Some modifications of Scott's theorem on injective spaces

D. Scott in his paper [5] on the mathematical models for the Church-Curry -calculus proved the following theorem.A topological space X. is an absolute extensor for the category of all topological spaces iff a contraction of X. is a topological space of Scott's open sets in a continuous lattice.In this paper we prove a generalization of this theorem for the category of , -closure spaces. The main theorem says that, for some cardinal numbers , , absolute extensors for the category of , -closure spaces are exactly , -closure spaces of , -filters in , >-semidistributive lattices (Theorem 3.5).If = and = we obtain Scott's Theorem (Corollary 2.1). If = 0 and = we obtain a characterization of closure spaces of filters in a complete Heyting lattice (Corollary 3.4). If = 0 and = we obtain a characterization of closure space of all principial filters in a completely distributive complete lattice (Corollary 3.3).     

On decidable consequence operators

The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.     

Logics of some kripke frames connected with Medvedev notion of informational types

Intermediate prepositional logics we consider here describe the setI() of regular informational types introduced by Yu. T. Medvedev [7]. He showed thatI() is a Heyting algebra. This algebra gives rise to the logic of infinite problems from [13] denoted here asLM ₁. Some other definitions of negation inI() lead to logicsLM _n (n ). We study inclusions between these and other systems, proveLM _n to be non-finitely axiomatizable (n ) and recursively axiomatizable (n < ). We also show that formulas in one variable do not separateLM from Heyting's logicH, andLM _n (n < ) from Scott's logic (H+S).     

Identification with an aggressor or a victim and its relation to creativity

Studied identification using a meta-contrast design. The first stimulus was the word 'I'. The second stimulus depicted an aggressor and a victim facing each other. The subliminal 'I' was flashed on either the victim or on the aggressor, or completely withheld. The subjects were 33 school children, aged 10–12 years. They also took a percept-genetic (PG) test of creativity, measuring willingness to return to and recognize early conceptions of a stimulus picture (a still-life). The results showed that the creative children reacted with less anxiety and defense when manipulated to identify with the aggressor than with the victim. The uncreative children showed the opposite reaction, namely a preference for the passive, surrendering victim.     

Latent trait models and dichotomization of graded responses

This paper discusses thecompatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called compatible with dichotomization.A distinction is made between polychotomization or dichotomization before the fact, that is, in constructing the response format, and polycho- or dichotomization after the fact, for example in dichotomizing existing graded response data.It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.     

Controversies and existence claims in chemistry: The theory of resonance

Controversies, i.e., multiple theory confrontations, may have a strong impact on the development of science. By an analysis of the so-called “resonance controversy” in chemistry the view that controversies and their resolution differ considerably from the process of theory succession is defended. It is argued that controversies are symptomatic of foundational problems, produce theory-scattering or domain-splitting, and induce ontological shifts. An explication is given of the role of existence claims and the applicability of Ockham's Razor in the resolution of controversies. The requirement of a realistic interpretation of theories at all times, as defended by some philosophers, is criticised.     

Integration of noxious stimulation across separate somatosensory communications systems: a functional theory of pain

Functional measurement analyses and psychophysical techniques were used to assess how separate, cross-modal, aversive events are integrated in judgements of pain. Subjects made magnitude estimations of noxious stimuli produced by a 6 X 6 factorial design of electric shocks and loud tones. Group data and most of the individual results were consistent with a model of linear pain summation: The estimates of pain approximated the linear sum of the pain estimates of the individual electrocutaneous and auditory components. The relation between painful sensation and current intensity could be described by a mildly expansive power function with an exponent of about 1.1. Auditorily produced painful sensation related to sound pressure level by a mildly compressive power function with an exponent of about 0.90 as a representative figure. Results are interpreted in terms of a functional theory of pain. Noxious events are first transformed to psychological scale values via stimulus-specific psychophysical transfer functions. The outputs of these functions are then combined with other pain-related internal representations of either sensory or cognitive origin, according to simple algebraic models.