18 found
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  1. R and Relevance Principle Revisited.Eunsuk Yang - 2013 - Journal of Philosophical Logic 42 (5):767-782.
    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.
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  2. Fuzzy R Systems and Algebraic Routley-Meyer Semantics.Eunsuk Yang - 2022 - Korean Journal of Logic 25 (3):313-332.
    Here algebraic Routley-Meyer semantics is addressed for two fuzzy versions of the logic of relevant implication R. To this end, two versions R t and R T of R and their fuzzy extensions FRt and FRT , respectively, are first discussed together with their algebraic semantics. Next algebraic Routley-Meyer semantics for these two fuzzy extensions is introduced. Finally, it is verified that these logics are sound and complete over the semantics.
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  3.  32
    Implicational Tonoid Logics: Algebraic and Relational Semantics.Eunsuk Yang & J. Michael Dunn - 2021 - Logica Universalis 15 (4):435-456.
    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 semantics, called Routley–Meyer–style semantics, for finitary those (...)
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  4.  22
    Three-valued Kripke-style Semantics For Pseudo- And Weak-boolean Logics.Eunsuk Yang - 2012 - Logic Journal of the IGPL 20 (1):187-206.
    This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean and weak-Boolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the three-valued 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 three-valued (...)
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  5.  82
    Algebraic Kripke-Style Semantics for Relevance Logics.Eunsuk Yang - 2014 - Journal of Philosophical Logic 43 (4):803-826.
    This paper deals with one kind of Kripke-style semantics, which we shall call algebraic Kripke-style 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 Kripke-style semantics for these systems and connect them with algebraic semantics.
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  6.  27
    Implicational Partial Galois Logics: Relational Semantics.Eunsuk Yang & J. Michael Dunn - 2021 - Logica Universalis 15 (4):457-476.
    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–Meyer-style relational semantics for finitary those logics.
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  7. Implicational Partial Gaggle Logics and Matrix Semantics.Eunsuk Yang - 2023 - Korean Journal of Logic 26 (2):131-144.
    Implicational tonoid logics and their extensions with abstract Galois properties have been introduced by Yang and Dunn. They introduced matrix semantics for the implicational tonoid logics but did not do for the extensions. Here we provide such semantics for implicational partial gaggle logics as one sort of such extensions. To this end, first we discuss implicational partial gaggle logics in Hilbert-style. We next introduce one kind of matrix semantics based on Lindenbaum– Tarski matrices for the logics and show that those (...)
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  8. Relational Semantics for Fuzzy Extensions of R : Set-theoretic Approach.Eunsuk Yang - 2023 - Korean Journal of Logic 26 (1):77-93.
    This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and R T of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and R T, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way.
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  9.  95
    Substructural Fuzzy-Relevance Logic.Eunsuk Yang - 2015 - Notre Dame Journal of Formal Logic 56 (3):471-491.
    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 weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The algebraic structures corresponding to (...)
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  10.  19
    Involutive Weak u-associative Fuzzy Logic WAuIBUL.Eunsuk Yang - 2024 - CHUL HAK SA SANG - Journal of Philosophical Ideas 92 (92):71-89.
    An involutive micanorm-based logic with a weak form of associativity is introduced and its finite standard completeness is addressed. More precisely, we first introduce the logic WAuIBUL as a [0, u]-continuous wau-uninorm analogue of the involutive logic IBUL. We next discuss its algebraic semantics. We then introduce involutive wau-uninorms as involutive uninorms with weak u-associativity in place of associativity and deal with related properties. We last provide finite strong standard completeness for WAuIBUL using a construction of Yang-style. -/- 약한 형식의 (...)
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  11.  28
    Substructural Nuclear (Image-Based) Logics and Operational Kripke-Style Semantics.Eunsuk Yang - 2024 - Studia Logica 112 (4):805-833.
    This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style 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 image-based_ logics, where _N_ further satisfies homomorphic image property. We then consider their algebraic semantics together with algebraic characterizations of those logics. Finally, we introduce _operational Kripke-style_ semantics for those logics and provide two sorts of completeness results for (...)
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  12.  21
    ItUML and Esteva-Godo-style standard completeness.Eunsuk Yang - 2023 - CHUL HAK SA SANG - Journal of Philosophical Ideas 89 (89):341-357.
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  13.  19
    Birkhoff’s and Mal’cev’s Theorems for Implicational Tonoid Logics.Eunsuk Yang - 2023 - Studia Logica 111 (3):501-519.
    In the context of implicational tonoid logics, this paper investigates analogues of Birkhoff’s two theorems, the so-called subdirect representation and varieties theorems, and of Mal’cev’s quasi-varieties 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 introduce an analogue of Mal’cev’s quasi-varieties theorem for algebras.
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  14.  4
    Fixed-pointed Involutive Micanorm-based Logics.Eunsuk Yang - 2022 - Korean Journal of Logic 25 (2):121-137.
    This paper considers standard completeness for fixed-pointed involutive micanorm-based logics. For this, we first discuss fixed-pointed involutive micanorm-based logics together with their algebraic semantics. Next, after introducing some examples of fixed-pointed involutive micanorms, we provide standard completeness results for those logics.
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  15. four-valued Kripke-style semantics for some neighbors of E, R, T.Eunsuk Yang - 2009 - Logique Et Analyse 52 (207):255-280.
  16.  21
    Nilpotent Minimum Logic NM and Pretabularity.Eunsuk Yang - 2020 - Bulletin of the Section of Logic 49 (1).
    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.
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  17.  26
    Routely-Meyer Semantics for some weak Boolean Logics, and some Translations.Eunsuk Yang - 2004 - Logic Journal of the IGPL 12 (5):355-369.
    In this paper we investigate some logics with weak Boolean negation , calling wB logics, obtained by dualizing intuitionistic negation . We first provide Routley-Meyer semantics for wB-IC , its neighbors wB-LC, wB-LC* ), and wB-S4, wB-S4c . We give completeness for each of them by using RM semantics. We next provide RM semantics for IC, the Dummett's LC, the wB-S4 with ¬ in place of − , and the pB-S4 with c , and give completeness for each system. Finally, (...)
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  18.  39
    Tr, te-r, tec-r.Eunsuk Yang - 2002 - Bulletin of the Section of Logic 31 (3):171-181.
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