Notes on Logics of Metric Spaces

In [14], we studied the computational behaviour of various first-order and modal languages interpreted in metric or weaker distance spaces. [13] gave an axiomatisation of an expressive and decidable metric logic. The main result of this paper is in showing that the technique of representing metric spaces by means of Kripke frames can be extended to cover the modal (hybrid) language that is expressively complete over metric spaces for the (undecidable) two-variable fragment of first-order logic with binary pred-icates interpreting the metric. The frame conditions needed correspond rather directly with a Boolean modal logic that is, again, of the same expressivity as the two-variable fragment. We use this representation to derive an axiomatisation of the modal hybrid variant of the two-variable fragment, discuss the compactness property in distance logics, and derive some results on (the failure of) interpolation in distance logics of various expressive power. Presented by Melvin Fitting     

A Duality for the Algebras of a Łukasiewicz <Emphasis Type="Italic">n</Emphasis> + 1-valued Modal System

In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research. Presented by Daniele Mundici     

Modal Logic for Other-World Agnostics: Neutrality and Halldén Incompleteness

The logic of ‘elsewhere,’ i.e., of a sentence operator interpretable as attaching to a formula to yield a formula true at a point in a Kripke model just in case the first formula is true at all other points in the model, has been applied in settings in which the points in question represent spatial positions (explaining the use of the word ‘elsewhere’), as well as in the case in which they represent moments of time. This logic is applied here to the alethic modal case, in which the points are thought of as possible worlds, with the suggestion that its deployment clarifies aspects of a position explored by John Divers un-der the name ‘modal agnosticism.’ In particular, it makes available a logic whose Halldén incompleteness explicitly registers the agnostic element of the position – its neutrality as between modal realism and modal anti-realism.     

The Tense Logic for Master Argument in Prior’s Reconstruction

In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K _t 4 plus a new axiom (P): ‘p Λ G p ⊃ P G p’. This formula was used by Prior in his original analysis of Master Argument. (P) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by (P) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. Presented by Jacek Malinowski     

The oceanic state: a conceptual elucidation in terms of modal contact

Despite its lengthy history in psychoanalysis, the psychological origins, essential features and value of the oceanic state remain open to dispute. This ambiguity has come at a cost to the clarity of theoretical discussions on the topic. In working towards a conceptual elucidation, the author maintains that there are three primary accounts of the oceanic state: the metaphysical one of Romain Rolland, the developmental one of Sigmund Freud, and the cognitive-perceptual one of Anton Ehrenzweig. Based on the notion of modal contact, he argues that the accounts share a general theoretical structure that establishes as the necessary criterion for all oceanic states the loosening of ego boundaries and sufficient contact between differentiated and undifferentiated modalities of the mind. However, within this common structure, the accounts employ dissimilar metapsychologies to promulgate oceanic states of appreciably distinct kinds. To support this view, the author carries out a comparative examination of the modal contacts involved in the primary accounts' oceanic states. To conclude, he reviews the main implications of the notion of modal contact vis-à-vis recent discussion on oceanic phenomena, and puts forward for consideration a pluralist account of the mind that can accommodate the existence of several kinds of oceanic states.     

Comparison of Return-on-Effort and Conventional Expectancy Theory Predictions of Work Effort and Job Performance: Results from Three Field Studies

It was predicted that a return-on-effort version of expectancy theory, an approach that examines the incremental benefits associated with increased effort, would yield superior predictions of work effort and job performance, in comparison with the conventional approach. Data were collected from the following three work settings: a manufacturing concern, a supermarket, and a bank. Unlike prior research that has uniformly found superior predictions using the return-on-effort model (and that has uniformly examined student samples), the present research found only modest support. Three possible boundary conditions were discussed—format effects, reward system responsiveness, and ability differences. The latter two, examined empirically via supplementary analyses, provided increased support for the return-on-effort model.