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The Implicative Conditional 隐含条件句
IF 1.5 1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-11-27 DOI: 10.1007/s10992-023-09715-6
Eric Raidl, Gilberto Gomes
{"title":"The Implicative Conditional","authors":"Eric Raidl, Gilberto Gomes","doi":"10.1007/s10992-023-09715-6","DOIUrl":"https://doi.org/10.1007/s10992-023-09715-6","url":null,"abstract":"<p>This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also named <i>implicative conditionals</i>, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent. <span>({pRightarrow q})</span> is thus defined as <span>({lnot } Diamond {(p wedge lnot q) wedge } Diamond {p wedge } Diamond {lnot q})</span>. We explore the logical properties of this conditional in a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"71 7","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Sound and Complete Tableaux Calculus for Reichenbach’s Quantum Mechanics Logic Reichenbach量子力学逻辑的完整表演算
IF 1.5 1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-11-18 DOI: 10.1007/s10992-023-09730-7
Pablo Caballero, Pablo Valencia
{"title":"A Sound and Complete Tableaux Calculus for Reichenbach’s Quantum Mechanics Logic","authors":"Pablo Caballero, Pablo Valencia","doi":"10.1007/s10992-023-09730-7","DOIUrl":"https://doi.org/10.1007/s10992-023-09730-7","url":null,"abstract":"<p>In 1944 Hans Reichenbach developed a three-valued propositional logic (RQML) in order to account for certain causal anomalies in quantum mechanics. In this logic, the truth-value <i>indeterminate</i> is assigned to those statements describing physical phenomena that cannot be understood in causal terms. However, Reichenbach did not develop a deductive calculus for this logic. The aim of this paper is to develop such a calculus by means of First Degree Entailment logic (FDE) and to prove it sound and complete with respect to RQML semantics. In Section 1 we explain the main physical and philosophical motivations of RQML. Next, in Sections 2 and 3, respectively, we present RQML and FDE syntax and semantics and explain the relation between both logics. Section 4 introduces <span>(varvec{mathcal {Q}})</span> calculus, an FDE-based tableaux calculus for RQML. In Section 5 we prove that <span>(varvec{mathcal {Q}})</span> calculus is sound and complete with respect to RQML three-valued semantics. Finally, in Section 6 we consider some of the main advantages of <span>(varvec{mathcal {Q}})</span> calculus and we apply it to Reichenbach’s analysis of causal anomalies.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"65 10","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Liar Paradox and “Meaningless” Revenge 说谎者悖论和“无意义的”复仇
IF 1.5 1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-11-16 DOI: 10.1007/s10992-023-09719-2
Jared Warren
{"title":"The Liar Paradox and “Meaningless” Revenge","authors":"Jared Warren","doi":"10.1007/s10992-023-09719-2","DOIUrl":"https://doi.org/10.1007/s10992-023-09719-2","url":null,"abstract":"<p>A historically popular response to the liar paradox (“this sentence is false”) is to say that the liar sentence is <i>meaningless</i> (or <i>semantically defective</i>, or <i>malfunctions</i>, or…). Unfortunately, like all other supposed solutions to the liar, this approach faces a revenge challenge. Consider the revenge liar sentence, “this sentence is either meaningless or false”. If it is true, then it is either meaningless or false, so not true. And if it is not true, then it can’t be either meaningless or false, so it must be true. Either way, we are back in a paradox. This paper provides a detailed and exhaustive discussion of the options for responding to revenge on behalf of “meaningless” theories. Though I attempt to discuss all of the options fairly, I will ultimately opt for one specific response and discuss some of its challenges. Various technical and logical matters will be discussed throughout the paper, but my focus will be philosophical, throughout. My overall conclusion is that the “meaningless” strategy is <i>at least</i> as well off in the face of revenge as any other approach to the liar and related paradoxes.</p>","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"76 10","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modal Information Logics: Axiomatizations and Decidability 模态信息逻辑:公理化和可判定性
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-11-03 DOI: 10.1007/s10992-023-09724-5
Søren Brinck Knudstorp
{"title":"Modal Information Logics: Axiomatizations and Decidability","authors":"Søren Brinck Knudstorp","doi":"10.1007/s10992-023-09724-5","DOIUrl":"https://doi.org/10.1007/s10992-023-09724-5","url":null,"abstract":"Abstract The present paper studies formal properties of so-called modal information logics (MILs)—modal logics first proposed in (van Benthem 1996) as a way of using possible-worlds semantics to model a theory of information. They do so by extending the language of propositional logic with a binary modality defined in terms of being the supremum of two states. First proposed in 1996, MILs have been around for some time, yet not much is known: (van Benthem 2017, 2019) pose two central open problems, namely (1) axiomatizing the two basic MILs of suprema on preorders and posets, respectively, and (2) proving (un)decidability. The main results of the first part of this paper are solving these two problems: (1) by providing an axiomatization [with a completeness proof entailing the two logics to be the same], and (2) by proving decidability. In the proof of the latter, an emphasis is put on the method applied as a heuristic for proving decidability ‘via completeness’ for semantically introduced logics; the logics lack the FMP w.r.t. their classes of definition, but not w.r.t. a generalized class. These results are build upon to axiomatize and prove decidable the MILs attained by endowing the language with an ‘informational implication’—in doing so a link is also made to the work of (Buszkowski 2021) on the Lambek Calculus.","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"10 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135821130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Subject-Matter and Intensional Operators II: Applications to the Theory of Topic-Sensitive Intentional Modals 主题与内涵运算符II:在主题敏感意向性情态理论中的应用
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-10-26 DOI: 10.1007/s10992-023-09722-7
Thomas Macaulay Ferguson
{"title":"Subject-Matter and Intensional Operators II: Applications to the Theory of Topic-Sensitive Intentional Modals","authors":"Thomas Macaulay Ferguson","doi":"10.1007/s10992-023-09722-7","DOIUrl":"https://doi.org/10.1007/s10992-023-09722-7","url":null,"abstract":"","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"63 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134909002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Axiomatizing Rumsfeld Ignorance 拉姆斯菲尔德无知的公理化
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-10-24 DOI: 10.1007/s10992-023-09725-4
Jie Fan
{"title":"Axiomatizing Rumsfeld Ignorance","authors":"Jie Fan","doi":"10.1007/s10992-023-09725-4","DOIUrl":"https://doi.org/10.1007/s10992-023-09725-4","url":null,"abstract":"","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135267115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Truth Meets Vagueness. Unifying the Semantic and the Soritical Paradoxes 真相与模糊相遇。统一语义悖论与社会悖论
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-10-09 DOI: 10.1007/s10992-023-09721-8
Riccardo Bruni, Lorenzo Rossi
{"title":"Truth Meets Vagueness. Unifying the Semantic and the Soritical Paradoxes","authors":"Riccardo Bruni, Lorenzo Rossi","doi":"10.1007/s10992-023-09721-8","DOIUrl":"https://doi.org/10.1007/s10992-023-09721-8","url":null,"abstract":"Abstract Semantic and soritical paradoxes display remarkable family resemblances. For one thing, several non-classical logics have been independently applied to both kinds of paradoxes. For another, revenge paradoxes and higher-order vagueness—among the most serious problems targeting solutions to semantic and soritical paradoxes—exhibit a rather similar dynamics. Some authors have taken these facts to suggest that truth and vagueness require a unified logical framework, or perhaps that the truth predicate is itself vague. However, a common core of semantic and soritical paradoxes has not been identified yet, and no explanation of their relationships has been provided. Here we aim at filling this lacuna, in the framework of many-valued logics. We provide a unified diagnosis of semantic and soritical paradoxes, identifying their source in a general form of indiscernibility. We then develop our diagnosis into a theory of paradoxicality, which formalizes both semantic and soritical paradoxes as arguments involving specific instances of our generalized indiscernibility principle, and correctly predicts which logics can non-trivially solve them.","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135094639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Logic-Sensitivity and Bitstring Semantics in the Square of Opposition 对当方阵中的逻辑敏感性和位串语义
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-10-06 DOI: 10.1007/s10992-023-09723-6
Lorenz Demey, Stef Frijters
{"title":"Logic-Sensitivity and Bitstring Semantics in the Square of Opposition","authors":"Lorenz Demey, Stef Frijters","doi":"10.1007/s10992-023-09723-6","DOIUrl":"https://doi.org/10.1007/s10992-023-09723-6","url":null,"abstract":"","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"243 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134944294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Logical Multilateralism 多边主义逻辑
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-09-25 DOI: 10.1007/s10992-023-09720-9
Heinrich Wansing, Sara Ayhan
{"title":"Logical Multilateralism","authors":"Heinrich Wansing, Sara Ayhan","doi":"10.1007/s10992-023-09720-9","DOIUrl":"https://doi.org/10.1007/s10992-023-09720-9","url":null,"abstract":"Abstract In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives.","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135768896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Abduction as Deductive Saturation: a Proof-Theoretic Inquiry 溯因作为演绎饱和:一个证明理论的探讨
1区 哲学
JOURNAL OF PHILOSOPHICAL LOGIC Pub Date : 2023-09-15 DOI: 10.1007/s10992-023-09718-3
Mario Piazza, Gabriele Pulcini, Andrea Sabatini
{"title":"Abduction as Deductive Saturation: a Proof-Theoretic Inquiry","authors":"Mario Piazza, Gabriele Pulcini, Andrea Sabatini","doi":"10.1007/s10992-023-09718-3","DOIUrl":"https://doi.org/10.1007/s10992-023-09718-3","url":null,"abstract":"Abstract Abductive reasoning involves finding the missing premise of an “unsaturated” deductive inference, thereby selecting a possible explanans for a conclusion based on a set of previously accepted premises. In this paper, we explore abductive reasoning from a structural proof-theory perspective. We present a hybrid sequent calculus for classical propositional logic that uses sequents and antisequents to define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as explanans when presented with an abductive problem. Specifically, we show that this set may not include the deductively minimal hypothesis due to the presence of redundant information. We also establish that the set of all analytic hypotheses exhausts all possible solutions to the given problem. Finally, we propose a deductive criterion for differentiating between the best explanans candidates and other hypotheses.","PeriodicalId":51526,"journal":{"name":"JOURNAL OF PHILOSOPHICAL LOGIC","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135396382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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