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  1. Alexandru Baltag & Sonja Smets, A Semantic-Modal View on Ramsey's Test.
    We present a semantic analysis of the Ramsey test, pointing out its deep underlying flaw: the tension between the “static” nature of AGM revision (which was originally tailored for revision of only purely ontic beliefs, and can be applied to higher-order beliefs only if given a “backwards-looking” interpretation) and the fact that, semantically speaking, any Ramsey conditional must be a modal operator (more precisely, a dynamic-epistemic one). Thus, a belief about a Ramsey conditional is in fact a higher-order belief, hence (...)
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  2. Alexandru Baltag & Sonja Smets (eds.) (forthcoming). Trends in Logic, Outstanding Contributions: Johan F. A. K. Van Benthem on Logical and Informational Dynamics. Springer.
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  3. Alexandru Baltag, Bryan Renne & Sonja Smets (2014). The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence. Annals of Pure and Applied Logic 165 (1):49-81.
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  4. Sonja Smets (2013). Reasoning About Quantum Actions: A Logician's Perspective. In. In Hanne Andersen, Dennis Dieks, Wenceslao González, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. 125--134.
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  5. Alexandru Baltag & Sonja Smets (2012). The Dynamic Turn in Quantum Logic. Synthese 186 (3):753 - 773.
    In this paper we show how ideas coming from two areas of research in logic can reinforce each other. The first such line of inquiry concerns the "dynamic turn" in logic and especially the formalisms inspired by Propositional Dynamic Logic (PDL); while the second line concerns research into the logical foundations of Quantum Physics, and in particular the area known as Operational Quantum Logic, as developed by Jauch and Piron (Helve Phys Acta 42: 842-848, 1969), Pirón (Foundations of Quantum Physics, (...)
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  6. Johan Benthem & Sonja Smets (2012). New Logical Perspectives on Physics. Synthese 186 (3):615 - 617.
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  7. Johan van Benthem & Sonja Smets (2012). New Logical Perspectives on Physics. Synthese 186 (3):615-617.
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  8. Alexandru Baltag & Sonja Smets (2011). Keep Changing Your Beliefs, Aiming for the Truth. Erkenntnis 75 (2):255-270.
    We investigate the process of truth-seeking by iterated belief revision with higher-level doxastic information . We elaborate further on the main results in Baltag and Smets (Proceedings of TARK, 2009a , Proceedings of WOLLIC’09 LNAI 5514, 2009b ), applying them to the issue of convergence to truth . We study the conditions under which the belief revision induced by a series of truthful iterated upgrades eventually stabilizes on true beliefs. We give two different conditions ensuring that beliefs converge to “full” (...)
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  9. Alexandru Baltag & Sonja Smets (2011). Quantum Logic as a Dynamic Logic. Synthese 179 (2):285 - 306.
    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 (...)
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  10. Diederik Aerts, Sonja Smets & Jean P. Van Bendegem (2010). The Contributions of Logic to the Foundations of Physics: Foreword. [REVIEW] Studia Logica 95 (1-2):1-3.
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  11. Alexandru Baltag, Sonja Smets & Jonathan Alexander Zvesper (2009). Keep 'Hoping' for Rationality: A Solution to the Backward Induction Paradox. Synthese 169 (2):301 - 333.
    We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation (...)
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  12. Alexandru Baltag & Sonja Smets (2008). Probabilistic Dynamic Belief Revision. Synthese 165 (2):179 - 202.
    We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief (...)
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  13. Sonja Smets (2006). From Intuitionistic Logic to Dynamic Operational Quantum Logic. Poznan Studies in the Philosophy of the Sciences and the Humanities 91 (1):257-275.
    Research within the operational approach to the logical foundations of physics has recently pointed out a new perspective in which quantum logic can be viewed as an intuitionistic logic with an additional operator to capture its essential, i.e., non-distributive, properties. In this paper we will offer an introduction to this approach. We will focus further on why quantum logic has an inherent dynamic nature which is captured in the meaning of "orthomodularity" and on how it motivates physically the introduction of (...)
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  14. Sonja Smets (2005). The Modes of Physical Properties in the Logical Foundations of Physics. Logic and Logical Philosophy 14 (1):37-53.
    We present a conceptual analysis of the notions of actual physical property and potential physical property as used by theoretical physicists/mathematicians working in the domain of operational quantum logic. We investigate how these notions are being used today and what role they play in the specified field of research. In order to do so, we will give a brief introduction to this area of research and explain it as a part of the discipline known as “mathematical metascience”. An in depth (...)
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  15. Alexandru Baltag & Sonja Smets, The Logic of Quantum Programs.
    We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound quantum systems. We give a syntax and a relational semantics in which we abstract away from phases and probabilities. We present a sound proof system for this logic, and we show how to characterize by logical means various forms of entanglement (e.g. the Bell states) and various (...)
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  16. Bob Coecke, David J. Moore & Sonja Smets (2004). Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples. In. In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. 527--555.
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  17. Sonja Smets (2003). In Defense of Operational Quantum Logic. Logic and Logical Philosophy 11:191-212.
    In the literature the work of C. Piron on OQL, “the operational quantum logic of the Geneva School”, has a few times been criticised. Those criticisms were often due to misunderstandings, as has already been pointed out in [19]. In this paper we follow the line of defense in favour of OQL by replying to the criticisms formulated some time ago in [4] and [17]. In order for the reader to follow our argumentation, we briefly analyze the basic conceptual machinery (...)
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  18. Erik Myin & Sonja Smets (2002). Could Dancing Be Coupled Oscillation? – The Interactive Approach to Linguistic Communication and Dynamical Systems Theory. Behavioral and Brain Sciences 25 (5):634-635.
    Although we applaud the interactivist approach to language and communication taken in the target article, we notice that Shanker & King (S&K) give little attention to the theoretical frameworks developed by dynamical system theorists. We point out how the dynamical idea of causality, viewed as multidirectional across multiple scales of organization, could further strengthen the position taken in the target article.
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  19. Sonja Smets, On Causation and a Counterfactual in Quantum Logic: The Sasaki Hook.
    We analyze G.M. Hardegree's interpretation of the Sasaki hook as a Stalnaker conditional and explain how he makes use of the basic conceptual machinery of OQL, i.e. the operational quantum logic which originated with the Geneva Approach to the foundations of physics. In particular we focus on measurements which are ideal and of the first kind, since these encode the content of the so-called Sasaki projections within the Geneva Approach. The Sasaki projections play a fundamental role when analyzing the condition (...)
     
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  20. Diederik Aerts, Jan Broekaert & Sonja Smets (1999). The Liar-Paradox in a Quantum Mechanical Perspective. Foundations of Science 4 (2):115-132.
    In this paper we concentrate on the nature of the liar paradox asa cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model (Aerts, Broekaert and Smets, 1999) that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.
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  21. Diederik Aerts, Bob Coecke & Sonja Smets (1999). On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects. In S. Smets J. P. Van Bendegem G. C. Cornelis (ed.), Metadebates on Science. Vub-Press and Kluwer. 291--302.
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  22. Gustaaf C. Cornelis, Sonja Smets & Jean Paul van Bendegem (eds.) (1999). Metadebates on Science: The Blue Book of 'Einstein Meets Magritte'. Kluwer Academic.
    How do scientists approach science? Scientists, sociologists and philosophers were asked to write on this intriguing problem and to display their results at the International Congress `Einstein Meets Magritte'. The outcome of their effort can be found in this rather unique book, presenting all kinds of different views on science. Quantum mechanics is a discipline which deserves and receives special attention in this book, mainly because it is fascinating and, hence, appeals to the general public. This book not only contains (...)
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  23. Diederik Aerts, Jan Broekaert & Sonja Smets (1998). Inconsistencies in Constituent Theories of World Views: Quantum Mechanical Examples. [REVIEW] Foundations of Science 3 (2):313-340.
    We put forward the hypothesis that there exist three basic attitudes towards inconsistencies within world views: (1) The inconsistency is tolerated temporarily and is viewed as an expression of a temporary lack of knowledge due to an incomplete or wrong theory. The resolution of the inconsistency is believed to be inherent to the improvement of the theory. This improvement ultimately resolves the contradiction and therefore we call this attitude the ‘regularising’ attitude; (2) The inconsistency is tolerated and both contradicting elements (...)
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