•  6
    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. Fin…Read more
  •  8
    ItUML and Esteva-Godo-style standard completeness
    CHUL HAK SA SANG - Journal of Philosophical Ideas 89 (89): 341-357. 2023.
  •  5
    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 …Read more
  •  14
    Implicational Partial Galois Logics: Relational Semantics
    Logica Universalis 15 (4): 457-476. 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–Meyer-style relational semantics for finitary those logics.
  •  19
    Implicational Tonoid Logics: Algebraic and Relational Semantics
    Logica Universalis 15 (4): 435-456. 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
  •  11
    Nilpotent Minimum Logic NM and Pretabularity
    Bulletin 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.
  •  27
    Tr, te-r, tec-r
    Bulletin of the Section of Logic 31 (3): 171-181. 2002.
  •  113
    R and Relevance Principle Revisited
    Journal of Philosophical Logic 42 (5): 767-782. 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
  •  11
    Routely-Meyer Semantics for some weak Boolean Logics, and some Translations
    Logic Journal of the IGPL 12 (5): 355-369. 2004.
    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, we give a translation of the classical …Read more
  •  67
    Algebraic Kripke-Style Semantics for Relevance Logics
    Journal of Philosophical Logic 43 (4): 803-826. 2014.
    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
  •  83
    Substructural Fuzzy-Relevance Logic
    Notre Dame Journal of Formal Logic 56 (3): 471-491. 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 weakening-free uninorm systems introduced by Metcalfe and Montagna and fuzzy companions of the system R of relevant implication and its neighbors. The a…Read more
  •  13
    Three-valued Kripke-style Semantics For Pseudo- And Weak-boolean Logics
    Logic Journal of the IGPL 20 (1): 187-206. 2012.
    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 Kripke…Read more