• Korean Journal of Logic
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• v.19 no.2
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• pp.295-322
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• 2016

This paper deals with Kripke-style semantics, which will be called algebraic Kripke-style semantics, for fuzzy logics based on uninorms (so called uninorm-based logics). First, we recall algebraic semantics for uninorm-based logics. In the general framework of uninorm-based logics, we next introduce various types of general algebraic Kripke-style semantics, and connect them with algebraic semantics. Finally, we analogously consider particular algebraic Kripke-style semantics, and also connect them with algebraic semantics.

• Korean Journal of Logic
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• v.22 no.3
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• pp.397-415
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• 2019

This paper deals with the pretabular property of some fuzzy logics. For this, we first introduce the involutive idempotent uninorm logics IdIUL and IUML and examine the relationship between IdIUL and the another well-known system $RM^T$. Next, we show that IUML is pretabular, whereas IdIUL is not.

• Korean Journal of Logic
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• v.17 no.2
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• pp.323-349
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• 2014

In this paper, we show that the standard completeness for the extension of UL with compensation-free reinforcement (cfr) $(({\phi}&{\psi}){\rightarrow}({\phi}{\wedge}{\psi})){\vee}(({\phi}{\vee}{\psi}){\rightarrow}({\phi}&{\psi}))$ can be established. More exactly, first, the compensation-freely reinforced uninorm logic $UL_{cfr}$ (the UL with (cfr)) is introduced. The algebraic structures of $UL_{cfr}$ are then defined, and its algebraic completeness is established. Next, standard completeness (i.e. completeness on [0, 1]) is established for $UL_{cfr}$ by using the method introduced in Yang (2009).

• Korean Journal of Logic
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• v.19 no.3
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• pp.437-461
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• 2016

This paper investigates weakening-free fuzzy logics with three weak forms of associativity (of multiplicative conjunction &). First, the wta-uninorm (based) logic $WA_tMUL$ and its two axiomatic extensions are introduced as weakening-free weakly associative fuzzy logics. The algebraic structures corresponding to the systems are then defined, and algebraic completeness results for them are provided. Next, standard completeness is established for $WA_tMUL$ and the two axiomatic extensions with an additional axiom using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.13 no.1
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• pp.1-20
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• 2010

This paper investigates a new proof of standard completeness (i.e. completeness on the real unit interval [0, 1]) for the uninorm (based) logic UL introduced by Metcalfe and Montagna in [15]. More exactly, standard completeness is established for UL by using nuclear completions method introduced in [8, 9].

• 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.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.14 no.1
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• pp.55-76
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• 2011

Fixed-point conjunctive left-continuous idempotent uninorms have been introduced (see e.g. [2, 3]). This paper studies a system for such uninorms. More exactly, one system obtainable from IUML (Involutive uninorm mingle logic) by dropping involution (INV), called here WUML (Weak Uninorm Mingle Logic), is first introduced. This is the system of fixed-point conjunctive left-continuous idempotent uninorms and their residua with weak negation. Algebraic structures corresponding to the system, i.e., WUML-algebras, are then defined, and algebraic completeness is provided for the system. Standard completeness is further established for WUML and IUML in an analogy to that of WNM (Weak nilpotent minimum logic) and NM (Nilpotent minimum logic) in [4].

• 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.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.