74 research outputs found
Categoricity and Possibility. A Note on Williamson's Modal Monism
The paper sketches an argument against modal monism, more specifically against the reduction of physical possibility to metaphysical possibility. The argument is based on the non-categoricity of quantum logic
The Contextual Character of Modal Interpretations of Quantum Mechanics
In this article we discuss the contextual character of quantum mechanics in
the framework of modal interpretations. We investigate its historical origin
and relate contemporary modal interpretations to those proposed by M. Born and
W. Heisenberg. We present then a general characterization of what we consider
to be a modal interpretation. Following previous papers in which we have
introduced modalities in the Kochen-Specker theorem, we investigate the
consequences of these theorems in relation to the modal interpretations of
quantum mechanics.Comment: 21 pages, no figures, preprint submitted to SHPM
Orthomodular logic. A proposal of a logic for quantum physics
Treballs Finals de Grau de Matemà tiques, Facultat de Matemà tiques, Universitat de Barcelona, Any: 2016, Director: Antoni Torrens TorrellClassical physics are widely known to be closely related to classical propositional calculus, whereas there does not exist a strongly settled analogue for quantum physics. We will focus on orthomodular logic and, in particular, we will study two different sentential logics that have been purposed with this aim over othomodular lattices. Thus, we will introduce their semantics from the foundations of quantum mechanics and presenting them by means of two different approaches whose equivalence will be shown. Additionally, we will give an adequate syntax for each proposal, the first one due to M. L. dalla Chiara and R. Giuntini and the last one to G. Kalmbach. Finally, completeness theorems will be discussed as well as the results that have
been reached
Discriminator logics (Research announcement)
A discriminator logic is the 1-assertional logic of a discriminator variety V having two constant terms 0 and 1 such that V ⊨ 0 1 iff every member of V is trivial. Examples of such logics abound in the literature. The main result of this research announcement asserts that a certain non-Fregean deductive system SBPC, which closely resembles the classical propositional calculus, is canonical for the class of discriminator logics in the sense that any discriminator logic S can be presented (up to definitional equivalence) as an axiomatic extension of SBPC by a set of extensional logical connectives taken from the language of S. The results outlined in this research announcement are extended to several generalisations of the class of discriminator logics in the main work
Quantum logic as a dynamic logic
We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear "no". Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth's proposal of applying Tarski's semantical methods to the analysis of physical theories, with an empirical-experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational-realistic tradition of Jauch and Piron, i.e. as an investigation of "the logic of yes-no experiments" (or "questions"). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the "non-classicality" of quantum behavior than any perspective based on static Propositional Logic
Modal-type orthomodular logic
In this paper we enrich the orthomodular structure by adding a modal
operator, following a physical motivation. A logical system is developed,
obtaining algebraic completeness and completeness with respect to a
Kripke-style semantic founded on Baer *-semigroups as in [20].Comment: submitted to the Mathematical Logic Quarterl
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