Three contributions to the two-valued propositional calculus

Summary Three chapters contain the results independent of each other. In the first chapter I present a set of axioms for the propositional calculus which are shorter than the ones known so far, in the second one I give a method of defining all ternary connectives, in the third one, I prove that the probability of propositional functions is preserved under reversible substitutions. This paper appeard orginally under the title “Trois contributions an calcul des propositions bivalent” inStudia Societatis Scientiarum Torunensis, Toruń, Polonia, Sectio A, vol. I (1948), pp. 3–15.     

Concerning axiomatizability of the quasivariety generated by a finite Heyting or topological Boolean algebra

In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve problem 4 asked in Rautenberg [10].     

Systemy S4 I S5 Lewisa a spójnik identyczności

Allatum est die 28 Septembris 1970     

O klasach normalnych i nienormalnych na terenie języka potocznego

Problematyka i glówne tezy tej pracy pochodz od pierwszego autora. Udzial drugiego autora sprowadza sie do propozycji utosamienia jeezyka potocznego z formalizmem logiki zda i logiki nazw oraz do pewnych sugestii odnonie systematyzacji materialuAllatum est die 2 Octobris 1965     

Motivation to comply with task rules and multitasking performance: The role of need for cognitive closure and goal importance

In three studies, we examined the role task rules play in multitasking performance. We postulated that rules should be especially important for individuals highly motivated to have structure and clear answers, i.e., those high on need for cognitive closure (NFC). High NFC should thus be related to greater compliance with task rules. Specifically, given high goal importance, NFC should be more strongly related to a multitasking strategy when multitasking is imposed by the rules, and to a mono-tasking strategy when monotasking is imposed by the rules. This should translate into better multitasking or mono-tasking performance, depending on condition. Overall, the results were supportive as NFC was related to a more mono-tasking strategy in the mono-tasking condition (Studies 1 and 2 only) and more dual-tasking strategy in the dual-tasking condition (Studies 1–3). This translated into respective differences in performance. The effects were significant only when goal importance was high (Study 1) and held when cognitive ability was controlled for (Study 2).