J. Log. Comput.最新文献_第9页

Logics based on linear orders of contaminating values 基于污染值的线性顺序的逻辑

J. Log. Comput. Pub Date : 2019-09-12 DOI: 10.1093/LOGCOM/EXZ009

R. Ciuni, T. M. Ferguson, D. Szmuc

引用次数: 26

Substituting strict equivalents 替换严格的等价物

J. Log. Comput. Pub Date : 2019-09-12 DOI: 10.1093/LOGCOM/EXZ002

David B. Martens

引用次数: 1

The fixed point property and a technique to harness double fixed point combinators 不动点的性质及利用双不动点组合子的技术

J. Log. Comput. Pub Date : 2019-07-10 DOI: 10.1093/LOGCOM/EXZ013

Giulio Manzonetto, A. Polonsky, A. Saurin, J. Simonsen

{"title":"The fixed point property and a technique to harness double fixed point combinators","authors":"Giulio Manzonetto, A. Polonsky, A. Saurin, J. Simonsen","doi":"10.1093/LOGCOM/EXZ013","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXZ013","url":null,"abstract":"\u0000 \u0000 \u0000 The ${lambda }$-calculus enjoys the property that each ${lambda }$-term has at least one fixed point, which is due to the existence of a fixed point combinator. It is unknown whether it enjoys the ‘fixed point property’ stating that each ${lambda }$-term has either one or infinitely many pairwise distinct fixed points. We show that the fixed point property holds when considering possibly open fixed points. The problem of counting fixed points in the closed setting remains open, but we provide sufficient conditions for a ${lambda }$-term to have either one or infinitely many fixed points. In the main result of this paper we prove that in every sensible ${lambda }$-theory there exists a ${lambda }$-term that violates the fixed point property.\u0000 \u0000 \u0000 \u0000 We then study the open problem concerning the existence of a double fixed point combinator and propose a proof technique that could lead towards a negative solution. We consider interpretations of the ${lambda } {mathtt{Y}}$-calculus into the ${lambda }$-calculus together with two reduction extension properties, whose validity would entail the non-existence of any double fixed point combinators. We conjecture that both properties hold when typed ${lambda } {mathtt{Y}}$-terms are interpreted by arbitrary fixed point combinators. We prove reduction extension property I for a large class of fixed point combinators.\u0000 \u0000 \u0000 \u0000 Finally, we prove that the ${lambda }{mathtt{Y}}$-theory generated by the equation characterizing double fixed point combinators is a conservative extension of the ${lambda }$-calculus.\u0000","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121929833","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: 6

Towards automated reasoning in Herbrand structures 走向Herbrand结构中的自动推理

J. Log. Comput. Pub Date : 2019-06-03 DOI: 10.1093/LOGCOM/EXZ011

L. Cohen, R. Rowe, Yoni Zohar

{"title":"Towards automated reasoning in Herbrand structures","authors":"L. Cohen, R. Rowe, Yoni Zohar","doi":"10.1093/LOGCOM/EXZ011","DOIUrl":"https://doi.org/10.1093/LOGCOM/EXZ011","url":null,"abstract":"\u0000 Herbrand structures have the advantage, computationally speaking, of being guided by the definability of all elements in them. A salient feature of the logics induced by them is that they internally exhibit the induction scheme, thus providing a congenial, computationally oriented framework for formal inductive reasoning. Nonetheless, their enhanced expressivity renders any effective proof system for them incomplete. Furthermore, the fact that they are not compact poses yet another proof-theoretic challenge. This paper offers several layers for coping with the inherent incompleteness and non-compactness of these logics. First, two types of infinitary proof system are introduced—one of infinite width and one of infinite height—which manipulate infinite sequents and are sound and complete for the intended semantics. The restriction of these systems to finite sequents induces a completeness result for finite entailments. Then, in search of effectiveness, two finite approximations of these systems are presented and explored. Interestingly, the approximation of the infinite-width system via an explicit induction scheme turns out to be weaker than the effective cyclic fragment of the infinite-height system.","PeriodicalId":398763,"journal":{"name":"J. Log. Comput.","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114112302","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

A bilateral Hilbert-style investigation of 2-intuitionistic logic 双直觉逻辑的双边hilbert式研究

J. Log. Comput. Pub Date : 2019-05-30 DOI: 10.1093/LOGCOM/EXZ010

S. Drobyshevich

引用次数: 6

Taking the path computably traveled 取可计算的路径

J. Log. Comput. Pub Date : 2019-05-29 DOI: 10.1093/LOGCOM/EXZ016

Johanna N. Y. Franklin, Daniel Turetsky

引用次数: 7

In defence of deontic diversity 捍卫宗教多样性

J. Log. Comput. Pub Date : 2019-04-17 DOI: 10.1093/LOGCOM/EXV057

S. Hansson