An analysis and generalization of Venn's diagrammatic decision procedure

Summary When testing logical formulae for validity by applying Venn's diagrams we are using a kind of picture writing i. e. a writing in which certain facts are represented by drawings rather than sentences. This diagrammatic decision procedure may however be translated into ordinary language. Translating for instance the respective procedure of testing the mood Darii we obtain the following reasoning.     

B-varieties with normal free algebras

The starting point for the investigation in this paper is the following McKinsey-Tarski's Theorem: if f and g are algebraic functions (of the same number of variables) in a topological Boolean algebra (TBA) and if C(f)C(g) vanishes identically, then either f or g vanishes identically. The present paper generalizes this theorem to B-algebras and shows that validity of that theorem in a variety of B-algebras (B-variety) generated by SCI _B -equations implies that its free Lindenbaum-Tarski's algebra is normal. This is important in the semantical analysis of SCI _B (the Boolean strengthening of the sentential calculus with identity, SCI) since normal B-algebras are just models of this logic. The rest part of the paper is concerned with relationships between some closure systems of filters, SCI _B -theories, B-varieties and closed sets of SCI _B -equations that have been derived both from the semantics of SCI _B and from the semantics of the usual equational logic.To the memory of Jerzy Supecki     

Physical and cognitive effort discounting of hypothetical monetary rewards

Effort discounting refers to the decrease in the subjective value of a reward as the effort required to obtain the reward increases. The main aims of this study were to ascertain whether the amount of the reward affects the steepness of the effort discounting process for hypothetical monetary rewards, to identify whether this steepness depends on the type of effort that is required, and to determine whether the steepness of different types of effort covary at the individual level. Two types of effort were studied under hypothetical choice situations: physical effort and cognitive effort. Both physical and cognitive effort discounting were well described by the hyperbolic model. Large rewards were discounted less steeply than small rewards for both types of effort. This finding agrees with the results of prior studies which have found that larger rewards have greater motivational power. In addition, the steepness of physical effort discounting was positively correlated with the steepness of cognitive effort discounting, which suggests that the effort discounting process is a trait‐like characteristic within an individual.     

Tradycyjna teoria wnioskowania bezpośredniego jako pewien fragment dwuwartościowego rachunku zdań

Allatwn est die 16 Septembris 1959     

O teorii klas zbudowanej na teorii przedmiotów

Allatum est die 28 Fanuarii 1960     

Perception of randomness and predicting uncertain events

Using randomly generated sequences of binary events we asked participants to make predictions about the next event. It turned out that while predicting uncertain events, people do not behave unsystematically. Our research identifies four types of relatively consistent strategies for predicting uncertain binary events: a strategy immune to short-run sequential dependencies consisting of the persistent prediction of long-run majority events, hereafter called the long-run momentum strategy; a strategy immune to short-run sequential dependencies consisting of the persistent prediction of long-run minority events, called the long-run contrarian strategy; a strategy sensitive to short-run sequential dependencies consisting of the prediction of short-run majority events, called the short-run momentum strategy; and a strategy sensitive to short-run sequential dependencies consisting of the prediction of short-run minority events, called the short-run contrarian strategy. When the character of events remains unknown, the most common strategy is the short-run momentum strategy. With the increase of a perceived randomness of the situation, people tend more often to use the short-run contrarian strategy. People differ in their general beliefs about the continuation or reversal of a trend in various natural and social processes. Trend believers, when facing sequences of binary events commonly perceived as random, tend to use momentum strategies, whereas those who believe in the trend's reversal tend to use contrarian strategies.