Interpolation and the projective Beth property in well-composed logics
| Autor: | Larisa Maksimova |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Discrete mathematics
Class (set theory) Pure mathematics Property (philosophy) Logic ComputerApplications_COMPUTERSINOTHERSYSTEMS Decidability TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Computer Science::Logic in Computer Science Minimal logic Representation (mathematics) Beth definability Analysis Axiom Mathematics Interpolation |
| Zdroj: | Algebra and Logic. 51:163-184 |
| ISSN: | 1573-8302 0002-5232 |
| Popis: | We study the interpolation and Beth definability problems in propositional extensions of minimal logic J. Previously, all J-logics with the weak interpolation property (WIP) were described, and it was proved that WIP is decidable over J. In this paper, we deal with so-called well-composed J-logics, i.e., J-logics satisfying an axiom (⊥ → A) ∨ (A → ⊥). Representation theorems are proved for well-composed logics possessing Craig’s interpolation property (CIP) and the restricted interpolation property (IPR). As a consequence, we show that only finitely many well-composed logics share these properties and that IPR is equivalent to the projective Beth property (PBP) on the class of well-composed J-logics. |
| Databáze: | OpenAIRE |
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