An Axiomatic Extension of the Uninorm Logic Revisited
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In this paper, we show that the standard completeness for the extension of UL with compensation-free reinforcement (cfr) ((φ & ψ) → (φ ∧ ψ)) ∨ ((φ ∨ ψ) → (φ & ψ)) can be established. More exactly, first, the compensation-freely reinforced uninorm logic ULcfr (the UL with (cfr)) is introduced. The algebraic structures of ULcfr are then defined, and its algebraic completeness is established. Next, standard completeness (i.e. completeness on [0, 1]) is established for ULcfr by using the method introduced in Yang (2009).
Abstract
In this paper, we show that the standard completeness for the extension of UL with compensation-free reinforcement (cfr) ((φ & ψ) → (φ ∧ ψ)) ∨ ((φ ∨ ψ) → (φ & ψ)) can be established. More exactly, first, the compensation-freely reinforced uninorm logic ULcfr (the UL with (cfr)) is introduced. The algebraic structures of ULcfr are then defined, and its algebraic completeness is established. Next, standard completeness (i.e. completeness on [0, 1]) is established for ULcfr by using the method introduced in Yang (2009).
참고문헌 (12)
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- 양은석, "On the Standard Completeness of an Axiomatic Extension of the Uninorm Logic", 논리연구, 12(2), pp.115~139 (2009), 한국논리학회
- 양은석, "Standard Completeness for the Weak Uninorm Mingle Logic WUML", 논리연구, 14(1), pp.55~75 (2011), 한국논리학회
- 양은석, "MTL의 표준 완전성", 논리연구, 16(3), pp.437~452 (2013), 한국논리학회