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Logic Journal of the IGPL最新文献

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John Crossley: A life intellectual 约翰·克罗斯利:一生的知识分子
4区 数学
Logic Journal of the IGPL Pub Date : 2023-05-31 DOI: 10.1093/jigpal/jzad001
Anil Nerode
{"title":"John Crossley: A life intellectual","authors":"Anil Nerode","doi":"10.1093/jigpal/jzad001","DOIUrl":"https://doi.org/10.1093/jigpal/jzad001","url":null,"abstract":"Journal Article John Crossley: A life intellectual Get access Anil Nerode Anil Nerode College of Arts and Sciences, Cornell University, Ithaca, New York, USA, an17@cornell.edu Search for other works by this author on: Oxford Academic Google Scholar Logic Journal of the IGPL, jzad001, https://doi.org/10.1093/jigpal/jzad001 Published: 31 May 2023 Article history Received: 08 February 2019 Revision received: 03 October 2019 Accepted: 23 October 2019 Published: 31 May 2023","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135348158","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
Logics and collaboration 逻辑与协作
IF 1 4区 数学
Logic Journal of the IGPL Pub Date : 2023-05-08 DOI: 10.1093/jigpal/jzad006
L. Sonenberg
{"title":"Logics and collaboration","authors":"L. Sonenberg","doi":"10.1093/jigpal/jzad006","DOIUrl":"https://doi.org/10.1093/jigpal/jzad006","url":null,"abstract":"\u0000 Since the early days of artificial intelligence (AI), many logics have been explored as tools for knowledge representation and reasoning. In the spirit of the Crossley Festscrift and recognizing John Crossley’s diverse interests and his legacy in both mathematical logic and computer science, I discuss examples from my own research that sit in the overlap of logic and AI, with a focus on supporting human–AI interactions.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47580993","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
Proof-carrying parameters in certified symbolic execution 认证符号执行中的携带证明参数
IF 1 4区 数学
Logic Journal of the IGPL Pub Date : 2023-05-01 DOI: 10.1093/jigpal/jzad008
Andrei Arusoaie, D. Lucanu
{"title":"Proof-carrying parameters in certified symbolic execution","authors":"Andrei Arusoaie, D. Lucanu","doi":"10.1093/jigpal/jzad008","DOIUrl":"https://doi.org/10.1093/jigpal/jzad008","url":null,"abstract":"\u0000 Complex frameworks for defining programming languages aim to generate various tools (e.g. interpreters, symbolic execution engines, deductive verifiers, etc.) using only the formal definition of a language. When used at an industrial scale, these tools are constantly updated, and at the same time, it is required to be trustworthy. Ensuring the correctness of such a framework is practically impossible. A solution is to generate proof objects as correctness artefacts that can be checked by an external trusted checker. A logic suitable for developing such frameworks is matching logic. K framework is a canonical example having matching logic-based foundation. Since the (symbolic) configurations of the programs are represented by matching logic patterns, the algorithms computing the dynamics of these configurations can be seen as pattern transformers and a proof object should be generated for the relationship between these patterns. In this paper, we show that conjunctions and disjunctions of patterns, produced by semantics or analysis rules, can be safely normalized using unification and antiunification algorithms. We also provide a prototype implementation of our proof object generation technique and a checker for certifying the generated objects.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48212967","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
On the relationships between some meta-mathematical properties of arithmetical theories 算术理论的一些元数学性质之间的关系
IF 1 4区 数学
Logic Journal of the IGPL Pub Date : 2023-03-27 DOI: 10.1093/jigpal/jzad015
Yong Cheng
{"title":"On the relationships between some meta-mathematical properties of arithmetical theories","authors":"Yong Cheng","doi":"10.1093/jigpal/jzad015","DOIUrl":"https://doi.org/10.1093/jigpal/jzad015","url":null,"abstract":"\u0000 In this work, we aim at understanding incompleteness in an abstract way via metamathematical properties of formal theories. We systematically examine the relationships between the following twelve important metamathematical properties of arithmetical theories: Rosser, EI (effectively inseparable), RI (recursively inseparable), TP (Turing persistent), EHU (essentially hereditarily undecidable), EU (essentially undecidable), Creative, $textbf{0}^{prime }$ (theories with Turing degree $textbf{0}^{prime }$), REW (all RE sets are weakly representable), RFD (all recursive functions are definable), RSS (all recursive sets are strongly representable), RSW (all recursive sets are weakly representable). Given any two properties $P$ and $Q$ in the above list, we examine whether $P$ implies $Q$.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47083373","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
The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic Bd 包含Routley和Meyer基本逻辑Bd的Belnap-Dunn逻辑的所有4值隐含展开的格
4区 数学
Logic Journal of the IGPL Pub Date : 2023-03-25 DOI: 10.1093/jigpal/jzad005
Gemma Robles, José M Méndez
{"title":"The lattice of all 4-valued implicative expansions of Belnap–Dunn logic containing Routley and Meyer’s basic logic B<i>d</i>","authors":"Gemma Robles, José M Méndez","doi":"10.1093/jigpal/jzad005","DOIUrl":"https://doi.org/10.1093/jigpal/jzad005","url":null,"abstract":"Abstract The well-known logic first degree entailment logic (FDE), introduced by Belnap and Dunn, is defined with $wedge $, $vee $ and $sim $ as the sole primitive connectives. The aim of this paper is to establish the lattice formed by the class of all 4-valued C-extending implicative expansions of FDE verifying the axioms and rules of Routley and Meyer’s basic logic B and its useful disjunctive extension B$^{textrm {d}}$. It is to be noted that Boolean negation (so, classical propositional logic) is definable in the strongest element in the said class.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136002173","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
Predicate counterparts of modal logics of provability: High undecidability and Kripke incompleteness 可证明性模态逻辑的谓词对应：高不可判定性和Kripke不完全性
IF 1 4区 数学
Logic Journal of the IGPL Pub Date : 2023-02-28 DOI: 10.1093/jigpal/jzad002
M. Rybakov
{"title":"Predicate counterparts of modal logics of provability: High undecidability and Kripke incompleteness","authors":"M. Rybakov","doi":"10.1093/jigpal/jzad002","DOIUrl":"https://doi.org/10.1093/jigpal/jzad002","url":null,"abstract":"\u0000 In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics $textbf {GL}$, $textbf {Grz}$, $textbf {wGrz}$ and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between $textbf {QwGrz}$ and $textbf {QGL.3}$ or between $textbf {QwGrz}$ and $textbf {QGrz.3}$ is $Pi ^1_1$-hard even in languages with three (sometimes, two) individual variables, two (sometimes, one) unary predicate letters, and a single proposition letter. As a corollary, it is proved that infinite families of modal predicate axiomatic systems, based on the classical first-order logic and the modal propositional logics $textbf {GL}$, $textbf {Grz}$, $textbf {wGrz}$ are not Kripke complete. Both $Pi ^1_1$-hardness and Kripke incompleteness results of the paper do not depend on whether the logics contain the Barcan formula.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47614232","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: 4
Binary modal logic and unary modal logic 二元模态逻辑与一元模态逻辑
4区 数学
Logic Journal of the IGPL Pub Date : 2023-01-24 DOI: 10.1093/jigpal/jzac083
Dick de Jongh, Fatemeh Shirmohammadzadeh Maleki
{"title":"Binary modal logic and unary modal logic","authors":"Dick de Jongh, Fatemeh Shirmohammadzadeh Maleki","doi":"10.1093/jigpal/jzac083","DOIUrl":"https://doi.org/10.1093/jigpal/jzac083","url":null,"abstract":"Abstract Standard unary modal logic and binary modal logic, i.e. modal logic with one binary operator, are shown to be definitional extensions of one another when an additional axiom $U$ is added to the basic axiomatization of the binary side. This is a strengthening of our previous results. It follows that all unary modal logics extending Classical Modal Logic, in other words all unary modal logics with a neighborhood semantics, can equivalently be seen as binary modal logics. This in particular applies to standard modal logics, which can be given simple natural axiomatizations in binary form. We illustrate this in the logic K. We call such logics binary expansions of the unary modal logics. There are many more such binary expansions than the ones given by the axiom $U$. We initiate an investigation of the properties of these expansions and in particular of the maximal binary expansions of a logic. Our results directly imply that all sub- and superintuitionistic logics with a standard modal companion also have binary modal companions. The latter also applies to the weak subintuitionistic logic WF of our previous papers. This logic doesn’t seem to have a unary modal companion.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136198035","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
Sahlqvist Completeness Theory for Hybrid Logic with Downarrow Binder 带下箭头绑定的混合逻辑的Sahlqvist完备性理论
4区 数学
Logic Journal of the IGPL Pub Date : 2023-01-16 DOI: 10.1093/jigpal/jzac079
Zhiguang Zhao
{"title":"Sahlqvist Completeness Theory for Hybrid Logic with Downarrow Binder","authors":"Zhiguang Zhao","doi":"10.1093/jigpal/jzac079","DOIUrl":"https://doi.org/10.1093/jigpal/jzac079","url":null,"abstract":"Abstract In the present paper, we continue the research in Zhao (2021, Logic J. IGPL) to develop the Sahlqvist completeness theory for hybrid logic with satisfaction operators and downarrow binders $mathcal {L}( @, {downarrow })$. We define the class of restricted Sahlqvist formulas for $mathcal {L}( @, {downarrow })$ following the ideas in Conradie and Robinson (2017, J. Logic Comput., 27, 867–900), but we follow a different proof strategy which is purely proof-theoretic, namely showing that for every restricted Sahlqvist formula $varphi $ and its hybrid pure correspondence $pi $, $textbf {K}_{mathcal {H}( @, {downarrow })}+varphi $ proves $pi $; therefore, $textbf {K}_{mathcal {H}( @, {downarrow })}+varphi $ is complete with respect to the class of frames defined by $pi $, using a modified version $textsf {ALBA}^{{downarrow }}_{textsf {Modified}}$ of the algorithm $textsf {ALBA}^{{downarrow }}$ defined in Zhao (2021, Logic J. IGPL).","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135694078","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
Non-contingency in a Paraconsistent Setting 非一致性设置中的非偶然性
4区 数学
Logic Journal of the IGPL Pub Date : 2023-01-16 DOI: 10.1093/jigpal/jzac081
Daniil Kozhemiachenko, Liubov Vashentseva
{"title":"Non-contingency in a Paraconsistent Setting","authors":"Daniil Kozhemiachenko, Liubov Vashentseva","doi":"10.1093/jigpal/jzac081","DOIUrl":"https://doi.org/10.1093/jigpal/jzac081","url":null,"abstract":"Abstract We study an extension of first-degree entailment (FDE) by Dunn and Belnap with a non-contingency operator $blacktriangle phi $ which is construed as ‘$phi $ has the same value in all accessible states’ or ‘all sources give the same information on the truth value of $phi $’. We equip this logic dubbed $textbf {K}^blacktriangle _{textbf {FDE}}$ with frame semantics and show how the bi-valued models can be interpreted as interconnected networks of Belnapian databases with the $blacktriangle $ operator modelling search for inconsistencies in the provided information. We construct an analytic cut system for the logic and show its soundness and completeness. We prove that $blacktriangle $ is not definable via the necessity modality $Box $ of $textbf {K}_{textbf{FDE}}$. Furthermore, we prove that in contrast to the classical non-contingency logic, reflexive, $textbf {S4}$ and $textbf {S5}$ (among others) frames are definable.","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135694089","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
Unification types in Euclidean modal logics 欧几里得模态逻辑中的统一类型
IF 1 4区 数学
Logic Journal of the IGPL Pub Date : 2023-01-01 DOI: 10.1093/jigpal/jzab036
Majid Alizadeh, Mohammad Ardeshir, P. Balbiani, M. Mojtahedi
{"title":"Unification types in Euclidean modal logics","authors":"Majid Alizadeh, Mohammad Ardeshir, P. Balbiani, M. Mojtahedi","doi":"10.1093/jigpal/jzab036","DOIUrl":"https://doi.org/10.1093/jigpal/jzab036","url":null,"abstract":"","PeriodicalId":51114,"journal":{"name":"Logic Journal of the IGPL","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60952143","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
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