• 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.

• 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.

• Korean Journal of Logic
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• v.6 no.1
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• pp.19-32
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• 2003

In this paper we investigate the relevance logic E-R of the Entailment E without the reductio (R), and its extensions Ee-R, Eec-R: Ee-R is the E-R with the expansion (e) and Eec-R the Ee-R with the chain (c). We give completeness for each E-R, Ee-R, and Eec-R by using Routley-Meyer semantics.

• Korean Journal of Logic
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• v.7 no.2
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• pp.105-120
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• 2004

In this paper, we provide Routley-Meyer semantics for the many-valued logics ${\L}C$ and LC, and give completeness for each of them. This result shows the following two: 1) Routley-Meyer semantics is very powerful in the sense that it can be used as the semantics for several sorts of logics, i.e., many-valued logic, not merely relevance logic and substructural logic. Note that each implication of ${\L}C$ and LC does not (partially) result in "paradoxes of material implication" 2) This implies that Routley-Meyer semantics can be also used not merely for relevance systems but also for other logical systems such as ${\L}C$ and LC, each of which has its own implication by which we can overcome (partially) the problem of "paradoxes of material implication".