논리연구 (Korean Journal of Logic)

한국논리학회 (Korean Association for Logic)
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누승적 미아놈 논리 IMIAL의 몇몇 공리적 확장

Some axiomatic extensions of the involutive mianorm Logic IMIAL

  • 양은석 (전북대학교 철학과, 비판적사고와논술연구소)
  • Yang, Eunsuk (Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University)
  • 투고 : 2017.07.24
  • 심사 : 2017.09.17
  • 발행 : 2017.10.31
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초록

이 글에서 우리는 누승적 미아놈 논리 IMIAL의 몇몇 공리적 확장 체계의 표준 완전성을 다룬다. 이를 위하여, 먼저 누승적 미아놈에 바탕을 둔 일곱 개의 논리 체계를 소개한다. 각 체계에 상응하는 대수적 구조를 정의한 후, 이들 체계가 대수적으로 완전하다는 것을 보인다. 다음으로, 이 논리 체계들 중 네 체계가 표준적으로 완전하다는 것 즉 단위 실수 [0, 1]에서 완전하다는 것을 제네이-몬테그나 방식의 구성을 사용하여 보인다.

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.

키워드

참고문헌

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