Mathematical Logic Quarterly最新文献

{"title":"Strong K-Modal BL-Algebras","authors":"Masoud Haveshki, Mahboobeh Mohamadhasani","doi":"10.1002/malq.70029","DOIUrl":"https://doi.org/10.1002/malq.70029","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we present the corresponding algebraic structure for <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-modal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation>$BL$</annotation>\u0000 </semantics></math>-logic (abbreviated as <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>KM</mi>\u0000 <mi>BL</mi>\u0000 </mrow>\u0000 <annotation>$mathbb {KM}{bm {BL}}$</annotation>\u0000 </semantics></math>) proposed by Eslami et al. [<i>Journal of Intelligent and Fuzzy Systems</i>] <b>29</b> (2015): 337–388, which we call a strong <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-modal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation>$BL$</annotation>\u0000 </semantics></math>-algebra. We demonstrate that the equivalent algebraic semantics for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>KM</mi>\u0000 <mi>BL</mi>\u0000 </mrow>\u0000 <annotation>$mathbb {KM}{bm {BL}}$</annotation>\u0000 </semantics></math> is the variety of strong <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-modal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation>$BL$</annotation>\u0000 </semantics></math>-algebras, and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>KM</mi>\u0000 <mi>BL</mi>\u0000 </mrow>\u0000 <annotation>$mathbb {KM}{bm {BL}}$</annotation>\u0000 </semantics></math> is algebraizable in the sense of Blok and Pigozzi. We prove that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>KM</mi>\u0000 <mi>BL</mi>\u0000 </mrow>\u0000 <annotation>$mathbb {KM}{bm {BL}}$</annotation>\u0000 </semantics></math> is strongly sound and complete with respect to strong <span></span><math>\u0000 <semantics>\u0000 <mi>K</mi>\u0000 <annotation>$K$</annotation>\u0000 </semantics></math>-modal <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <annotation>$BL$</annotation>\u0000 </semantics></math>-algebras. The local deduction theorem is also est","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205365","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}

{"title":"A Common External Framework for Kleene and McCarthy Algebras","authors":"Gandolfo Vergottini,&nbsp;Antonio Ledda,&nbsp;Pierluigi Graziani","doi":"10.1002/malq.70026","DOIUrl":"https://doi.org/10.1002/malq.70026","url":null,"abstract":"<p>Algebras of disjoint alternatives (ADAs), introduced by Manes, are extensions of McCarthy algebras by a unary operator acting as an oracle for the halting problem, and provide a semantics for the equational theory of the <i>if–then–else</i> construct.</p><p>We study the variety of ADAs in the signature without the constant <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math> of Manes' formulation, and prove a representation theorem: every ADA has an essentially unique representation as an algebra of pairs <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>B</mi>\u0000 <mo>,</mo>\u0000 <mi>F</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(B,F)$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math> is a Boolean algebra and <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math> a distinguished filter of <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></math>. This refines Manes' construction, which captures the ADAs possessing a fixed point of the negation, i.e. the case <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>F</mi>\u0000 <mo>=</mo>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$F=B$</annotation>\u0000 </semantics></math>.</p><p>Since regular double Stone algebras admit a similar representation due to Katriňák, we derive that the two varieties are term-equivalent, and hence so are ADAs, three-valued Łukasiewicz algebras, and three-valued MV-algebras. As consequences, we obtain a categorical equivalence between ADAs and Boolean algebras with a distinguished filter, extending Manes' equivalence, and the amalgamation property for the variety of ADAs.</p><p>The representation accommodates, in a single framework, the connectives of Kleene's strong, McCarthy's sequential, and weak Kleene logics, modeling three distinct forms of error propagation in computation. Finally, we outline exploratory connections with rough sets and assume–guarantee contracts.</p>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 4","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/malq.70026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149027813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Representations of QFS-Domains","authors":"Fan Feng,&nbsp;Zhenzhu Yuan,&nbsp;Qingguo Li","doi":"10.1002/malq.70025","DOIUrl":"https://doi.org/10.1002/malq.70025","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we propose the strong* proximity lattices, and prove that the categories <span></span><math>\u0000 <semantics>\u0000 <mi>QFS</mi>\u0000 <annotation>$mathbf {QFS}$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <mi>PL</mi>\u0000 </mrow>\u0000 <annotation>$mathbf {S^{ast }PL}$</annotation>\u0000 </semantics></math> are categorically equivalent, building on the framework established by Achim Jung and Philipp Sünderhauf. <span></span><math>\u0000 <semantics>\u0000 <mi>QFS</mi>\u0000 <annotation>$mathbf {QFS}$</annotation>\u0000 </semantics></math> denotes the category of all QFS-domains and continuous functions. <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mo>*</mo>\u0000 </msup>\u0000 <mi>PL</mi>\u0000 </mrow>\u0000 <annotation>$mathbf {S^{ast }PL}$</annotation>\u0000 </semantics></math> denotes the category of the strong* proximity lattices with the approximable relations. This answers the question posed by Achim Jung at the conference ISDT'13.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 3","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148238104","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}

{"title":"Weak, Strong and Mixed Extensions of Relations to Spaces of Ultrafilters","authors":"Leonardo Raffaello Maximilian Gasparro,&nbsp;Lorenzo Luperi Baglini","doi":"10.1002/malq.70022","DOIUrl":"https://doi.org/10.1002/malq.70022","url":null,"abstract":"<p>The use of nonstandard methods to characterize properties of weak, strong and mixed extensions of congruences to ultrafilters has been the main topic of several recent papers, focused mostly on congruences and divisions. We show that similar methods can be used to extend these characterizations to arbitrary relations and their interplay.</p>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 3","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/malq.70022","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148095671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148066608","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}

{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148077869","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}

{"title":"On The (k,s)-Hilfer Fractional Derivatives via Wirtinger-Type Inequalities and Their Analytical Applications","authors":"Muhammad Samraiz,&nbsp;Areej Yussouf,&nbsp;Saima Naheed","doi":"10.1002/malq.70020","DOIUrl":"https://doi.org/10.1002/malq.70020","url":null,"abstract":"<div>\u0000 \u0000 <p>This article introduces a novel definition of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>s</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(k,s)$</annotation>\u0000 </semantics></math>-Hilfer fractional derivative. Based on this derivative, some fractional Wirtinger type inequalities are established for the <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$L_{p}$</annotation>\u0000 </semantics></math> spaces, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p &gt; 1$</annotation>\u0000 </semantics></math> by using Hölder's inequality. Various related special cases are also presented. To validate our main results, examples with graphical representations are provided. Applications of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>,</mo>\u0000 <mi>s</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(k,s)$</annotation>\u0000 </semantics></math>-Hilfer fractional Wirtinger-type inequalities are demonstrated in terms of arithmetic mean and geometric mean-type inequality.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147687008","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}

{"title":"A Monotone Infinitary Operation on Ordinals","authors":"Paolo Lipparini","doi":"10.1002/malq.70019","DOIUrl":"https://doi.org/10.1002/malq.70019","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce an <span></span><math>\u0000 <semantics>\u0000 <mi>ω</mi>\u0000 <annotation>$ omega$</annotation>\u0000 </semantics></math>-ary operation on the class of the ordinals, which is strictly monotone in all significant cases. We provide order-theoretical characterizations as the rank of a sequence in a well-founded order and as a mixed sum of the ordinals in the sequence.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147614996","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}

{"title":"Right-Continuous Mappings and Fuzzy Ideals","authors":"Takashi Kuraoka","doi":"10.1002/malq.70018","DOIUrl":"https://doi.org/10.1002/malq.70018","url":null,"abstract":"<div>\u0000 \u0000 <p>We introduce the concept of right-continuous mappings from [0,1) to the power set of finite elements in a complete semilattice and define a closure operator on the set <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>P</mi>\u0000 <mi>r</mi>\u0000 </msub>\u0000 <annotation>$P_r$</annotation>\u0000 </semantics></math> of right-continuous mappings. We show that the lattice of fuzzy ideals on the semilattice of finite elements is isomorphic to the lattice of closed elements concerning the closure operator. Furthermore, we give equivalent conditions for regular closure operators on the set of right-continuous mappings to be quasi-algebraic. Finally, we prove the lattice of fuzzy ideals on the set of finite elements in an algebraic semilattice is subdirectly embedded into the product of copies of the semilattice, and show the subdirect embedding has a universal mapping property.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567827","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}

{"title":"Graphical Insights and Applications of Fractional Minkowski and Fejér-Hermite-Hadamard Type Inequalities","authors":"Zeeshan Anwar,&nbsp;Saima Naheed,&nbsp;Ahsan Mehmood,&nbsp;Muhammad Samraiz","doi":"10.1002/malq.70015","DOIUrl":"https://doi.org/10.1002/malq.70015","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, the Minkowski and Fejér-Hermite-Hadamard (H-H) type inequalities are generalized by utilizing the modified Atangana-Baleanu (A-B) fractional operators. These fractional operators, defined by their nonlocal and nonsingular kernels provide a new way to generalize these classical inequalities. The inequalities are verified through several illustrative examples and corresponding graphs. A new application involving the digamma function is presented to demonstrate the significance of the results. This research opens new avenues for establishing further inequalities via fractional operators.</p></div>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"72 2","pages":""},"PeriodicalIF":0.4,"publicationDate":"2026-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567233","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}