Learning to Coordinate; a Recursion Theoretic Perspective

We consider two players each of whom attempts to predict the behavior of the other, using no more than the history of earlier predictions. Behaviors are limited to a pair of options, conventionally denoted by 0, 1. Such players face the problem of learning to coordinate choices. The present paper formulates their situation recursion theoretically, and investigates the prospects for success. A pair of players build up a matrix with two rows and infinitely many columns, and are said to “learn” each other if cofinitely many of the columns show the same number in both rows (either 0 or 1). Among other results we prove that there are two collections of players that force all other players to choose their camp. Each collection is composed of players that learn everyone else in the same collection, but no player that learns all members of one collection learns any member of the other. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the algebraization of a Feferman's predicate

Summary This paper is devoted to the algebraization of an arithmetical predicate introduced by S. Feferman. To this purpose we investigate the equational class of Boolean algebras enriched with an operation , which translates such predicate, and an operation , which translates the usual predicate Theor. We deduce from the identities of this equational class some properties of and some ties between and ; among these properties, let us point out a fixed-point theorem for a sufficiently large class of - polynomials. The last part of this paper concerns the duality theory for - algebras.Allatum est die 24 Maii 1976     

Partially Undetermined Many-Valued Events and Their Conditional Probability

A logic for classical conditional events was investigated by Dubois and Prade. In their approach, the truth value of a conditional event may be undetermined. In this paper we extend the treatment to many-valued events. Then we support the thesis that probability over partially undetermined events is a conditional probability, and we interpret it in terms of bets in the style of de Finetti. Finally, we show that the whole investigation can be carried out in a logical and algebraic setting, and we find a logical characterization of coherence for assessments of partially undetermined events.     

Equational Characterization of the Subvarieties of BL Generated by t-norm Algebras

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains.     

Rosser orderings and free variables

It is shown that for arithmetical interpretations that may include free variables it is not the Guaspari-Solovay system R that is arithmetically complete, but their system R ^–. This result is then applied to obtain the nonvalidity of some rules under arithmetical interpretations including free variables, and to show that some principles concerning Rosser orderings with free variables cannot be decided, even if one restricts oneself to usual proof predicates.     

Three Complexity Problems in Quantified Fuzzy Logic

We prove that the sets of standard tautologies of predicate Product Logic and of predicate Basic Logic, as well as the set of standard-satisfiable formulas of predicate Basic Logic are not arithmetical, thus finding a rather satisfactory solution to three problems proposed by Hájek in [H01].     

Normal body scheme and absent phantom limb experience in amputees while dreaming

While dreaming amputees often experience a normal body image and the phantom limb may not be present. However, dreaming experiences in amputees have mainly been collected by questionnaires. We analysed the dream reports of amputated patients with phantom limb collected after awakening from REM sleep during overnight videopolysomnography (VPSG). Six amputated patients underwent overnight VPSG study. Patients were awakened during REM sleep and asked to report their dreams. Three patients were able to deliver an account of a dream. In all dreaming recalls, patients reported that the amputated limbs were intact and completely functional and they no longer experienced phantom limb sensations. Phantom limb experiences, that during wake result from a conflict between a pre-existing body scheme and the sensory information on the missing limb, were suppressed during sleep in our patients in favour of the image of an intact body accessed during dream.     

Δ-core Fuzzy Logics with Propositional Quantifiers, Quantifier Elimination and Uniform Craig Interpolation

In this paper we investigate the connections between quantifier elimination, decidability and Uniform Craig Interpolation in Δ-core fuzzy logics added with propositional quantifiers. As a consequence, we are able to prove that several propositional fuzzy logics have a conservative extension which is a Δ-core fuzzy logic and has Uniform Craig Interpolation.