• 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.

• Korean Journal of Logic
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• v.16 no.3
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• pp.381-406
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• 2013

This paper deals with the question whether the para-completeness theory of Kripkian style can avoid the revenge problem. According to the para-completeness theory, there are some sentences that are neither true nor false. And the liar sentence is the exemplar of such sentences. But the para-completeness theory has been criticised to give rise to the revenge problem, since Kripke suggested his theory. Maudlin argues that he can construct the para-completeness theory which avoids the problem by appealing to his foundationalist semantics. The aim of this paper shows that the para-completeness theory, including Maudlin's, cannot avoid the problem. Furthermore, it is argued that Maudlin's view is ad hoc suggestion just to avoid the problem.

• Korean Journal of Logic
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• v.21 no.3
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• pp.353-371
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• 2018

This paper deals with Routley-Meyer-style semantics, which will be called algebraic Routley-Meyer-style semantics, for the fuzzy logic system MTL. First, we recall the monoidal t-norm logic MTL and its algebraic semantics. We next introduce algebraic Routley-Meyer-style semantics for it, and also connect this semantics with algebraic semantics.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1521-1536
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• 2017

This paper introduces a representation style of variable binding using dependent types when formalizing meta-theoretic properties. The style we present is a variation of the Coquand-McKinna-Pollack's locally-named representation. The main characteristic is the use of dependent families in defining expressions such as terms and formulas. In this manner, we can handle many syntactic elements, among which wellformedness, provability, soundness, and completeness are critical, in a compact manner. Another point of our paper is to investigate the roles of free variables and constants. Our idea is that fresh constants can entirely play the role of free variables in formalizing meta-theories of first-order predicate logic. In order to show the feasibility of our idea, we formalized the soundness and completeness of LJT with respect to Kripke semantics using the proof assistant Coq, where LJT is the intuitionistic first-order predicate calculus. The proof assistant Coq supports all the functionalities we need: intentional type theory, dependent types, inductive families, and simultaneous substitution.

• Korean Journal of Logic
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• v.18 no.3
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• pp.437-456
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• 2015

This paper deals with Routley-Meyer semantics for two versions of R of Relevance. For this, first, we introduce two systems $R^t$, $R^T$ and their corresponding algebraic semantics. We next consider Routley-Meyer semantics for these systems.

• Journal of Korean Philosophical Society
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• v.116
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• pp.257-280
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• 2010

I try to formalize the system of modal logic and interpret it in view of constructivism through this study. As to the meaning of a sentence, as we saw, Frege endorsed extensions in view of the fact that they are enough to provide for a compositional account for truth, in particular that (1) the assignment of extensions to expressions is compositional ; (2) the assignment of extensions to sentences coincides with the assignment of truth values. But nobody would be willing to admit that a truth value is what a sentence means and that consequently all true sentences are synonymous. So, if what we are after is meaning in the intuitive sense, then extensions would not do. This consideration has later become the point of departure of modal and intensional semantics. So, it is clear that the language of modal logic do not allow for an extensional interpretation. ${\square}$ is syntactically on a par with ${\vdash}$, hence within the extensional framework it would have to denote a unary truth function. This means that if modal logic is to be interpreted, we need a semantics which is not extensional. The first attempt to build a feasible intensional semantics was presented by Saul Kripke. He came to the conclusion that we must let sentences denote not truth values, but rather subsets of a given set. He called elements of the underlying set possible world. Hence each sentence is taken to denote the set of those possible world in which it is true. This lets us explicate necessity as 'truth in every possible world' and possibility as 'truth in at least one possible world'. But it is clear that the system of modal logic is not only an enlargement of propositional logic, as long as the former contains the new symbols, but that it is of an other nature. In fact, the modal logic is intensional, in that the operators do not determine the functions of truth any more. But this new element is not given a priori, but a posteriori from construction by logicist.