Abstract sequent axiomatizations of finitary universal Horn theories: Abstract Proof Theory versus General Algebraic Logic (Paperback) (ISBN-13: 9781794595545)

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

Author: Alexej P. Pynko
ISBN-10: 1794595546
ISBN-13: 9781794595545
Publisher: Independently Published
Language: English
Published: 01/22/2019
Pages: 80
Format: Paperback
Weight: 0.26lbs
Size: 9.02h x 5.98w x 0.17d