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- Title
On structural completeness versus almost structural completeness problem: A discriminator varieties case study.
- Authors
CAMPERCHOLI, MIGUEL; STRONKOWSKI, MICHAŁ M.; VAGGIONE, DIEGO
- Abstract
We study the following problem: determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a propositional logic/deductive system in the language with formulas for verum, which is a theorem, and falsum, which is not a theorem. Assume also that L has an adequate semantics given by a discriminator variety. Then L is structurally complete if and only if it is maximal. All such logics/deductive systems are almost structurally complete.
- Subjects
STRUCTURAL analysis (Engineering); DISCRIMINANT analysis; BOOLEAN functions; UNIVERSAL algebra; SEMANTICS; FREE algebras
- Publication
Logic Journal of the IGPL, 2015, Vol 23, Issue 2, p235
- ISSN
1367-0751
- Publication type
Case Study
- DOI
10.1093/jigpal/jzu032