A Categorial Semantic Representation of Quantum Event Structures

Zafiris, Elias; Karakostas, Vassilios

doi:10.1007/s10701-013-9733-5

Cited by 12 publications

(12 citation statements)

References 16 publications

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“…These technicalities, however, bear no further significance for present purposes. 7 Such a conceptual viewpoint has been also suggested in Davis (1977) and Takeuti (1978) and, recently, within a category-theoretic perspective of quantum theory, by Zafiris and Karakostas (2013).…”

Section: Contextual Account Of Truthmentioning

confidence: 86%

Correspondence Truth and Quantum Mechanics

Karakostas

2013

Axiomathes

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The logic of a physical theory reflects the structure of the propositions referring to the behaviour of a physical system in the domain of the relevant theory. It is argued in relation to classical mechanics that the propositional structure of the theory allows truth-value assignment in conformity with the traditional conception of a correspondence theory of truth. Every proposition in classical mechanics is assigned a definite truth value, either 'true' or 'false', describing what is actually the case at a certain moment of time. Truth-value assignment in quantum mechanics, however, differs; it is known, by means of a variety of 'no go' theorems, that it is not possible to assign definite truth values to all propositions pertaining to a quantum system without generating a Kochen-Specker contradiction. In this respect, the Bub-Clifton 'uniqueness theorem' is utilized for arguing that truth-value definiteness is consistently restored with respect to a determinate sublattice of propositions defined by the state of the quantum system concerned and a particular observable to be measured. An account of truth of contextual correspondence is thereby provided that is appropriate to the quantum domain of discourse. The conceptual implications of the resulting account are traced down and analyzed at length. In this light, the traditional conception of correspondence truth may be viewed as a species or as a limit case of the more generic proposed scheme of contextual correspondence when the non-explicit specification of a context of discourse poses no further consequences.Comment: 19 page

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Section: Contextual Account Of Truthmentioning

confidence: 86%

Correspondence Truth and Quantum Mechanics

Karakostas

2013

Axiomathes

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“…In this work we aim to establish that the concept of complementarity, pertaining to any non-Boolean quantal physical description, is mathematically formalized, conceptually further clarified and physically extended, through the categorical notion of adjunction that has been recently proved to exist between the category of quantum event algebras and the category of presheaves on Boolean event algebras (Zafiris [45], see also Zafiris & Karakostas [50] for a more detailed treatment including in addition the involved logical aspects). To this end, in Section 2, we provide a category-theoretic representation of a quantum algebra of events via the adjunction of suitably qualified functors of Boolean probing frames to it, capable of carrying all the information encoded in the former.…”

Section: On the Structure Of The Complementarity Conceptmentioning

confidence: 99%

Category-Theoretic Interpretative Framework of the Complementarity Principle in Quantum Mechanics

Zafiris

Karakostas

2019

Int J Theor Phys

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This study aims to provide an analysis of the complementarity principle in quantum theory through the establishment of partial structural congruence relations between the quantum and Boolean kinds of event structure. Specifically, on the basis of the existence of a categorical adjunction between the category of quantum event algebras and the category of presheaves of variable Boolean event algebras, we establish a twofold complementarity scheme consisting of a generalized/global and a restricted/local conceptual dimension, where the latter conception is subordinate to and constrained by the former. In this respect, complementarity is not only understood as a relation between mutually exclusive experimental arrangements or contexts of co-measurable observables, as envisaged by the original conception, but it is primarily comprehended as a reciprocal relation concerning information transfer between two hierarchically different structural kinds of event structure that can be brought into partial congruence by means of the established adjunction. It is further argued that the proposed category-theoretic framework of complementarity naturally advances a contextual realist conceptual stance towards our deeper understanding of the microphysical nature of reality.

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“…The second of these two new approaches is the categorial semantics approach engaged by Elias Zafiris and Vassilios Karakostas, where one considers Boolean frames: Boolean algebras are pasted together so as to reconstruct geometrically structures associated with quantum logic [39]. The main idea of this approach is the introduction of a topological covering scheme of a quantum event algebra of families of local Boolean logical frames; these frames provide local covers of a quantum event algebra via complete Boolean algebras.…”

Section: Logic and Experience In Quantum Mechanicsmentioning

confidence: 99%

Uncertainty Relations and Possible Experience

Jaeger

2016

Mathematics

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Abstract:The uncertainty principle can be understood as a condition of joint indeterminacy of classes of properties in quantum theory. The mathematical expressions most closely associated with this principle have been the uncertainty relations, various inequalities exemplified by the well known expression regarding position and momentum introduced by Heisenberg. Here, recent work involving a new sort of "logical" indeterminacy principle and associated relations introduced by Pitowsky, expressable directly in terms of probabilities of outcomes of measurements of sharp quantum observables, is reviewed and its quantum nature is discussed. These novel relations are derivable from Boolean "conditions of possible experience" of the quantum realm and have been considered both as fundamentally logical and as fundamentally geometrical. This work focuses on the relationship of indeterminacy to the propositions regarding the values of discrete, sharp observables of quantum systems. Here, reasons for favoring each of these two positions are considered. Finally, with an eye toward future research related to indeterminacy relations, further novel approaches grounded in category theory and intended to capture and reconceptualize the complementarity characteristics of quantum propositions are discussed in relation to the former.

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A Categorial Semantic Representation of Quantum Event Structures

Cited by 12 publications

References 16 publications

Correspondence Truth and Quantum Mechanics

Correspondence Truth and Quantum Mechanics

Category-Theoretic Interpretative Framework of the Complementarity Principle in Quantum Mechanics

Uncertainty Relations and Possible Experience

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