On the Standard Completeness of an Axiomatic Extension of the Uninorm Logic
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This paper investigates an extension of the uninorm (based) logic UL, which is obtained by adding (t-weakening, Wt) ((φ & ψ) ∧ t) → φ to UL introduced by Metcalfe and Montagna in [8]. First, the t-weakening uninorm logic ULWt (the UL with Wt) is introduced. The algebraic structures corresponding to ULWt is then defined, and its algebraic completeness is established. Next standard completeness (i.e. completeness on the real unit interval [0, 1]) is established for this logic by using Jenei and Montagna-style approach for proving standard completeness in [3, 6].
Abstract
This paper investigates an extension of the uninorm (based) logic UL, which is obtained by adding (t-weakening, Wt) ((φ & ψ) ∧ t) → φ to UL introduced by Metcalfe and Montagna in [8]. First, the t-weakening uninorm logic ULWt (the UL with Wt) is introduced. The algebraic structures corresponding to ULWt is then defined, and its algebraic completeness is established. Next standard completeness (i.e. completeness on the real unit interval [0, 1]) is established for this logic by using Jenei and Montagna-style approach for proving standard completeness in [3, 6].
참고문헌 (10)
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