2014/07/01 by Miguel Campercholi, Campercholi, Miguel, Michał M. Stronkowski +3
Computer Science · #Advanced Algebra and Logic #Rough Sets and Fuzzy Logic #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.1407.0175
We study the following problem: Determine which almost structurally complete\nquasivarieties are structurally complete. We propose a general solution to this\nproblem and then a solution in the semisimple case. As a consequence, we obtain\na characterization of structurally complete discriminator varieties.\n An interesting corollary in logic follows: Let L be a consistent\npropositional logic/deductive system in the language with formulas for verum,\nwhich is a theorem, and falsum, which is not a theorem. Assume also that L\nhas an adequate semantics given by a discriminator variety. Then L is\nstructurally complete if and only if it is maximal. All such logics/deductive\nsystems are almost structurally complete.\n