Andrew Schumann

In decision making quite often we face permanently changeable and potentially infinite databases when we cannot apply conventional algorithms for choosing a solution. A decision process on infinite databases (e.g. on a database containing a contradiction) is called troubleshooting. A decision on these databases is called creative reasoning. One of the first heuristic semi-logical means for creative decision making were proposed in the theory of inventive problem solving (TIPS) by Genrich Altshuller. In this paper, I show that his approach corresponds to the so-called content-generic logic established by Soviet philosophers as an alternative to mathematical logic. The main assumption of content-genetic is that we cannot reduce our thinking to a mathematical combination of signs or to a language as such and our thought is ever cyclic and reflexive so that it contains ever a history.

It is a Preface to Volumes 7:3 and 7:4 (2018) consisting of articles presented at the International Interdisciplinary Conference Ideas and Society on the 150^th anniversary of the birth of Leon Petrażycki, held on November 24, 2017, in Rzeszów, Poland.

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.

We have proposed to use some features of swarm behaviours in modelling business processes. Due to these features we deal with a propagation of business processes in all accessible directions. This propagation is involved into our formalization instead of communicating sequential processes. As a result, we have constructed a business process diagram language based on the swarm behavior and an extension of that language in the form of reflexive management language.

In this paper, we consider different ways of designing reversible logic gates on Physarum polycephalum motions using controlling stimuli such as attractants and repellents. Repellents are needed because of uncertainty in the direction of plasmodium propagation to eliminate some directions as unimportant. In this way, we can construct conventional reversible logic gates: the CNOT gate, the FREDKIN gate, the TOFFOLI gate, etc. Combinations of reversible logic gates are regarded as matrix multiplications. Nevertheless, the plasmodium in its networking can permanently change its decisions and without repellents we have an extension of matrix multiplication group theory. Within this extension we can design unconventional reversible logic gates, where the number of inputs and outputs is uncertain.

One of the main assumptions of mathematical tools in science is represented by the idea of measurability and additivity of reality. For discovering the physical universe additive measures such as mass, force, energy, temperature, etc. are used. Economics and conventional business intelligence try to continue this empiricist tradition and in statistical and econometric tools they appeal only to the measurable aspects of reality. However, a lot of important variables of economic systems cannot be observable and additive in principle. These variables can be called symbolic values or symbolic meanings and studied within symbolic interactionism, the theory developed since George Herbert Mead and Herbert Blumer. In statistical and econometric tools of business intelligence we accept only phenomena with causal connections measured by additive measures. In the paper we show that in the social world we deal with symbolic interactions which can be studied by non-additive labels (symbolic meanings or symbolic values). For accepting the variety of such phenomena we should avoid additivity of basic labels and construct a new probabilistic method in business intelligence based on non-Archimedean probabilities

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 device