Abstract
In this paper, we propose a unified logical framework for representing and analyzing various forms of correlated information change. Our main thesis is that “logical dynamics,” in the sense of van Benthem (Exploring logical dynamics. CSLI Publications, Stanford, 1996; Logical dynamics of information and interaction. Cambridge University Press, Cambridge, 2011), and in particular dynamic epistemic notions of conditional, as developed in Baltag and Smets (Electron Notes Theor Comput Sci 165:5–21, 2006a; Stud Log 89:185–209, 2008a; Texts in logic and games. Amsterdam University Press, Amsterdam, pp 9–58, 2008b), play a central role in understanding and modeling a wide range of apparently very different information-gathering phenomena which do have one specific feature in common, namely the very act of learning new information may directly change the reality that is being learned. On the one hand, we focus on the way in which an introspective agent changes her beliefs when learning new higher-order information, i.e., information that may refer to her own beliefs. On the other hand, we analyze situations in which an observer learns about a phenomenon by performing observations that may perturb the very phenomenon under study, as in the case of quantum measurements, or observations in social sciences, psychology and medicine. Our formal techniques are based on ideas from dynamic logic and on the modeling of “dynamic conditionals.” We offer a semantics based on “test frames,” i.e., Kripke frames labeled by propositional formulae which yields a unified setting for the two types of correlated information change under study. We show how this framework can be used to analyze the ontic and epistemic–informational aspects of quantum measurements and to compare them with other types of observation, testing, belief revision, counterfactual conditionals, etc.
Highlights
In this paper, we focus on modeling situations that exhibit a particular form of “correlated information change,” i.e., situations in which the very act of learning new information may influence the result and changes the very phenomenon under study
We focus on the way in which an introspective agent changes her beliefs when learning new higher-order information, i.e., information that may refer to her own beliefs
We focus on modeling situations that exhibit a particular form of “correlated information change,” i.e., situations in which the very act of learning new information may influence the result and changes the very phenomenon under study
Summary
We focus on modeling situations that exhibit a particular form of “correlated information change,” i.e., situations in which the very act of learning new information may influence the result and changes the very phenomenon under study. We will come back to this specific example later on, for it is important to note what all these examples have in common: namely that a true (respectively, false) property can become false (respectively, true) by the very act of observing, learning, communicating or accepting (the truth of) that property To deal with this range of different information-gathering phenomena, coming from areas as diverse as quantum physics and the social sciences, a unified logical setting is required. The common formal setting that can subsume the different approaches of belief revision and quantum observations is given by what we call “test frames,” these are labeled Kripke frames in which the basic relations R P are labeled by “propositions” (subsets P of the state space) Such structures are special cases of socalled dynamic frames and are well studied in the context of propositional dynamic logic (PDL) (Harel et al 2000). We end with some concluding remarks about the erosion of the distinction between “ontic” and “epistemic” in the quantum realm, arguing that far from reducing quantum behavior to a purely informational phenomenon, this shows that on the contrary knowledge and information gathering are “real” physical phenomena, with real consequences in the actual world
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