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1

Slime mould games based on rough set theory

Pancerz K., Schumann A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

531--544

EN

We define games on the medium of plasmodia of slime mould, unicellular organisms that look like giant amoebae. The plasmodia try to occupy all the food pieces they can detect. Thus, two different plasmodia can compete with each other. In particular, we consider game-theoretically how plasmodia of Physarum polycephalum and Badhamia utricularis fight for food. Placing food pieces at different locations determines the behavior of plasmodia. In this way, we can program the plasmodia of Physarum polycephalum and Badhamia utricularis by placing food, and we can examine their motion as a Physarum machine—an abstract machine where states are represented as food pieces and transitions among states are represented as movements of plasmodia from one piece to another. Hence, this machine is treated as a natural transition system. The behavior of the Physarum machine in the form of a transition system can be interpreted in terms of rough set theory that enables modeling some ambiguities in motions of plasmodia. The problem is that there is always an ambiguity which direction of plasmodium propagation is currently chosen: one or several concurrent ones, i.e., whether we deal with a sequential, concurrent or massively parallel motion. We propose to manage this ambiguity using rough set theory. Firstly, we define the region of plasmodium interest as a rough set; secondly, we consider concurrent transitions determined by these regions as a context-based game; thirdly, we define strategies in this game as a rough set; fourthly, we show how these results can be interpreted as a Go game.

2

Two Squares of Oppositions and Their Applications in Pairwise Comparisons Analysis

Schumann A., Woleński J.

Fundamenta Informaticae

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2016

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Vol. 144, nr 3/4

241--254

EN

This paper examines two main possibilities of pairwise comparisons analysis: first, pairwise comparisons within a lattice, in this case these comparisons can be measurable by numbers; second, comparisons beyond any lattice, in this case these comparisons cannot be measurable in principle. We show that the first approach to pairwise comparisons analysis is based on the conventional square of opposition and its generalization, but the second approach is based on unconventional squares of opposition. Furthermore, the first approach corresponds to lateral inhibition in transmission signals and the second approach corresponds to lateral activation in transmission signals.

3

Decisions involving databases, fuzzy databases and codatabases

Schumann A., Woleński J.

Operations Research and Decisions

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2015

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Vol. 25, No. 3

59--72

EN

The authors consider the following three ways of decision making: (i) decisions involving databases by means of standard tools of sequential logic and universal algebra; (ii) decisions involving fuzzy databases by means of fuzzy logic; (iii) decision involving continuously growing databases (codatabases) using the tools of Bayesian networks.

4

Probabilities on streams and reflexive games

Schumann A.

Operations Research and Decisions

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2014

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Vol. 24, No. 1

71--96

EN

Probability measures on streams (e.g. on hypernumbers and p-adic numbers) have been defined. It was shown that these probabilities can be used for simulations of reflexive games. In particular, it can be proved that Aumann’s agreement theorem does not hold for these probabilities. Instead of this theorem, there is a statement that is called the reflexion disagreement theorem. Based on this theorem, probabilistic and knowledge conditions can be defined for reflexive games at various reflexion levels up to the infinite level.

5

Towards an Object-Oriented Programming Language for Physarum Polycephalum Computing : A Petri Net Model Approach

Schumann A., Pancerz K.

Fundamenta Informaticae

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2014

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Vol. 133, nr 2/3

271--285

EN

Our research is focused on creation of a new object-oriented programming language for Physarum polycephalum computing. Physarum polycephalum is a one-cell organism that can be used for developing a biological architecture of different abstract devices, among others, the digital ones. In the paper, we use an abstract graphical language in the form of Petri nets to describe the Physarum polycephalum behavior. Petri nets are a good formalism to assist designers and support hardware design tools, especially in developing concurrent systems. At the beginning stage considered in this paper, we show how to build Petri net models, and next implement them as Physarum polycephalum machines, of basic logic gates AND, OR, NOT, and simple combinational circuits on the example of the 1-to-2 demultiplexer.

6

On the history of logic in the Russian Empire (1850–1917)

Schumann A.

Czasopismo Techniczne. Nauki Podstawowe

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2014

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R. 111, z. 1-NP

185--194

EN

In 1850 a very important decision for the whole history of humanities and social sciences in Russia was made by Nicholas I, the Emperor of Russia: to eliminate the teaching of philosophy in public universities in order to protect the regime from the Enlightenment ideas. Only logic and experimental psychology were permitted, but only if taught by theology professors. On the one hand, this decision caused the development of the Russian theistic philosophy enhanced by modern methodology represented by logic and psychology of that time. On the other hand, investigations in symbolic logic performed mainly at the Kazan University and the Odessa University were a bit marginal. Because of the theistic nature of general logic, from 1850 to 1917 in Russia there was a gap between philosophical and mathematical logics.

PL

W 1850 r. car Rosji Mikołaj I wydał ważny dla nauk humanistycznych w Rosji edykt: wyeliminować nauczanie filozofii w uczelniach publicznych w celu ochrony systemu naukowego od idei Oświecenia. Tylko logika i psychologia eksperymentalna były dozwolone, jeśli prowadzili je profesorowie teologii. Z jednej strony, taka decyzja spowodowała rozwój rosyjskiej filozofii teistycznej wzmocnionej przez nowoczesne metodologie reprezentowane przez logikę i psychologię tamtych czasów. Z drugiej strony, badania w logice symbolicznej prowadzone głównie na uniwersytetach w Kazaniu i Odessie miały charakter marginalny. Ze względu na ogólny charakter teistyczny logiki, w Rosji w latach 1850–1917 nie było związków między logiką filozoficzną i matematyczną.