Moortgat, M. (1996b) `Labeled deduction in the composition of form and meaning '. In H.J. Ohlbach & U. Reyle (eds.) Logic, Language and Reasoning.  Home/Search   Document Details and Download   Summary   Related Articles

.... a 2 V (3(33(3iffl h) ffl d) given the definition of the canonical valuation ( For (z) we have to find b 0 ; c 0 ; d 0 ; e 0 ; f 0 such that a 3b 0 ; d 0 3e 0 ; b 0 c 0 ffl d 0 ; e 0 f 0 ffl d; c 0 3i; f 0 3h: 22 Natasha Kurtonina and Michael Moortgat Let us put f 0 = 3h; e 0 = f 0 ffl d = 3h ffl d; d 0 = 3e 0 = 3(3h ffl d) c 0 = 3i; b 0 = c 0 ffl d 0 = 3i ffl 3(3h ffl d) Together they imply a 3(3i ffl 3(3h ffl d) i.e. a 2 V (3(3i ffl 3(3h ffl d) can be shown to follow from ( Similarly for the other direction. y) a A AA ....

....see Moortgat 1995. This paper also establishes a Cut Elimination result for the language extended with 3; 2 # . Definition 0.1 Lambek style axiomatic presentation. A A A B B C A C 3A B ( A 2 # B A C=B ( A ffl B C ( B AnC 38 Natasha Kurtonina and Michael Moortgat Definition 0.2 Dosen style axiomatization. A A A B B C A C 32 # A A A 2 # 3A A=B ffl B A A (A ffl B) B B ffl BnA A A Bn(B ffl A) A B 3A 3B A B 2 # A 2 # B A B C D A=D B=C A B C D A ffl C B ffl D A B C D DnA CnB The formulations of Def 0.1 and Def ....

Moortgat, M. (1996b) `Labeled deduction in the composition of form and meaning '. In H.J. Ohlbach & U. Reyle (eds.) Logic, Language and Reasoning.

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