2016/06/16 by Richard DeJonghe, DeJonghe, Richard, Kimberly Frey +3
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #FOS: Physical sciences #Logic (math.LO) #Logic, Reasoning, and Knowledge #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.1606.05330
openalex publication_date 2016/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well-known that a Hilbert-style deduction system for first-order classical logic is sound and complete for a model theory built using all Boolean algebras as truth-value algebras if and only if it is sound and complete for a model theory utilizing only irreducible Boolean algebras (which are all isomorphic to the two-element Boolean algebra). In this paper, we prove an analogous result for any first-order logic with an algebraic semantics satisfying certain minimal assumptions, and we then apply our result to first-order quantum logic.