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
- | Publisher: Independently published
- | Publication Date: Jan 22, 2019
- | Number of Pages: 78 pages
- | Language: English
- | Binding: Paperback
- | ISBN-10: 1794595546
- | ISBN-13: 9781794595545
