Giaquinta, Mariano; Modica, Giuseppe; Souček, Jiří An extended propositional logic. (English) Zbl 1353.03015 Bull. Inst. Math., Acad. Sin. (N.S.) 10, No. 1, 73-100 (2015). Summary: Motivated by quantum mechanics we discuss an extended propositional logic (EPL) basing its syntax on partitions of sets. Every complete partition define a context and in every context EPL reduces to a classical propositional logic. Partitions lead to a notion of incompatibility expressing that knowledge cannot be refined without changing context. We also deal with interpretations, tautologies and semantic consequences in EPL. MSC: 03B60 Other nonclassical logic 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) Keywords:nonclassical propositional logic; foundations of quantum mechanics; contexts PDFBibTeX XMLCite \textit{M. Giaquinta} et al., Bull. Inst. Math., Acad. Sin. (N.S.) 10, No. 1, 73--100 (2015; Zbl 1353.03015) Full Text: Link