Towards a Paraconsistent Quantum Set Theory
نویسندگان
چکیده
منابع مشابه
Towards a Paraconsistent Quantum Set Theory
In this paper, we will attempt to establish a connection between quantum set theory, as developed by Ozawa, Takeuti and Titani (see, for example, [13], [12], [10]), and topos quantum theory, as developed by Isham, Butterfield and Döring, amongst others (see, for example, [8], [6], [3]). Towards this end, we will study algebraic valued set-theoretic structures whose truth values correspond to th...
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Paraconsistent logics are logics that can be used to base inconsistent but non-trivial systems. In paraconsistent set theories, we can quantify over sets that in standard set theories (that are based on classical logic), if consistent, would lead to contradictions, such as the Russell set, R = {x : x / ∈ x}. Quasi-set theories are mathematical systems built for dealing with collections of indis...
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We show that a paraconsistent set theory proposed in Weber (2010) is strong enough to provide a quite classical non-primitive notion of identity, so that the relation is an equivalence relation and also obeys full substitutivity: a=b(F(a)F(b)). With this as background it is shown that the proposed theory also proves x(xx). While not by itself showing that the proposed system is trivial in t...
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We develop the old idea of von Neumann of a set theory with an internal quantum logic in a modern categorical guise (i.e. taking the objects of the category H of (Pre-)Hilbert spaces and linear maps as the sets of the basic level). We will see that in this way it is possible to clarify the relationship between categorification and quantization and besides this to understand that in some sense a...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2015
ISSN: 2075-2180
DOI: 10.4204/eptcs.195.12