논리연구 (Korean Journal of Logic)

한국논리학회 (Korean Association for Logic)
권호 표지

좌 우, n-멱등 공리를 갖는 미아놈 논리

Mianorm-based Logics with right and left n-potency axioms

  • 양은석 (전북대학교 철학과, 비판적사고와논술연구소)
  • Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Jeonbuk National University)
  • 투고 : 2019.11.05
  • 심사 : 2020.02.20
  • 발행 : 2020.02.29
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초록

이 글에서 우리는 좌, 우 n-멱등 공리를 갖는 미아놈에 기반한 논리를 다룬다. 이를 위하여 먼저 미아놈에 바탕을 둔 좌, 우 n-멱등 공리를 갖는 논리 체계 PrnMIAL, PlnMIAL을 소개한다. 각 체계에 상응하는 대수적 구조를 정의한 후, 이들 체계가 대수적으로 완전하다는 것을 보인다. 다음으로, 이 논리 체계들이 표준적으로 완전하다는 것 즉 단위 실수 [0, 1에서 완전하다는 것을 제네이-몬테그나 방식의 구성을 사용하여 보인다. 마지막으로 이를 고정점을 갖는 누승적 확장에 대한 연구로 확대한다.

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.

키워드

참고문헌

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