• Korean Journal of Logic
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• v.23 no.1
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• pp.1-23
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• 2020

This paper deals with mianorm-based logics with right and left n-potency axioms and their fixpointed involutive extensions. For this, first, right and left n-potent logic systems based on mianorms, their corresponding algebraic structures, and their algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0, 1], known as standard completeness, is established for these systems via Yang's construction in the style of Jenei-Montagna. Finally, further standard completeness results are introduced for their fixpointed involutive extensions.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1998.10a
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• pp.607-610
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• 1998

• 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.