Annals of Pure and Applied Logic最新文献_第4页

Positive definability patterns 正可定义性模式

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-11-28 DOI: 10.1016/j.apal.2024.103539

Ori Segel

引用次数: 0

Strong standard completeness theorems for S5-modal Łukasiewicz logics 5-模态Łukasiewicz逻辑的强标准完备性定理

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-11-22 DOI: 10.1016/j.apal.2024.103529

Diego Castaño , José Patricio Díaz Varela , Gabriel Savoy

引用次数: 0

Semiconic idempotent logic II: Beth definability and deductive interpolation 半符号幂等逻辑II：贝丝可定义性与演绎插值

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-11-15 DOI: 10.1016/j.apal.2024.103528

Wesley Fussner , Nikolaos Galatos

{"title":"Semiconic idempotent logic II: Beth definability and deductive interpolation","authors":"Wesley Fussner , Nikolaos Galatos","doi":"10.1016/j.apal.2024.103528","DOIUrl":"10.1016/j.apal.2024.103528","url":null,"abstract":"<div><div>Semiconic idempotent logic <strong>sCI</strong> is a common generalization of intuitionistic logic, semilinear idempotent logic <strong>sLI</strong>, and in particular relevance logic with mingle. We establish the projective Beth definability property and the deductive interpolation property for many extensions of <strong>sCI</strong>, and identify extensions where these properties fail. We achieve these results by studying the (strong) amalgamation property and the epimorphism-surjectivity property for the corresponding algebraic semantics, viz. semiconic idempotent residuated lattices. Our study is made possible by the structural decomposition of conic idempotent models achieved in the prequel, as well as a detailed analysis of the structure of idempotent residuated chains serving as index sets in this decomposition. Here we study the latter on two levels: as certain enriched Galois connections and as enhanced monoidal preorders. Using this, we show that although conic idempotent residuated lattices do not have the amalgamation property, the natural class of stratified and conjunctive conic idempotent residuated lattices has the strong amalgamation property, and thus has surjective epimorphisms. This extends to the variety generated by stratified and conjunctive conic idempotent residuated lattices, and we establish the (strong) amalgamation and epimorphism-surjectivity properties for several important subvarieties. Using the algebraizability of <strong>sCI</strong>, this yields the deductive interpolation property and the projective Beth definability property for the corresponding substructural logics extending <strong>sCI</strong>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 3","pages":"Article 103528"},"PeriodicalIF":0.6,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143148056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Failure of the Blok–Esakia Theorem in the monadic setting 一元情况下block - esakia定理的失效

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-11-14 DOI: 10.1016/j.apal.2024.103527

G. Bezhanishvili , L. Carai

引用次数: 0

Universal proof theory: Feasible admissibility in intuitionistic modal logics 通用证明理论：直觉模态逻辑中的可行可接受性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-10-23 DOI: 10.1016/j.apal.2024.103526

Amirhossein Akbar Tabatabai , Raheleh Jalali

{"title":"Universal proof theory: Feasible admissibility in intuitionistic modal logics","authors":"Amirhossein Akbar Tabatabai , Raheleh Jalali","doi":"10.1016/j.apal.2024.103526","DOIUrl":"10.1016/j.apal.2024.103526","url":null,"abstract":"<div><div>We introduce a general and syntactically defined family of sequent-style calculi over the propositional language with the modalities <span><math><mo>{</mo><mo>□</mo><mo>,</mo><mo>◇</mo><mo>}</mo></math></span> and its fragments as a formalization for constructively acceptable systems. Calling these calculi <em>constructive</em>, we show that any strong enough constructive sequent calculus, satisfying a mild technical condition, feasibly admits all Visser's rules. This means that there exists a polynomial-time algorithm that, given a proof of the premise of a Visser's rule, provides a proof for its conclusion. As a positive application, we establish the feasible admissibility of Visser's rules in sequent calculi for several intuitionistic modal logics, including <span><math><mi>CK</mi></math></span>, <span><math><mi>IK</mi></math></span>, their extensions by the modal axioms <em>T</em>, <em>B</em>, 4, 5, and the axioms for bounded width and depth and their fragments <span><math><msub><mrow><mi>CK</mi></mrow><mrow><mo>□</mo></mrow></msub></math></span>, propositional lax logic and <span><math><mi>IPC</mi></math></span>. On the negative side, we show that if a strong enough intuitionistic modal logic (satisfying a mild technical condition) does not admit at least one of Visser's rules, it cannot have a constructive sequent calculus. Consequently, no intermediate logic other than <span><math><mi>IPC</mi></math></span> has a constructive sequent calculus.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103526"},"PeriodicalIF":0.6,"publicationDate":"2024-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142561348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Bi-colored expansions of geometric theories 几何理论的双色展开

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-10-18 DOI: 10.1016/j.apal.2024.103525

S. Jalili , M. Pourmahdian , M. Khani

{"title":"Bi-colored expansions of geometric theories","authors":"S. Jalili , M. Pourmahdian , M. Khani","doi":"10.1016/j.apal.2024.103525","DOIUrl":"10.1016/j.apal.2024.103525","url":null,"abstract":"<div><div>This paper concerns the study of expansions of models of a geometric theory <em>T</em> by a color predicate <em>p</em>, within the framework of the Fraïssé-Hrushovski construction method. For each <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, we define a pre-dimension function <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> on the class of Bi-colored models of <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>∀</mo></mrow></msup></math></span> and consider the subclass <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> consisting of models with hereditary positive <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>. We impose certain natural conditions on <em>T</em> that enable us to introduce a complete <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-theory <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> for the rich models in <span><math><msubsup><mrow><mi>K</mi></mrow><mrow><mi>α</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span>. We show how the transfer of certain model-theoretic properties, such as NIP and strong-dependence, from <em>T</em> to <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>, depends on whether <em>α</em> is rational or irrational.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103525"},"PeriodicalIF":0.6,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Equiconsistency of the Minimalist Foundation with its classical version 极简主义基础与其经典版本的等价一致性

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-10-16 DOI: 10.1016/j.apal.2024.103524

Maria Emilia Maietti, Pietro Sabelli

{"title":"Equiconsistency of the Minimalist Foundation with its classical version","authors":"Maria Emilia Maietti, Pietro Sabelli","doi":"10.1016/j.apal.2024.103524","DOIUrl":"10.1016/j.apal.2024.103524","url":null,"abstract":"<div><div>The Minimalist Foundation, for short <strong>MF</strong>, was conceived by the first author with G. Sambin in 2005, and fully formalized in 2009, as a common core among the most relevant constructive and classical foundations for mathematics. To better accomplish its minimality, <strong>MF</strong> was designed as a two-level type theory, with an intensional level <strong>mTT</strong>, an extensional one <strong>emTT</strong>, and an interpretation of the latter into the first.</div><div>Here, we first show that the two levels of <strong>MF</strong> are indeed equiconsistent by interpreting <strong>mTT</strong> into <strong>emTT</strong>. Then, we show that the classical extension <span><math><msup><mrow><mi>emTT</mi></mrow><mrow><mi>c</mi></mrow></msup></math></span> is equiconsistent with <strong>emTT</strong> by suitably extending the Gödel-Gentzen double-negation translation of classical logic in the intuitionistic one. As a consequence, <strong>MF</strong> turns out to be compatible with classical predicative mathematics à la Weyl, contrary to the most relevant foundations for constructive mathematics.</div><div>Finally, we show that the chain of equiconsistency results for <strong>MF</strong> can be straightforwardly extended to its impredicative version to deduce that Coquand-Huet's Calculus of Constructions equipped with basic inductive types is equiconsistent with its extensional and classical versions too.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103524"},"PeriodicalIF":0.6,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Some properties of precompletely and positively numbered sets 预完全正数集的一些性质

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-10-09 DOI: 10.1016/j.apal.2024.103523

Marat Faizrahmanov

{"title":"Some properties of precompletely and positively numbered sets","authors":"Marat Faizrahmanov","doi":"10.1016/j.apal.2024.103523","DOIUrl":"10.1016/j.apal.2024.103523","url":null,"abstract":"<div><div>In this paper, we prove a joint generalization of Arslanov's completeness criterion and Visser's ADN theorem for precomplete numberings which, for the Gödel numbering <span><math><mi>x</mi><mo>↦</mo><msub><mrow><mi>W</mi></mrow><mrow><mi>x</mi></mrow></msub></math></span>, has been proved by Terwijn (2018). The question of whether this joint generalization takes place in each precomplete numbering has been raised in his joint paper with Barendregt in 2019. Then we consider the properties of completeness and precompleteness of numberings in the context of the positivity property. We show that no completion of a positive numbering is a minimal cover of that numbering, and that the Turing completeness of any set <em>A</em> is equivalent to the existence of a positive precomplete <em>A</em>-computable numbering of any infinite family with positive <em>A</em>-computable numbering. In addition, we prove that each <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-computable numbering (<span><math><mi>n</mi><mo>⩾</mo><mn>2</mn></math></span>) of a <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-computable non-principal family has a <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-computable minimal cover <em>ν</em> such that for every computable function <em>f</em> there exists an integer <em>n</em> with <span><math><mi>ν</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>)</mo><mo>=</mo><mi>ν</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"176 2","pages":"Article 103523"},"PeriodicalIF":0.6,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Strong reducibilities and set theory 强还原性与集合论

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-10-01 DOI: 10.1016/j.apal.2024.103522

Noah Schweber

引用次数: 0

Dividing and forking in random hypergraphs 随机超图中的分割和分叉

IF 0.6 2区数学

Annals of Pure and Applied Logic Pub Date : 2024-09-24 DOI: 10.1016/j.apal.2024.103521

Hirotaka Kikyo , Akito Tsuboi

引用次数: 0