Abstract sequent axiomatizations of finitary universal Horn theories: Abstract Proof Theory versus General Algebraic Logic - Softcover

Pynko, Dr Alexej P.

Softcover

ISBN 10: 1794595546 ISBN 13: 9781794595545

Publisher: Independently published, 2019

Synopsis

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.

Edition details

• Publisher: Independently published
• Publication date: 2019
• Language: English
• ISBN 10: 1794595546
• ISBN 13: 9781794595545
• Binding: Paperback
• Number of pages: 78