Abstract sequent axiomatizations of finitary universal Horn theories Abstract Proof Theory versus General Algebraic Logic
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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
| Publisher Name | Independently Published |
|---|---|
| Author Name | Hagendorf, Col |
| Format | Audio |
| Bisac Subject Major | MAT |
| Language | NG |
| Isbn 10 | 1794595546 |
| Isbn 13 | 9781794595545 |
| Target Age Group | min:NA, max:NA |
| Dimensions | 00.90" H x 20.05" L x 98.00" W |
| Page Count | 80 |
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