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Modal‐type orthomodular logic

Graciela Domenech, Hector Freytes & Christian de Ronde

Mathematical Logic Quarterly 55 (3):307-319 (2009)

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Interpreting the Modal Kochen–Specker theorem: Possibility and many worlds in quantum mechanics.Christian de Ronde, Hector Freytes & Graciela Domenech - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 45:11-18.details In this paper we attempt to physically interpret the Modal Kochen–Specker theorem. In order to do so, we analyze the features of the possible properties of quantum systems arising from the elements in an orthomodular lattice and distinguish the use of “possibility” in the classical and quantum formalisms. Taking into account the modal and many worlds non-collapse interpretation of the projection postulate, we discuss how the MKS theorem rules the constraints to actualization, and thus, the relation between actual and possible (...) realms. (shrink) Download Export citation Bookmark 12 citations
The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictiory Powers in the Potential Realm.Newton C. A. da Costa & Christian de Ronde - unknowndetails In [7] the authors of this paper argued in favor of the possibility to consider a Paraconsistent Approach to Quantum Superpositions. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints -coming from present technical and experimental developments in QM- that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against the PAQS [1, 2, 3]. In [11, 12] it (...) Download Export citation Bookmark 2 citations
Modality, Potentiality and Contradiction in Quantum Mechanics.Christian de Ronde - unknowndetails In [9], Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause [1, 2, 3] have raised several arguments against this approach and claimed that —taking into account (...) Download Export citation Bookmark 11 citations
A Defense of the Paraconsistent Approach to Quantum Superpositions.Christian de Ronde - unknowndetails In, Newton da Costa together with the author of this paper argued in favor of the possibility to consider quantum superpositions in terms of a paraconsistent approach. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against this approach. In the present paper we attempt to answer the main (...) Download Export citation Bookmark 10 citations
Physical Properties as Modal Operators in the Topos Approach to Quantum Mechanics.Hector Freytes, Graciela Domenech & Christian de Ronde - 2014 - Foundations of Physics 44 (12):1357-1368.details In the framework of the topos approach to quantum mechanics we give a representation of physical properties in terms of modal operators on Heyting algebras. It allows us to introduce a classical type study of the mentioned properties. Download Export citation Bookmark

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