Studia LogicaPub Date : 2023-12-09DOI: 10.1007/s11225-023-10084-z
Angelina Ilić-Stepić, Zoran Ognjanović, Aleksandar Perović
{"title":"The Logic ILP for Intuitionistic Reasoning About Probability","authors":"Angelina Ilić-Stepić, Zoran Ognjanović, Aleksandar Perović","doi":"10.1007/s11225-023-10084-z","DOIUrl":"https://doi.org/10.1007/s11225-023-10084-z","url":null,"abstract":"<p>We offer an alternative approach to the existing methods for intuitionistic formalization of reasoning about probability. In terms of Kripke models, each possible world is equipped with a structure of the form <span>(langle H, mu rangle )</span> that needs not be a probability space. More precisely, though <i>H</i> needs not be a Boolean algebra, the corresponding monotone function (we call it measure) <span>(mu : H longrightarrow [0,1]_{mathbb {Q}})</span> satisfies the following condition: if <span>(alpha )</span>, <span>(beta )</span>, <span>(alpha wedge beta )</span>, <span>(alpha vee beta in H)</span>, then <span>(mu (alpha vee beta ) = mu (alpha ) + mu (beta ) - mu (alpha wedge beta ))</span>. Since the range of <span>(mu )</span> is the set <span>([0,1]_{mathbb {Q}})</span> of rational numbers from the real unit interval, our logic is not compact. In order to obtain a strong complete axiomatization, we introduce an infinitary inference rule with a countable set of premises. The main technical results are the proofs of strong completeness and decidability.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138561507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-12-08DOI: 10.1007/s11225-023-10080-3
Ivan Chajda, Helmut Länger, Jan Paseka
{"title":"Representability of Kleene Posets and Kleene Lattices","authors":"Ivan Chajda, Helmut Länger, Jan Paseka","doi":"10.1007/s11225-023-10080-3","DOIUrl":"https://doi.org/10.1007/s11225-023-10080-3","url":null,"abstract":"<p>A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element of this lattice or poset by using the so-called twist product construction, respectively. We extend this construction of Kleene lattices and Kleene posets by considering a fixed subset instead of a fixed element. Moreover, we show that in some cases, this generating poset can be embedded into the resulting Kleene poset. We investigate the question when a Kleene poset can be represented by a Kleene poset obtained by the mentioned construction. We show that a direct product of representable Kleene posets is again representable and hence a direct product of finite chains is representable. This does not hold in general for subdirect products, but we show some examples where it holds. We present large classes of representable and non-representable Kleene posets. Finally, we investigate two kinds of extensions of a distributive poset <span>({textbf{A}})</span>, namely its Dedekind-MacNeille completion <span>({{,mathrm{textbf{DM}},}}({textbf{A}}))</span> and a completion <span>(G({textbf{A}}))</span> which coincides with <span>({{,mathrm{textbf{DM}},}}({textbf{A}}))</span> provided <span>({textbf{A}})</span> is finite. In particular we prove that if <span>({textbf{A}})</span> is a Kleene poset then its extension <span>(G({textbf{A}}))</span> is also a Kleene lattice. If the subset <i>X</i> of principal order ideals of <span>({textbf{A}})</span> is involution-closed and doubly dense in <span>(G({textbf{A}}))</span> then it generates <span>(G({textbf{A}}))</span> and it is isomorphic to <span>({textbf{A}})</span> itself.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138556262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-11-16DOI: 10.1007/s11225-023-10081-2
Asadollah Fallahi, James Gordon Raftery
{"title":"On Pretabular Extensions of Relevance Logic","authors":"Asadollah Fallahi, James Gordon Raftery","doi":"10.1007/s11225-023-10081-2","DOIUrl":"https://doi.org/10.1007/s11225-023-10081-2","url":null,"abstract":"<p>We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom <span>((prightarrow q)vee (qrightarrow p))</span> has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.</p>","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138510223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-11-14DOI: 10.1007/s11225-023-10075-0
Yang Song, Hitoshi Omori, Jonas R. B. Arenhart, Satoshi Tojo
{"title":"A Generalization of Beall’s Off-Topic Interpretation","authors":"Yang Song, Hitoshi Omori, Jonas R. B. Arenhart, Satoshi Tojo","doi":"10.1007/s11225-023-10075-0","DOIUrl":"https://doi.org/10.1007/s11225-023-10075-0","url":null,"abstract":"Abstract In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as off-topic , whereas the two classical values are read as true and on-topic and false and on-topic . Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making use of our new framework, we will offer a new interpretation of the logic of Catuskoti which combines Beall’s proposal of having FDE as the correct logic with the on-topic/off-topic divide. Finally, we will offer a general result that will allow us to make sense of a family of infectious logics in terms of Beall’s on-topic/off-topic reading.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-11-14DOI: 10.1007/s11225-023-10076-z
Fengkui Ju
{"title":"A Logical Theory for Conditional Weak Ontic Necessity in Branching Time","authors":"Fengkui Ju","doi":"10.1007/s11225-023-10076-z","DOIUrl":"https://doi.org/10.1007/s11225-023-10076-z","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134991801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-11-10DOI: 10.1007/s11225-023-10074-1
Juan Manuel Cornejo, Hernn Javier San Martín, Valeria Sígal
{"title":"On a Class of Subreducts of the Variety of Integral srl-Monoids and Related Logics","authors":"Juan Manuel Cornejo, Hernn Javier San Martín, Valeria Sígal","doi":"10.1007/s11225-023-10074-1","DOIUrl":"https://doi.org/10.1007/s11225-023-10074-1","url":null,"abstract":"","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-11-10DOI: 10.1007/s11225-023-10078-x
Luis Estrada-González, Ricardo Arturo Nicolás-Francisco
{"title":"Connexive Negation","authors":"Luis Estrada-González, Ricardo Arturo Nicolás-Francisco","doi":"10.1007/s11225-023-10078-x","DOIUrl":"https://doi.org/10.1007/s11225-023-10078-x","url":null,"abstract":"Abstract Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135137852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Studia LogicaPub Date : 2023-10-10DOI: 10.1007/s11225-023-10071-4
Hans Rott
{"title":"Difference-Making Conditionals and Connexivity","authors":"Hans Rott","doi":"10.1007/s11225-023-10071-4","DOIUrl":"https://doi.org/10.1007/s11225-023-10071-4","url":null,"abstract":"Abstract Today there is a wealth of fascinating studies of connexive logical systems. But sometimes it looks as if connexive logic is still in search of a convincing interpretation that explains in intuitive terms why the connexive principles should be valid. In this paper I argue that difference-making conditionals as presented in Rott ( Review of Symbolic Logic 15, 2022) offer one principled way of interpreting connexive principles. From a philosophical point of view, the idea of difference-making demands full, unrestricted connexivity, because neither logical truths nor contradictions or other absurdities can ever ‘make a difference’ (i.e., be relevantly connected) to anything. However, difference-making conditionals have so far been only partially connexive. I show how the existing analysis of difference-making conditionals can be reshaped to obtain full connexivity. The classical AGM belief revision model is replaced by a conceivability-limited revision model that serves as the semantic base for the analysis. The key point of the latter is that the agent should never accept any absurdities.","PeriodicalId":48979,"journal":{"name":"Studia Logica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}