• Korean Journal of Logic
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• v.17 no.1
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• pp.197-217
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• 2014

In my previous papers, I have argued that the so-called 'Uncontested Principle' does not hold for indicative conditionals based on inductive reasoning. This is mainly because if we accept that a material conditional '$A{\supset}C$' can be inferred from an indicative conditional based on inductive reasoning '$A{\rightarrow}_iC$', we get an absurd consequence such that we cannot distinguish between claiming 'C' to be probably true and claiming 'C' to be absolutely true on the assumption 'A'. However, in his recent paper "Uncontested Principle and Inductive Argument", Eunsuk Yang objects that my argument is unsuccessful in disputing the Uncontested Principle. In this paper, I show that his objections are irrelevant to my argument against the Uncontested Principle.

• 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.20 no.2
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• pp.273-292
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• 2017

In this paper, we deal with some axiomatic extensions of the involutive micanorm logic IMICAL. More precisely, first, the two involutive micanorm-based logics $P_nIMICAL$ and $FP_nIMICAL$ are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for $FP_nIMICAL$ using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.15 no.3
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• pp.323-347
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• 2012

After Byeongdeok Lee(2008) argued against the so-called uncontested principle (UP), Song(2008) and Choi(2011) gave arguments against Lee(2008) and instead for UP. One important point to mention in their arguments is that they all accept that UP is justifiable in deduction. First, I show that there are some problems in their arguments. Next, I show that UP itself is not justifiable in deduction; it is only justifiable under some (restrictive) conditions.

• Korean Journal of Logic
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• v.20 no.3
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• pp.313-333
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• 2017

In this paper, we deal with standard completeness of some axiomatic extensions of the involutive mianorm logic IMIAL. More precisely, first, seven involutive mianorm-based logics are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for four of them using construction in the style of Jenei-Montagna.

• Korean Journal of Logic
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• v.18 no.1
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• pp.65-83
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• 2015

This paper deals with non-algebraic Kripke-style semantics for three-valued paraconsistent logic: set-theoretical Kripke-style semantics. We first recall two three-valued paraconsistent systems. We next introduce set-theoretical Kripke-style semantics for them.

• Korean Journal of Logic
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• v.18 no.2
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• pp.197-215
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• 2015

In this paper, we deal with standard completeness of some axiomatic extensions of the involutive micanorm logic IMICAL. More precisely, first, four involutive micanorm-based logics are introduced. Their algebraic structures are then defined, and their corresponding algebraic completeness is established. Next, standard completeness is established for two of them using construction in the style of Jenei-Montagna.

• 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.3
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• pp.441-461
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• 2014

This paper deals with one sort of Kripke-style semantics for three-valued paraconsistent logic: algebraic Kripke-style semantics. We first introduce two three-valued systems, define their corresponding algebraic structures, and give algebraic completeness results for them. Next, we introduce algebraic Kripke-style semantics for them, and then connect them with algebraic semantics.

• 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.