Equivalential Universal Horn Theories: Algebraic Systems Versus Pure Algebras Within General Algebraic Logic (Paperback) (ISBN-13: 9781794517554)

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

Author: Alexej P. Pynko
ISBN-10: 1794517553
ISBN-13: 9781794517554
Publisher: Independently Published
Language: English
Published: 01/21/2019
Pages: 72
Format: Paperback
Weight: 0.24lbs
Size: 9.02h x 5.98w x 0.15d