{"product_id":"abstract-sequent-axiomatizations-of-finitary-alexej-p-pynko-9781794595545","title":"Abstract sequent axiomatizations of finitary universal Horn theories: Abstract Proof Theory versus General Algebraic Logic","description":"Here, we introduce and study the concept of abstract sequent axiomatization of generalized logics based upon the concept of abstract derivation from absolutely free algebras to arbitrary ones. As a general result, we prove thatany logic having a deduction theorem has an equivalent abstract sequent axiomatization.Conversely, we prove that any algebraizable logic having an algebraizableabstract sequent axiomatization has a deduction theorem. As for sentential logics, we prove that any conjunctive self-extensional logic has an algebraizable abstract sequent axiomatization equivalent to the intrinsic variety of the logic.As a consequence, we prove that any algebraizable self-extensional conjunctivelogic has a deduction theorem. Finally, we explore several non-protoalgebraicsentential logics, each being proved to have an algebraizable abstract sequentaxiomatization equivalent to the intrinsic variety of the logic\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Alexej P. Pynko\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1794595546\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781794595545\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Independently Published\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 01\/22\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 80\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.26lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.02h x 5.98w x 0.17d","brand":"Alexej P. Pynko","offers":[{"title":"Paperback","offer_id":48113729732863,"sku":"9781794595545","price":150.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_d25b64be-d5a5-42a8-bfc4-eb7a7f6f0956.jpg?v=1769616935","url":"https:\/\/www.whiterainbookhouse.com\/products\/abstract-sequent-axiomatizations-of-finitary-alexej-p-pynko-9781794595545","provider":"WR Book House","version":"1.0","type":"link"}