
2Involutive Weak uassociative Fuzzy Logic WAuIBULCHUL HAK SA SANG  Journal of Philosophical Ideas 92 (92): 7189. 2024.약한 형식의 결합 원리를 만족하는 누승적인 미카놈에 기반한 논리 체계를 소개하고 그 체계의 유한 표준 완전성을 다룬다. 보다 구체적으로 논리 체계 WAuIBUL을 누승적 유니놈 논리 IUML의 [0, u]연속인 wau유니놈 일반화로 먼저 소개한다. 그리고 이 체계의 대수적 완전성을 다룬다. 다음으로 결합 원리 대신에 약한 u결합 원리를 만족하는 누승적 유니놈으로 누승적 wau유니놈을 소개하고 그 성질을 다룬다. 마지막으로 유한 집합 위에서 WAuIBUL의 표준 완전성을 보인다.

14Substructural Nuclear (ImageBased) Logics and Operational KripkeStyle SemanticsStudia Logica 112 (4): 805833. 2024.This paper deals with substructural nuclear (imagebased) logics and their algebraic and Kripkestyle semantics. More precisely, we first introduce a class of substructural logics with connective _N_ satisfying nucleus property, called here substructural _nuclear_ logics, and its subclass, called here substructural _nuclear imagebased_ logics, where _N_ further satisfies homomorphic image property. We then consider their algebraic semantics together with algebraic characterizations of those log…Read more

12ItUML and EstevaGodostyle standard completenessCHUL HAK SA SANG  Journal of Philosophical Ideas 89 (89): 341357. 2023.

10Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid LogicsStudia Logica 111 (3): 501519. 2023.In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the socalled subdirect representation and varieties theorems, and of Mal’cev’s quasivarieties theorem. More precisely, we first recall the class of implicational tonoid logics. Next, we establish the subdirect product representation theorem for those logics and then consider some more related results such as completeness. Thirdly, we consider the varieties theorem for them. Finally, we …Read more

17Implicational Partial Galois Logics: Relational SemanticsLogica Universalis 15 (4): 457476. 2021.Implicational tonoid logics and their relational semantics have been introduced by Yang and Dunn. This paper extends this investigation to implicational partial Galois logics. For this, we first define some implicational partial gaggle logics as special kinds of implicational tonoid logics called “implicational partial Galois logics.” Next, we provide Routley–Meyerstyle relational semantics for finitary those logics.

26Implicational Tonoid Logics: Algebraic and Relational SemanticsLogica Universalis 15 (4): 435456. 2021.This paper combines two classes of generalized logics, one of which is the class of weakly implicative logics introduced by Cintula and the other of which is the class of gaggle logics introduced by Dunn. For this purpose we introduce implicational tonoid logics. More precisely, we first define implicational tonoid logics in general and examine their relation to weakly implicative logics. We then provide algebraic semantics for implicational tonoid logics. Finally, we consider relational semanti…Read more

17Nilpotent Minimum Logic NM and PretabularityBulletin of the Section of Logic 49 (1). 2020.This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM, and examine the relationships between NMnfp and the another known extended system NM—. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.

121R and Relevance Principle RevisitedJournal of Philosophical Logic 42 (5): 767782. 2013.This paper first shows that some versions of the logic R of Relevance do not satisfy the relevance principle introduced by Anderson and Belnap, the principle of which is generally accepted as the principle for relevance. After considering several possible (but defective) improvements of the relevance principle, this paper presents a new relevance principle for (three versions of) R, and explains why this principle is better than the original and others

18RoutelyMeyer Semantics for some weak Boolean Logics, and some TranslationsLogic Journal of the IGPL 12 (5): 355369. 2004.In this paper we investigate some logics with weak Boolean negation , calling wB logics, obtained by dualizing intuitionistic negation . We first provide RoutleyMeyer semantics for wBIC , its neighbors wBLC, wBLC* ), and wBS4, wBS4c . We give completeness for each of them by using RM semantics. We next provide RM semantics for IC, the Dummett's LC, the wBS4 with ¬ in place of − , and the pBS4 with c , and give completeness for each system. Finally, we give a translation of the classical …Read more

75Algebraic KripkeStyle Semantics for Relevance LogicsJournal of Philosophical Logic 43 (4): 803826. 2014.This paper deals with one kind of Kripkestyle semantics, which we shall call algebraic Kripkestyle semantics, for relevance logics. We first recall the logic R of relevant implication and some closely related systems, their corresponding algebraic structures, and algebraic completeness results. We provide simpler algebraic completeness proofs. We then introduce various types of algebraic Kripkestyle semantics for these systems and connect them with algebraic semantics

86Substructural FuzzyRelevance LogicNotre Dame Journal of Formal Logic 56 (3): 471491. 2015.This paper proposes a new topic in substructural logic for use in research joining the fields of relevance and fuzzy logics. For this, we consider old and new relevance principles. We first introduce fuzzy systems satisfying an old relevance principle, that is, Dunn’s weak relevance principle. We present ways to obtain relevant companions of the weakeningfree uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The a…Read more

Fourvalued Kripkestyle semantics for some neighbors of E, R, TLogique Et Analyse 52 (207): 255280. 2009.

16Threevalued Kripkestyle Semantics For Pseudo And Weakboolean LogicsLogic Journal of the IGPL 20 (1): 187206. 2012.This article investigates Kripkestyle semantics for two sorts of logics: pseudoBoolean and weakBoolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the threevalued Dummett–Gödel logic; S53pB is the modal logic S5 but with its orthonegation replaced by a pB negation. Examples of wB logic are G3wB and S53wB.G3wB is G3 with a wB negation in place of its pB negation; S53wB is S5 with a wB negation replacing its orthonegation. For each system, we provide a threevalued Kripke…Read more
Areas of Specialization
Science, Logic, and Mathematics 
Areas of Interest
Science, Logic, and Mathematics 