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- W4297797337 abstract "Effect algebras form a formal algebraic description of the structure of the so-called effects in a Hilbert space which serves as an event-state space for effects in quantum mechanics. This is why effect algebras are considered as logics of quantum mechanics, more precisely as an algebraic semantics of these logics. Because every productive logic is is equipped with a connective implication, we introduce here such a concept and demonstrate its properties. In particular, we show that this implication is connected with conjunction via a certain unsharp residuation which is formulated on the basis of a strict unsharp residuated poset. Though this structure is rather complicated, it can be converted back into an effect algebra and hence it is sound. Further, we study the Modus Ponens rule for this implication by means of so-called deductive systems and finally we study the contraposition law." @default.
- W4297797337 created "2022-10-01" @default.
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- W4297797337 creator A5063985495 @default.
- W4297797337 date "2019-08-14" @default.
- W4297797337 modified "2023-10-17" @default.
- W4297797337 title "Properties of the connective implication in effect algebras" @default.
- W4297797337 doi "https://doi.org/10.48550/arxiv.1908.05315" @default.
- W4297797337 hasPublicationYear "2019" @default.
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