{"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}
{"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}
{"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}
{"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}
{"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}
{"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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