Search results for: Lidia Obojska

Items from 1 to 13 out of 13 results

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The p-semisimple property for some generalizations of BCI algebras and its applications

Lidia Obojska, Andrzej Walendziak

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica > 2020 > 19 > 79-94

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.

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The Parthood of Indiscernibles

Lidia Obojska

Axiomathes > 2019 > 29 > 5 > 427-439

In the following work we propose to incorporate the main feature of quantum mechanics, i.e., the concept of indiscernibility. To achieve this goal, first we present two models of set theories: a quasi-set theory (QST) and a non-antisymmetric mereology (NAM). Next, we show how specific objects of QST—m-atoms—can be defined within NAM. Finally, we introduce a concept of a parthood of indiscernibles...

article

Mereologa a klasyczna teoria zbiorów

Lidia Obojska

Matematyka Poglądowa > 2016 > 3 > 31-36

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Some remarks of Jan Śleszyński regarding foundations of mathematics of Stanisław Leśniewski

Lidia Obojska

Czasopismo Techniczne > -

Jan Śleszyński, a great mathematician, is considered a pioneer of Polish logic; however, he was not connected with the famous Warsaw School of Logic (WSL). He believed that his mission was a critical evaluation of work of other logicians in the field of foundations of mathematics and proof theory. Among his writings we find several notes regarding the work of Stanisław Leśniewski (the co-founder of...

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"Exact Sciences and Mathematics in Central-Eastern Europe from the mid-XIX Century till WWII." The scientific conference.

Lidia Obojska

Antiquitates Mathematicae > 2015 > 9

article

Kilka uwag na temat koncepcji mnogościowych Richarda Dedekinda i Stanisława Leśniewskiego

Lidia Obojska

Kwartalnik Historii Nauki i Techniki > 2014 > 59 > 1 > 95-107

Mereology, is a part-whole theory, also called the theory of collective sets. It was founded in1916 by Stanislaw Lesniewski and this is an alternative theory versus the classical set theory by Georg Cantor. These two theories are usually teamed up together as Leśniewski himself was referring to the concept of the set by Cantor and Cantor is considered the "main" ideologist of the set theory...

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Elementy logiki w polskiej szkole matematycznej. Wkład Stanisława Leśniewskiego

Lidia Obojska

Zagadnienia Filozoficzne w Nauce > 2013 > 53 > 165-197

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...

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ALGEBRAICZNE ASPEKTY MEREOLOGII NIEEKSTENSJONALNEJ

Lidia Obojska

Roczniki Filozoficzne > 2012 > 60 > 1 > 105-124

Mereologia klasyczna, nazywana również˙ mereologia˛ ekstensjonalna˛ została dość szczegółowo przebadana przez wielu autorów. Udowodniono, z˙e jest to model odpowiadający algebrom Boole’a bez zera. Model nieco słabszy, w którym relacja pierwotna bycia częścią nie spełnia zasady ekstensjonalności, może zostać nazwany mereologią nieekstensjonalną. Jak dotychczas nie istnieje systematyczna analiza takiego...

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Some Remarks on Rings

Lidia Obojska, Paul O’Hara

Commentationes Mathematicae > 2010 > 50 > 1

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...

article

“Primary Relations” In a New Foundational Axiomatic Framework

Lidia Obojska

Journal of Philosophical Logic > 2007 > 36 > 6 > 641-657

The new system of axioms we propose is based on the foundational theory of De Giorgi et al. Scuola Normale Superiore di Pisa, Preprints di Matematica 26: 1 (1996) slightly modified. In that paper (which is dedicated to a new axiomatic framework for mathematics, informatics and logic) the authors use two kinds of primitive notions: relations and qualities. Since their system is based on the distribution...

article

Testing for Nonlinearity in the Solar Wind Flow

Wiesław M. Macek, Lidia Obojska

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear... > 1998 > 9 > 1-2 > 221-229

We analyse a time series of the velocities of the low-speed stream measured by the Helios spacecraft in the inner heliosphere, which is a region of space dominated by the solar wind flow. We use a moving average (linear) filter to give a faithful representation of the system's nonlinear behaviour. We have found that trajectories describing the system in phase space asymptotically approach the attractor...

article

Testing for nonlinearity in the solar wind flow

Wiesław M. Macek, Lidia Obojska

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear... > 1998 > 9 > 1-2 > 221-229

article

Fractal Analysis of the Solar Wind Flow in the Inner Heliosphere

Wiesław M. Macek, Lidia Obojska

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear... > 1997 > 8 > 10 > 1601-1607

We argue that the inner heliosphere is a chaotic system. We invoke time series analysis of the measurements by the Helios spacecraft (near the Sun) in low-speed streams. The slope of the calculated correlation function saturates at some finite value of the embedding dimension, indicating a low-dimension of the attractor of about 3.5. Furthermore, the largest calculated positive Lyapunov exponent...

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