Abstract General Algebraic Logic

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.