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Abstract General Algebraic Logic
Abstract General Algebraic Logic
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Here, we develop foundations of Abstract General Algebraic Logiс upon the basis of the conceptions of abstract languages, calculi and translations.We mainly concentrate on advanced appilcations of it to many-place sequent calculi over abstract languages extending various important results previously obtained for either formal or many-sorted first-order languages to abstract ones. This, in particular, concerns the issues of fuzzy semantics(especially, not necessarily distributive one for t…

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Here, we develop foundations of Abstract General Algebraic Logiс upon the basis of the conceptions of abstract languages, calculi and translations.We mainly concentrate on advanced appilcations of it to many-place sequent calculi over abstract languages extending various important results previously obtained for either formal or many-sorted first-order languages to abstract ones. This, in particular, concerns the issues of fuzzy semantics(especially, not necessarily distributive one for two-side ortho-structural rules) and deduction theorem for multiplicative calculi with structural rules.Among other things, the abstract framework elaborated here provides a perfectly formal view onto both sequent calculi with places as finite sets and their algebraization.

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Here, we develop foundations of Abstract General Algebraic Logiс upon the basis of the conceptions of abstract languages, calculi and translations.We mainly concentrate on advanced appilcations of it to many-place sequent calculi over abstract languages extending various important results previously obtained for either formal or many-sorted first-order languages to abstract ones. This, in particular, concerns the issues of fuzzy semantics(especially, not necessarily distributive one for two-side ortho-structural rules) and deduction theorem for multiplicative calculi with structural rules.Among other things, the abstract framework elaborated here provides a perfectly formal view onto both sequent calculi with places as finite sets and their algebraization.

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