{"product_id":"equivalential-universal-horn-theories-alexej-p-pynko-9781794517554","title":"Equivalential Universal Horn Theories: Algebraic Systems Versus Pure Algebras Within General Algebraic Logic","description":"As a peliminary point, we start from extending Mal'cev's conceptof rational equivalence of prevarieties ofpure algebras to those of algebraic systemsjustifying this extension by a Mal'cev-stylecategorical characterization.Next, we extend the concept of equivalentpurely-algebraic semantics, being a prevariety ofpure algebras, to prevarieities of algebraic systems.In this way, the concept of equivalential UHTarises as the respective extension of the oneof algebraizable UHT, each equivalential UHT having a unique(modulo rational equivalence) equivalentalgebraic semantics.We then apply our general theory of equivalence ofuniversal Horn theories to reducing the problemof finding extensions of an equivalential UHT to thatof finding subprevarieties of its equivalent algebraic semantics.Our general elaboration is well-applicable tosequent calculi with structural rules assiciated with finitely-valued logics with equality determinantknown to be equivalential.Finally, we exemplify our general study by exploringfour examples of non-algebraizable sequent calculiof such a kind, one of them being equivalent tothe corresponding sentential logic\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Alexej P. Pynko\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 1794517553\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9781794517554\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\/21\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 72\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.24lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.02h x 5.98w x 0.15d","brand":"Alexej P. Pynko","offers":[{"title":"Paperback","offer_id":48136902934783,"sku":"9781794517554","price":6.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_0b5c916b-8799-4a45-a908-dd2c3bc58219.jpg?v=1770165220","url":"https:\/\/www.whiterainbookhouse.com\/products\/equivalential-universal-horn-theories-alexej-p-pynko-9781794517554","provider":"WR Book House","version":"1.0","type":"link"}