The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating (...) axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability. (shrink)

Two main schemes explain how a system adapts to its environment. Evolutionary models are grounded on three usual processes (variation, transmission, selection) acting at the population level. Learning models are concerned with the endogenous search for a better performance at the individual level. The first ones were initially favored by biology and the second well illustrated by game theory. The article examines first how game theory went to evolution and how biology later considered learning. It shows some examples of a (...) hybrid use of models of each type. It finally proposes a common framework for both types of models. (shrink)

Abduction was first introduced in the epistemological context of scientific discovery. It was more recently analyzed in artificial intelligence, especially with respect to diagnosis analysis or ordinary reasoning. These two fields share a common view of abduction as a general process of hypotheses formation. More precisely, abduction is conceived as a kind of reverse explanation where a hypothesis H can be abduced from events E if H is a good explanation of E. The paper surveys four known schemes for abduction (...) that can be used in both fields. Its first contribution is a taxonomy of these schemes according to a common semantic framework based on belief revision. Its second contribution is to produce, for each non-trivial scheme, a representation theorem linking its semantic framework to a set of postulates. Its third contribution is to present semantic and axiomatic arguments in favor of one of these schemes, ordered abduction, which has never been vindicated in the literature. (shrink)

Despite its importance in various fields, analogical reasoning has not yet received a unified formal representation. Our contribution proposes a general scheme of inference that is compatible with different types of logic (deductive, probabilistic, non-monotonic). Firstly, analogical assessment precisely defines the similarity of two objects according to their properties, in a relative rather than absolute way. Secondly, analogical inference transfers a new property from one object to a similar one, thanks to an over-hypothesis linking two sets of properties. The belief (...) strength in the conclusion is then directly related to the belief strength in this meta-hypothesis. (shrink)

L’article propose d’abord une version simplifiée d’une ontologie universelle, conçue comme un cadre général de description du monde matériel et mental. Il examine les notions d’entité, de propriété, de relation et de temporalité et leurs développements conjoints en termes de rapport entre les parties et le tout ou encore d’émergence d’une entité nouvelle. Il illustre ensuite les principes précédents en ce qui concerne la science économique, dont les entités de base sont les agents, les biens et les institutions. Il insiste (...) sur le couplage que cette dernière réalise entre leurs propriétés physiques ou psychologiques et le raisonnement qu’elle propose en termes d’équilibre et plus récemment d’apprentissage. Classification JEL : A12. (shrink)

RésuméEn dépit de son importance dans divers domaines, le raisonnement analogique n'a pas encore reçu de représentation formelle unifiée. Notre contribution propose un schéma d'inférence général, compatible avec différentes logiques (déductive, probabiliste, non monotone). Premièrement, un énoncé analogique définit précisément la similarité entre deux objets en fonction de leurs propriétés, de façon relative et non absolue. Deuxièmement, une inférence analogique transfère une propriété nouvelle d'un objet à un objet similaire, grâce à une hypothèse d'arrière-plan qui relie deux ensembles de propriétés. (...) Le degré de croyance dans la conclusion est alors directement relié au degré de croyance dans cette méta-hypothèse. (shrink)

The Sleeping Beauty problem is presented in a formalized framework which summarizes the underlying probability structure. The two rival solutions proposed by Elga and Lewis differ by a single parameter concerning her prior probability. They can be supported by considering, respectively, that Sleeping Beauty is “fuzzy-minded” and “blank-minded”, the first interpretation being more natural than the second. The traditional absent -minded driver problem is reinterpreted in this framework and sustains Elga’s solution.

The paper studies a specific adaptive learning rule when each player faces a unidimensional strategy set. The rule states that a player keeps on incrementing her strategy in the same direction if her utility increased and reverses direction if it decreased. The paper concentrates on games on the square [0,1]×[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,1]\times [0,1]$$\end{document} as mixed extensions of 2×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\times 2$$\end{document} games. We study in general the (...) behavior of the system in the interior as well as on the borders of the strategy space. We then describe the system asymptotic behavior for symmetric, zero-sum, and twin games. Original patterns emerge. For instance, for the “prisoner’s dilemma” with symmetric initial conditions, the system goes directly to the symmetric Pareto optimum. For “matching pennies,” the system follows slowly expanding cycles around the mixed strategy equilibrium. (shrink)

Introduction. Bert HAMMINGA and Neil DE MARCHI: Préface. Bert HAMMINGA and Neil DE MARCHI: Idealization and the Defence of Economics: Notes Toward a History. Part I: General Observations on Idealization in Economics. Kevin D. HOOVER: Six Queries about Idealization in an Empirical Context. Bernard WALLISER: Three Generalization Processes for Economic Models. Steven COOK and David HENDRY: The Theory of Reduction in Econometrics. Maarten C.W. JANSSEN: Economic Models and Their Applications. Adolfo GARCÍA DE LA SIENRA: Idealization and Empirical Adequacy (...) in Economic Theory. Izabella NOWAKOWA and Leszek NOWAK: On Correspondence between Economic Theories. Uskali MÄKI: Isolation, Idealization and Truth in Economics. Part II: Case Studies of Idealization in Economics. Nancy CARTWRIGHT: Mill and Menger: Ideal Elements and Stable Tendencies. Wolfgang BALZER: Exchange Versus Influence: A Case of Idealization. Kees COOLS, Bert HAMMINGA, Theo A.F. KUIPERS: Truth Approximation by Concretization in Capital Structure Theory. Daniel M. HAUSMAN: Paul Samuelson as Dr. Frankenstein: When an Idealization Runs Amuck. Hugo A. KEUZENKAMP: What if an Idealization is Problematic? The Case of the Homogeneity Condition in Consumer Demand. Werner DIEDERICH: Nowak on Explanation and Idealization in Marx's 'Capital'. Gérard JORLAND: Idealization and Transformation. Jack BIRNER: Idealizations and Theory Development in Economics. Some History and Logic of the Logic Discovery. Discussions. Leszek NOWAK: The Idealizational Methodology and Economics. Replies to Diederich, Hoover, Janssen, Jorland and Mäki. (shrink)

Anderson and Csima :245–264, 2014) defined a jump operator, the bounded jump, with respect to bounded Turing reducibility. They showed that the bounded jump is closely related to the Ershov hierarchy and that it satisfies an analogue of Shoenfield jump inversion. We show that there are high bounded low sets and low bounded high sets. Thus, the information coded in the bounded jump is quite different from that of the standard jump. We also consider whether the analogue of the Jump (...) Theorem holds for the bounded jump: do we have A≤bTB\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A \le _{bT}B$$\end{document} if and only if Ab≤1Bb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^b \le _1 B^b$$\end{document}? We show the forward direction holds but not the reverse. (shrink)

The network is moving towards a global informational equilibrium that is irrevocable – if inter‐individual communication persists as the only driving force behind the network's evolution. On the basis of an example, this chapter compares the respective changes in the values of the main characteristic variables at the level of the network as a whole, and that of each cluster considered separately. Any local informational equilibrium achieved by a cluster is therefore fundamentally unstable, as it is constantly threatened by such (...) a phenomenon. It follows that the cumulative formation of local clusters of actors corresponding to a progressive regionalization of the effective space of the network is then erased as at least one category shared by all actors allows each of them to escape from the cluster in which they would otherwise remain enclosed. Maintaining separations between regions dividing the network space before the homogenization process ends means that it does not only have advantages. (shrink)

Voir son cerveau en première personne s’activer à l’occasion de la réalisation d’une tâche semble établir plus qu’une corrélation en décrivant ce qui serait un lien de causalité entre le corps et son cerveau. Le corps est une surface et un résultat dont la conscience ne perçoit le processus vivant qu’en retard sur la vitalité et la mobilité du cerveau. Nous sommes en retard sur notre cerveau mais notre conscience du présent ne peut avoir accès à la temporalité de sa (...) condition. La transparence du cerveau in vivo implique des dispositifs neuro-expérientiels. (shrink)

The specter of epistemic closure haunts current epistemology: some regard the refutation of closure as obvious, while others take its denial to be an epistemicoutrage. To some extent, the strong difference of opinion has its source in certain misapprehensions. This paper tries to formulate and clarify the key issues dividing the two sides and contends that, in certain respects, the difference between the friend and the foe of closure may be more a matter of semantics than substance. The paper goes (...) on to argue that once the substantial issues have been properly formulated, there is a limit to how far deductive reasoning can take the parties to the dispute. (shrink)

Biographie et bibliographie complète du professeur Justin Mossay (1920-2012).

There is a story related concerning Bertrand Russell that makes what I hope is anelegant introduction to the following paper. It is said that as a young man LordRussell, while out for a walk, became, in the course of his meditations, perfectlyconvinced of the validity of the ontological argument for the existence of God.Alas, he did not have a notebook handy and by the time he returned to his studyto write down his discovery found that he had completely lost the (...) train of thoughtwhich had led to so remarkable a conclusion . In the followingpaper I will attempt nothing so grand as the retrieval of Russell‟s lost insight. Iwill however, be attempting a recuperation of another kind. To be brief, I will beasking what the ontological argument meant to its originator, Anselm ofCanterbury, as well as how it might be significant for contemporary discussionsconcerning the so-called “negative theology.” Here I refer in particular to theongoing debate between Jacques Derrida and Jean-Luc Marion to which, asMarion himself has recognized, Anselm‟s thought has a vital contribution tomake. (shrink)