstract":"We introduce a logical theory of differentiation for a real-valued function on a finite dimensional real Euclidean space. A real-valued continuous function is represented by a localic approximable mapping between two semi-strong proximity lattices, representing the two stably locally compact Euclidean spaces for the domain and the range of the function. Similarly, the Clarke subgradient, equivalently the L-derivative, of a locally Lipschitz map, which is non-empty, compact and convex valued, is represented by an approximable mapping. Approximable mappings of the latter type form a bounded complete domain isomorphic with the function space of Scott continuous functions of a real variable into the domain of non-empty compact and convex subsets of the finite dimensional Euclidean space partially ordered with reverse inclusion. Corresponding to the notion of a single-tie of a locally Lipschitz function, used to derive the domain-theoretic L-derivative of the function, we introduce the dual notion of a single-knot of approximable mappings which gives rise to Lipschitzian approximable mappings. We then develop the notion of a strong single-tie and that of a strong knot leading to a Stone duality result for locally Lipschitz maps and Lipschitzian approximable mappings. The strong single-knots, in which a Lipschitzian approximable mapping belongs, are employed to define the Lipschitzian derivative of the approximable mapping. The latter is dual to the Clarke subgradient of the corresponding locally Lipschitz map defined domain-theoretically using strong single-ties. A stricter notion of strong single-knots is subsequently developed which captures approximable mappings of continuously differentiable maps providing a gradient Stone duality for these maps. Finally, we derive a calculus for Lipschitzian derivative of approximable mapping for some basic constructors and show that it is dual to the calculus satisfied by the Clarke subgradient.","PeriodicalId":313950,"journal":{"name":"2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"189 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133598507","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