Formalization of functionally complete propositional calculus with the functor of implication as the only primitive term

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments.To the memory of Jerzy Supecki     

Categorical and algebraic aspects of Martin-Löf Type Theory

In the paper there are introduced and discussed the concepts of an indexed category with quantifications and a higher level indexed category to present an algebraic characterization of some version of Martin-Löf Type Theory. This characterization is given by specifying an additional equational structure of those indexed categories which are models of Martin-Löf Type Theory. One can consider the presented characterization as an essentially algebraic theory of categorical models of Martin-Löf Type Theory. The paper contains a construction of an indexed category with quantifications from terms and types of the language of Martin-Löf Type Theory given in the manner of Troelstra [11]. The paper contains also an inductive definition of a valuation of these terms and types in an indexed category with quantifications.     

Behavior of visual evoked potentials (pattern reversal VECP) in smokers

Twenty six clinically healthy smokers were studied with transient pattern visual-evoked potentials. In comparison with a sample of "normal" subjects we found a difference of some parameters (P less than 0.05): the P2-latency and the interocular difference of latency on average were 6-7 ms respectively 2 ms larger. Thirteen subjects have had a prolonged P2-latency (P less than 0.05) and/or a difference in interocular latencies larger than 5 ms. These findings may suggest on subclinical disturbances of visual system and indicators of an special sensitivity of that person. The findings are possibly related to tobacco-alcohol amblyopia.     

On a problem of P(α, δ, π) concerning generalized Alexandroff s cube

Universality of generalized Alexandroff's cube plays essential role in theory of absolute retracts for the category of , -closure spaces. Alexandroff's cube. is an , -closure space generated by the family of all complete filters. in a lattice of all subsets of a set of power .Condition P(, , ) says that is a closure space of all , -filters in the lattice ( ), .Assuming that P (, , ) holds, in the paper [2], there are given sufficient conditions saying when an , -closure space is an absolute retract for the category of , -closure spaces (see Theorems 2.1 and 3.4 in [2]).It seems that, under assumption that P (, , ) holds, it will be possible to givean uniform characterization of absolute retracts for the category of , -closure-spaces.Except Lemma 3.1 from [1], there is no information when the condition P (, , ) holds or when it does not hold.The main result of this paper says, that there are examples of cardinal numbers, , , such that P (, , ) is not satisfied.Namely it is proved, using elementary properties of Lebesgue measure on the real line, that the condition P (, ₁, 2 ) is not satisfied.Moreover it is shown that fulfillment of the condition is essential assumption in, Theorems 2.1 and 3.4 from [1] i.e. it cannot be eliminated.     

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.     

Cognitive dysfunction in compulsive checkers: Further explorations

Recent evidence suggests a relationship between certain memory deficits and compulsive-checking behavior. The present study explores this relationship in the context of several additional memory capacities not yet investigated. Using the Maudsley Obsessional-Compulsive Inventory and the Everyday Checking Behavior Scale four groups of Ss were identified: (1) frequent checkers, (2) occasional checkers, (3) infrequent checkers and (4) noncheckers. Consistent with previous research, a memory-for-actions task indicated a deficit among compulsive checkers. Furthermore, checking status was found to be negatively related to memory functioning as measured by the Wechsler Memory Scale (WMS) and the Cognitive Failures Questionnaire (CFQ). This memory deficit was most pronounced on the Logical Memory subtest of the WMS. Checkers appear to have difficulty recalling details of meaningfully linked sequences, either presented in narrative form or engaged in personally. Although the reasons for these checking-related deficits are not clear, a complete understanding of checking phenomena will involve an appreciation of the role played by memory deficits.     

Understanding dark side personality at work: Distinguishing and reviewing nonlinear,interactive, differential,and reciprocal effects

The topic of dark side personality at work has received considerable research attention over the past decade, and both qualitative and quantitative reviews of this field have already been published. To show the relevance of dark personality in the work context, existing reviews have typically focused on systematically discussing the different criteria that have been linked to dark traits (e.g., job performance, work attitudes, leadership emergence, etc.). In contrast, and complementing this earlier work, the current review paper summarizes the available literature on this topic by structuring it in terms of the nature of the relationships studied rather than in terms of the types of outcome variables. Doing so, the focus shifts from “What are the outcomes of dark traits?” to “How are dark traits related to work outcomes?” Scrutinizing the nature of these relationships, we specifically focus on four types of effects (i.e., nonlinear, interactive, differential, and reciprocal) that highlight the complexity of how dark side traits operate in the work context. Structured this way, this review first provides a conceptual underpinning of each of these complex effects, followed by a summary of the empirical literature published over the past 10 years. To conclude, we present an integration of this field, provide suggestions for future research, and highlight concrete assessment challenges.