Pub Date : 2023-11-15DOI: 10.1007/s11787-023-00340-0
Alexander De Klerck, Leander Vignero, L. Demey
{"title":"Morphisms Between Aristotelian Diagrams","authors":"Alexander De Klerck, Leander Vignero, L. Demey","doi":"10.1007/s11787-023-00340-0","DOIUrl":"https://doi.org/10.1007/s11787-023-00340-0","url":null,"abstract":"","PeriodicalId":48558,"journal":{"name":"Logica Universalis","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139275871","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}
Pub Date : 2023-11-07DOI: 10.1007/s11787-023-00341-z
Alex Citkin, Alexei Muravitsky
{"title":"Preface to the Rejection Special Issue","authors":"Alex Citkin, Alexei Muravitsky","doi":"10.1007/s11787-023-00341-z","DOIUrl":"https://doi.org/10.1007/s11787-023-00341-z","url":null,"abstract":"","PeriodicalId":48558,"journal":{"name":"Logica Universalis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475497","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}
Pub Date : 2023-09-23DOI: 10.1007/s11787-023-00339-7
Urszula Wybraniec-Skardowska
Abstract Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation Cn (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations $$Cn^+$$ Cn+ ( $$Cn^+ = Cn$$ Cn+=Cn ) and dual consequences $$Cn^{-1}$$ Cn-1 (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and $$Cn^-$$ Cn- (Wójcicki in Bull Sect Log 2(2):54–57, 1973)).
逻辑和哲学文献提供了不同的推理分类。例如，在波兰关于这一主题的文献中，利沃夫-华沙学派的代表接受了三个流行的说法:Jan Łukasiewicz, Tadeusz Czeżowski和Kazimierz Ajdukiewicz (Ajdukiewicz In Logika pragmatyczna[语用逻辑])。华沙PWN(1965年，第2版。1974年)。译为:语用逻辑。赖德尔＆;PWN，多德雷赫特，1975年)。本文的作者对这些分类进行了修改，区分了以下类型的推理:(1)演绎推理和(2)非演绎推理，并根据它们的前提与结论通过经典逻辑蕴涵关系结合的方式，在这两种推理中分别增加了两种类型。因此，四种推理类型:单边演绎(包括其子类型:演绎推理和证明)，双边演绎(包括完全归纳)，还原(包括子类型:解释和验证)，逻辑无价值(包括类比推理，统计推理)，对应于四个可导算子。它们是在Tarski演绎系统的公理化理论的基础上，通过推论运算Cn正式定义的(Tarski in Monatshefte Math - Phys 37:31 61 - 404, 1930a, C R社会科学，Vars 23:22 - 29,1930b)。此外，还给出了这些算子的某些元学性质，以及它们与Tarski推论运算$$Cn^+$$ C n + ($$Cn^+ = Cn$$ C n + = C n)和对偶结果$$Cn^{-1}$$ C n - 1 (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33-40, 1959, Słupecki等人在Stud Log 29:76-123, 1971, wybraniecskardowska, in:wybraniek - skardowska, Bryll(编)Z badazinad teoriozdaiodrzuconych[在拒绝命题理论的研究]，系列B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969)，和$$Cn^-$$ C n - (Wójcicki在公牛节日志2(2):54-57,1973))。
{"title":"Operator Counterparts of Types of Reasoning","authors":"Urszula Wybraniec-Skardowska","doi":"10.1007/s11787-023-00339-7","DOIUrl":"https://doi.org/10.1007/s11787-023-00339-7","url":null,"abstract":"Abstract Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: unilateral deductive (incl. its sub-types: deductive inference and proof), bilateral deductive (incl. complete induction), and reductive (incl. the sub-types: explanation and verification), logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski’s axiomatic theory of deductive systems, by means of the consequence operation Cn (Tarski in Monatshefte Math Phys 37:361–404, 1930a, C R Soc Sci Lett Vars 23:22–29, 1930b). Also, certain metalogical properties of these operators are given, as well as their relations with Tarski’s consequence operations $$Cn^+$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> ( $$Cn^+ = Cn$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mi>n</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>=</mml:mo> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> ) and dual consequences $$Cn^{-1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mi>n</mml:mi> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> (Słupecki in Zeszyty Naukowe Uniwersytetu Wrocławskiego Seria B Nr 3:33–40, 1959, Słupecki et al. in Stud Log 29:76–123, 1971, Wybraniec-Skardowska, in: Wybraniec-Skardowska, Bryll (eds) Z badań nad teorią zdań odrzuconych [Studies in the Theory of Rejected Propositions], Series B, Studia i Monografie, Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Opole, 1969), and $$Cn^-$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>C</mml:mi> <mml:msup> <mml:mi>n</mml:mi> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> (Wójcicki in Bull Sect Log 2(2):54–57, 1973)).","PeriodicalId":48558,"journal":{"name":"Logica Universalis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135965228","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}
Pub Date : 2023-09-16DOI: 10.1007/s11787-023-00334-y
Alexei Muravitsky
{"title":"On Consequence and Rejection as Operators","authors":"Alexei Muravitsky","doi":"10.1007/s11787-023-00334-y","DOIUrl":"https://doi.org/10.1007/s11787-023-00334-y","url":null,"abstract":"","PeriodicalId":48558,"journal":{"name":"Logica Universalis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135304820","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}
Pub Date : 2023-09-14DOI: 10.1007/s11787-023-00338-8
Tomasz Skura
Abstract A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.
摘要给出了具有强否定的正逻辑的扩展被一类有限树所表征的一个充分条件。
{"title":"Finite Tree-Countermodels via Refutation Systems in Extensions of Positive Logic with Strong Negation","authors":"Tomasz Skura","doi":"10.1007/s11787-023-00338-8","DOIUrl":"https://doi.org/10.1007/s11787-023-00338-8","url":null,"abstract":"Abstract A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.","PeriodicalId":48558,"journal":{"name":"Logica Universalis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134911664","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}
Pub Date : 2023-09-14DOI: 10.1007/s11787-023-00337-9
Gabriele Pulcini, Achille C. Varzi
Abstract A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$textsf{CPN}$$ CPN , that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$textsf{CPN}$$ CPN enjoys strong normalization along with strong confluence (and, hence, uniqueness of normal forms).
{"title":"Complementary Proof Nets for Classical Logic","authors":"Gabriele Pulcini, Achille C. Varzi","doi":"10.1007/s11787-023-00337-9","DOIUrl":"https://doi.org/10.1007/s11787-023-00337-9","url":null,"abstract":"Abstract A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$textsf{CPN}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>CPN</mml:mi> </mml:math> , that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$textsf{CPN}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>CPN</mml:mi> </mml:math> enjoys strong normalization along with strong confluence (and, hence, uniqueness of normal forms).","PeriodicalId":48558,"journal":{"name":"Logica Universalis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134911666","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}
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