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  1.  35
    The Logic of Fast and Slow Thinking.Anthia Solaki, Francesco Berto & Sonja Smets - forthcoming - Erkenntnis:1-30.
    We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences (...)
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  2.  5
    Dynamic Epistemic Logics of Diffusion and Prediction in Social Networks.Alexandru Baltag, Zoé Christoff, Rasmus K. Rendsvig & Sonja Smets - 2019 - Studia Logica 107 (3):489-531.
    We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this diffusion policy, threshold models develop dynamically towards a guaranteed fixed point. We construct a (...)
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  3.  67
    The Logic of Justified Belief, Explicit Knowledge, and Conclusive Evidence.Alexandru Baltag, Bryan Renne & Sonja Smets - 2014 - Annals of Pure and Applied Logic 165 (1):49-81.
    We present a complete, decidable logic for reasoning about a notion of completely trustworthy evidence and its relations to justifiable belief and knowledge, as well as to their explicit justifications. This logic makes use of a number of evidence-related notions such as availability, admissibility, and “goodness” of a piece of evidence, and is based on an innovative modification of the Fitting semantics for Artemovʼs Justification Logic designed to preempt Gettier-type counterexamples. We combine this with ideas from belief revision and awareness (...)
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  4.  19
    Truth-Tracking by Belief Revision.Alexandru Baltag, Nina Gierasimczuk & Sonja Smets - 2019 - Studia Logica 107 (5):917-947.
    We study the learning power of iterated belief revision methods. Successful learning is understood as convergence to correct, i.e., true, beliefs. We focus on the issue of universality: whether or not a particular belief revision method is able to learn everything that in principle is learnable. We provide a general framework for interpreting belief revision policies as learning methods. We focus on three popular cases: conditioning, lexicographic revision, and minimal revision. Our main result is that conditioning and lexicographic revision can (...)
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  5. Keep 'Hoping' for Rationality: A Solution to the Backward Induction Paradox.Alexandru Baltag, Sonja Smets & Jonathan Alexander Zvesper - 2009 - 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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  6. Probabilistic Dynamic Belief Revision.Alexandru Baltag & Sonja Smets - 2008 - 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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  7.  59
    Quantum Logic as a Dynamic Logic.Alexandru Baltag & Sonja Smets - 2011 - 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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  8.  46
    The Modes of Physical Properties in the Logical Foundations of Physics.Sonja Smets - 2005 - 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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  9.  68
    Keep Changing Your Beliefs, Aiming for the Truth.Alexandru Baltag & Sonja Smets - 2011 - 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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  10. The Dynamic Turn in Quantum Logic.Alexandru Baltag & Sonja Smets - 2012 - 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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  11.  20
    Keep ‘Hoping’ for Rationality: A Solution to the Backward Induction Paradox.Alexandru Baltag, Sonja Smets & Jonathan Alexander Zvesper - 2009 - Synthese 169 (2):301-333.
    We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on plausibility models. Similarly to other epistemic statements, 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 when a given node is reached can be thought of as (...)
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  12. The Logic of Quantum Programs.Alexandru Baltag & Sonja Smets - unknown
    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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  13.  93
    The Liar-Paradox in a Quantum Mechanical Perspective.Diederik Aerts, Jan Broekaert & Sonja Smets - 1999 - 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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  14. From Intuitionistic Logic to Dynamic Operational Quantum Logic.Sonja Smets - 2006 - 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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  15.  5
    Beliefs and Evidence in Justification Models.Alexandru Baltag, Virginie Fiutek & Sonja Smets - 2016 - In Lev Beklemishev, Stéphane Demri & András Máté (eds.), Advances in Modal Logic, Volume 11. CSLI Publications. pp. 156-176.
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  16. Inconsistencies in Constituent Theories of World Views: Quantum Mechanical Examples. [REVIEW]Diederik Aerts, Jan Broekaert & Sonja Smets - 1998 - 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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  17.  7
    Logic of Dynamics and Dynamics of Logic: Some Paradigm Examples.Bob Coecke, David J. Moore & Sonja Smets - 2004 - In S. Rahman J. Symons (ed.), Logic, Epistemology, and the Unity of Science. Kluwer Academic Publisher. pp. 527--555.
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  18.  26
    A Topological Approach to Full Belief.Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün & Sonja Smets - 2019 - Journal of Philosophical Logic 48 (2):205-244.
    Stalnaker, 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide a topological semantics for belief, in particular, for Stalnaker’s notion of belief defined as ‘epistemic possibility of knowledge’, in terms of the closure of the interior operator on extremally disconnected spaces. This semantics extends the standard topological interpretation of knowledge with a new topological semantics for belief. We prove that the belief (...)
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  19.  9
    The Logic of Observation and Belief Revision in Scientific Communities.Hanna Sofie van Lee & Sonja Smets - forthcoming - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie:1-24.
    Scientists collect evidence in order to confirm or falsify scientific theories. Unfortunately, scientific evidence may sometimes be false or deceiving and as a consequence lead individuals to believe in a false theory. By interaction between scientists, such false beliefs may spread through the entire community. There is currently a debate about the effect of various network configurations on the epistemic reliability of scientific communities. To contribute to this debate from a logical perspective, this paper introduces an epistemic logical framework of (...)
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  20. On the Origin of Probabilities in Quantum Mechanics: Creative and Contextual Aspects.Diederik Aerts, Bob Coecke & Sonja Smets - 1999 - In S. Smets J. P. Van Bendegem G. C. Cornelis (ed.), Metadebates on Science. Vub-Press & Kluwer. pp. 291--302.
  21. Logic and Quantum Physics.Sonja Smets - 2010 - Journal of the Indian Council of Philosophical Research 27 (2).
     
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  22.  11
    On Causation and a Counterfactual in Quantum Logic: The Sasaki Hook.Sonja Smets - 2001 - Logique Et Analyse 44.
    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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  23.  19
    In Defense of Operational Quantum Logic.Sonja Smets - 2002 - 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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  24.  11
    Beliefs Supported by Binary Arguments.Chenwei Shi, Sonja Smets & Fernando R. Velázquez-Quesada - 2018 - Journal of Applied Non-Classical Logics 28 (2-3):165-188.
    In this paper, we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favour or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of Dung’s (...)
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  25.  74
    The Contributions of Logic to the Foundations of Physics: Foreword. [REVIEW]Diederik Aerts, Sonja Smets & Jean P. Van Bendegem - 2010 - Studia Logica 95 (1-2):1-3.
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  26.  58
    A Semantic-Modal View on Ramsey's Test.Alexandru Baltag & Sonja Smets - unknown
    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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  27.  22
    Logics of Informational Interactions.Alexandru Baltag & Sonja Smets - 2015 - Journal of Philosophical Logic 44 (6):595-607.
    The pre-eminence of logical dynamics, over a static and purely propositional view of Logic, lies at the core of a new understanding of both formal epistemology and the logical foundations of quantum mechanics. Both areas appear at first sight to be based on purely static propositional formalisms, but in our view their fundamental operators are essentially dynamic in nature. Quantum logic can be best understood as the logic of physically-constrained informational interactions between subsystems of a global physical system. Similarly, epistemic (...)
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  28.  31
    Could Dancing Be Coupled Oscillation? – The Interactive Approach to Linguistic Communication and Dynamical Systems Theory.Erik Myin & Sonja Smets - 2002 - 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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  29.  21
    New Logical Perspectives on Physics.Johan Benthem & Sonja Smets - 2012 - Synthese 186 (3):615 - 617.
  30.  16
    New Logical Perspectives on Physics.Johan van Benthem & Sonja Smets - 2012 - Synthese 186 (3):615-617.
  31.  14
    Reasoning About Quantum Actions: A Logician's Perspective.Sonja Smets - 2013 - In Hanne Andersen, Dennis Dieks, Wenceslao González, Thomas Uebel & Gregory Wheeler (eds.), New Challenges to Philosophy of Science. Springer Verlag. pp. 125--134.
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  32.  6
    Dynamic Epistemic Logic of Diffusion and Prediction in Threshold Models.Alexandru Baltag, Zoé Christoff, Rasmus Kraemmer Rendsvig & Sonja Smets - unknown
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  33. Johan van Benthem on Logic and Information Dynamics.Alexandru Baltag & Sonja Smets (eds.) - 2014 - Springer International Publishing.
     
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  34.  18
    Metadebates on Science: The Blue Book of 'Einstein Meets Magritte'.Gustaaf C. Cornelis, Sonja Smets & Jean Paul van Bendegem (eds.) - 1999 - 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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