MV-algebra extended
نویسنده
چکیده
In this paper, we propose extensions of affine classical linear algebra(ACL-algebra) and many-valued algebra(MV-algebra), the emphasis is being on the latter. MV-algebras are algebraic models of à Lukasiewicz א0-valued logic(à Lא0) and that was established long back in 1958 by C.C. Chang. MV-algebra is recently studied from the angle of fuzzy set theory. Also it is investigated in connection with substructural logics. CL-algebras are algebraic models of multiplicative additive fragment of linear logic(MALL). Linear logic was introduced by J. -Y. Girard and in A.S. Troelstra’s terms ‘is interesting from a logical point of view, and potentially of considerable interest for computer science’. Affine CL-algebra is a special case of CL-algebra. Logic corresponding to this algebra is MALL with one structural rule weakening. Interconnection between à Lukasiewicz logic, linear logic and other substructural logics has been an important topic of research in recent years [1].
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