• Korean Journal of Logic
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• v.11 no.2
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• pp.171-197
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• 2008

In this paper we deal with new standard completeness proofs of some systems introduced by Metcalfe and Montagna in [10]. For this, this paper investigates several fuzzy-relevance logics, which can be regarded as neighbors of the R of Relevance with mingle (RM). First, the monoidal uninorm idempotence logic MUIL, which is intended to cope with the tautologies of left-continuous conjunctive idempotent uninorms and their residua, and some schematic extensions of it are introduced as neighbors of RM. The algebraic structures corresponding to them are defined, and standard completeness, completeness on the real unit interval [0, 1], results for them are provided.

• Korean Journal of Logic
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• v.21 no.1
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• pp.39-57
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• 2018

This paper deals with non-algebraic Kripke-style semantics, i.e, set-theoretical Kripke-style semantics, for weakening-free non-commutative fuzzy logics. We first recall an extension of the pseudo-uninorm based fuzzy logic HpsUL, $CnHpsUL^*$. We next introduce set-theoretical Kripke-style semantics for it.

• Korean Journal of Logic
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• v.17 no.1
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• pp.181-196
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• 2014

This paper deals with Kripke-style semantics for fuzzy logics. More exactly, I introduce algebraic Kripke-style semantics for some weakening-free extensions of the uninorm based fuzzy logic UL. For this, first, I introduce several weakening-free extensions of UL, define their corresponding algebraic structures, and give algebraic completeness. Next, I introduce several algebraic Kripke-style semantics for those systems, and connect these semantics with algebraic semantics.

• Korean Journal of Logic
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• v.16 no.1
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• pp.1-15
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• 2013

Yang [12] investigated weakening-free fuzzy logics expanded by the delta connective $\Delta$, which can be interpreted as Baaz's projection and its generalizations. In this paper, we keep investigating such logics with an alternative delta connective $\Delta$, which can be regarded as a variant of the Baaz projection. The main difference is that although our new $\Delta$ satisfies many properties of Baaz projection, it can nether be interpreted as Baaz's projection itself nor its generalizations. For this, we first introduce several weakening-free fuzzy logics with the alternative connective $\Delta$. The algebraic structures corresponding to the systems are then defined, and their algebraic completeness is proved.

• Korean Journal of Logic
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• v.19 no.1
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• pp.107-126
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• 2016

This paper deals with Kripke-style semantics for weakening-free non-commutative fuzzy logics. As an example, we consider an algebraic Kripke-style semantics for an extension of the pseudo-uninorm based fuzzy logic HpsUL, $CnHpsUL^*$. For this, first, we recall the system $CnHpsUL^*$, define its corresponding algebraic structures $CnHpsUL^*$-algebras, and algebraic completeness results for it. We next introduce a Kripke-style semantics for $CnHpsUL^*$, and connect it with algebraic semantics.