Studia Logica 89 (2):187-211 (2008)

Authors
Sonja Smets
University of Amsterdam
Alexandru Baltag
University of Amsterdam
Abstract
In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-008-9126-5
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References found in this work BETA

Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
The Logic of Quantum Mechanics.Garrett Birkhoff & John von Neumann - 1937 - Journal of Symbolic Logic 2 (1):44-45.

View all 17 references / Add more references

Citations of this work BETA

Quantum Logic as a Dynamic Logic.Alexandru Baltag & Sonja Smets - 2011 - Synthese 179 (2):285 - 306.
The Logic of Empirical Theories Revisited.Johan Benthem - 2012 - Synthese 186 (3):775 - 792.
A Computational Learning Semantics for Inductive Empirical Knowledge.Kevin T. Kelly - 2014 - In Alexandru Baltag & Sonja Smets (eds.), Johan van Benthem on Logic and Information Dynamics. Springer International Publishing. pp. 289-337.

View all 8 citations / Add more citations

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