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.     

Geography and computer ethics: An Eastern European perspective

Several context-specific social and political factors in Eastern and Central Europe are described — factors that must be considered while developing strategies to introduce Computer Ethics. Poland is used as a primary example. GNP per capita, the cost of hardware and software, uneven and scant distribution of computing resources, and attitudes toward work and authority are discussed. Such “geographical factors” must be taken into account as the new field of Computer Ethics develops.     

The relation between subjective distance and emotional involvement: Further experiment

The purpose of this experiment has been to test the value of an exponent of the power function describing the relation between emotional involvement and subjective distance, called the inverse square root law (Ekman and Bratfisch 1965). A group of 113 subjects were instructed to estimate 65 inter-city distances with Opole, Poland, as the center, and, next, to estimate the importance attributed to the cities, their own personal interest in them and involvement to them. The experiment partly confirmed the results obtained in original investigations, that is the inverse square root law holds true for cities of a range of distance not exceeding about 5000 km. For more distant cities a different trend has been observed, namely an increase of emotional involvement with increase of subjective distance to these cities. This might lead to the supposition that the relation between emotional involvement and subjective distance could be described by a parabolic relation.     

Simplified Kripke-Style Semantics for Some Normal Modal Logics

Studia Logica - Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics $$\mathrm {K45}$$, $$\mathrm {KB4}$$ ($$=\mathrm...     

Food deprivation induces conspecific pup-killing in mice

Periods of 24 to 48 hours of food deprivation reliably induced pup-killing in 30–50% of non-killer male mice. The behavior was prevented by previous experience with young and did not perseverate to non-deprived states. Castrated males and intact females also exhibited pup-killing following food deprivation, suggesting that the behavior is neither sexdependent nor related to the presence of testosterone. The findings are discussed in terms of their relationship to predatory behaviors and population dynamics.