Name
Abstract | ||
|---|---|---|
In this article we investigate infinitary propositional logics from the perspective of their completeness properties in abstract algebraic logic. It is well-known that every finitary logic is complete with respect to its relatively (finitely) subdirectly irreducible models. We identify two syntactical notions formulated in terms of (completely) intersection-prime theories that follow from finitarity and are sufficient conditions for the aforementioned completeness properties. We construct all the necessary counterexamples to show that all these properties define pairwise different classes of logics. Consequently, we obtain a new hierarchy of logics going beyond the scope of finitarity. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s11225-016-9699-3 | Studia Logica |
Keywords | Field | DocType |
Abstract algebraic logic,Consequence relations,Infinitary logics,Completeness properties | Discrete mathematics,T-norm fuzzy logics,Łukasiewicz logic,Algebra,Algebraic logic,Classical logic,Monoidal t-norm logic,Principle of bivalence,Abstract algebraic logic,Intermediate logic,Mathematics | Journal |
Volume | Issue | ISSN |
105 | 3 | 0039-3215 |
Citations | PageRank | References |
2 | 0.39 | 7 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tomás Lávicka | 1 | 2 | 0.73 |
| Carles Noguera | 2 | 462 | 33.93 |