Subalgebras and sublogics of -logics
Ján Šipoš (1978)
Mathematica Slovaca
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Ján Šipoš (1978)
Mathematica Slovaca
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Pavel Pták, John David Maitland Wright (1985)
Aplikace matematiky
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It is shown that for any quantum logic one can find a concrete logic and a surjective homomorphism from onto such that maps the centre of onto the centre of . Moreover, one can ensure that each finite set of compatible elements in is the image of a compatible subset of . This result is “best possible” - let a logic be the homomorphic image of a concrete logic under a homomorphism such that, if is a finite subset of the pre-image of a compatible subset of , then...
Vladimír Rogalewicz (1991)
Mathematica Slovaca
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Mirko Navara, Josef Tkadlec (1991)
Commentationes Mathematicae Universitatis Carolinae
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The main result of this paper is Theorem 3.3: Every concrete logic (i.e., every set-representable orthomodular poset) can be enlarged to a concrete logic with a given automorphism group and with a given center. Since every sublogic of a concrete logic is concrete, too, and since not every state space of a (general) quantum logic is affinely homeomorphic to the state space of a concrete logic [8], our result seems in a sense the best possible. Further, we show that every group is an automorphism...
Tomasz Jarmużek, Jacek Malinowski (2019)
Bulletin of the Section of Logic
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In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without...