In the presented paper we would like to focus on the scientific activity of the one of the members of the Warsaw School of Logic. It is supposed that the world famous formalisms of Polish logicians were mainly stimulated by Stanisław Leśniewski. If this is true, Leśniewski can be considered as the main ideologist of Warsaw School. The first part of this paper is dedicated to a very brief presentation of the history of Polish logic in the period 1910-1939. Next, we present the main ideas of the Warsaw School of Logic and in particular the contribution of Stanisław Leśniewski: his original system of three theories: protothetics, ontology and mereology and their novelty in comparison with classical thought. Finally, we try to show the influence of Leśniewski’s innovative ideas on other members of the school.
Algebraic structures such as Rings, Fields, Boolean Algebras (Set Theory) and \(\sigma\)-Fields are well known and much has been written about them. In this paper we explore some properties of rings related to the distribution law. Specifically, we shall show that for rings there exists only one distribution law. Moreover, for the ring \((Z_{p(p−1)n} +, \cdot)\), where \((p, n) = 1\) there exist isomorphic groups \((G, +)\), \((H, \cdot)\), \(G, H \subset Z_{p(p−1)n}\) of the order \((p − 1)\). Finally, we note that every ring \((Z_{pn}, +, \cdot)\) contains subfields \(\text{mod}(pn)\).
Celem niniejszego artykułu jest opracowanie metodyki szacowania pozycji ekonomicznej państwa. Do oceny pozycji ekonomicznej zastosowano analizę formalną w oparciu o model siły ekonomicznej Sułka i dokonano analizy jej czynników. Oceniono stopień niezależności zmiennych uwzględnionych w modelu formalnym. W przypadku gdy są one silnie skorelowane, rozdzielono je lub, jeśli nie było to możliwe, utworzono nowe czynniki, które łączą skorelowane jednostki. Zastosowano różne metody predykcji siły ekonomicznej, w szczególności oparte na sieciach neuronowych, które nie wymagają normalnego rozkładu błędów. Na koniec oszacowano pozycję gospodarczą państwa na podstawie analizy formalnej, prognoz oraz w porównaniu z wybranymi rankingami gospodarczymi. Wszystkie wyniki opracowano dla Nigerii.
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The scope of this manuscript is to propose a method of estimation of state's economic position. To evaluate an economic position, we apply formal analysis on Sułek's model of economic power, and analyze its factors. We evaluate whether the variables taken in a formal model are independent or not. In case they are strongly correlated, we split them or, if it is not possible, we create new factors which puts together correlated units. We apply various methods of predictions of economic power; in particular neural networks which do not require the normal distribution of errors. Finally, we estimate the state's economic position on the basis of formal analysis, predictions, and in comparison to selected economic rankings. All the results are figured out for Nigeria.
This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.