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Theory of Mind and Empathy. Part I - Model of Social Emotional Thinking

Przybyszewski A. W., Polkowski L. T.

Fundamenta Informaticae

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2017

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Vol. 150, nr 2

221--230

EN

There are two very different approaches to understand functioning of the brain. First, there is a huge progress in the research of the neurological and neurophysiological properties of different brain substructures, circuits, networks, single cells, synapses and their molecular properties. It contributes to the progress of research in the fields of basic medical sciences and the dramatic increase in average life expectancy. On the another side that does not directly follows neurological developments, it is our introspection related to individual ways of thinking in order to solve different problems that also involve human creativity (cognitive theory of mind). We use many diverse ways of thinking, and they depend on different circumstances. Especially interesting are influences of intuition, feelings and emotions on our creativity, which is in a large part are also related to the social interactions (affective empathy). In this work, we formalise emotional scales and transfer of emotions between individuals (social emotional thinking). We also demonstrate a continuity of the emotion transfer mappings, and an importance of the interactions between emotional faces. It is not only human specific to show and to react to face emotions, but strong and wide human social interactions are based on the precise emotional social thinking. By measuring critical values of face deformations that may influence mutual emotions, we can test precision and tolerance of human visual and emotional systems. By introduction indiscernibility relations between individual reading of face parts deformation, we have used rough set theory to probe social emotional thinking. As one of us have demonstrated that the visual system has properties that follows rough set theory (cognitive theory of mind), this work extends this concept to the social emotional interactions (cognitive and affective theory of mind). As in modern world IT - information technology - has became driving factor in the process of globalisation by creating effective channels of information exchange; hence it becomes extremely important to analyse emotional meaning (cognitive empathy) for this vast information flow. By using as described here, rough set theory to determine, which parts of information have significant emotional influence, our model may give grounds to increase the collective well-being.

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From Leśniewski, Łukasiewicz, Tarski to Pawlak : Enriching Rough Set Based Data Analysis. A Retrospective Survey

Polkowski L. T.

Fundamenta Informaticae

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2017

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Vol. 154, nr 1/4

343--358

EN

This work is dedicated to Profesor Andrzej Ehrenfeucht, the eleve of the Warsaw School of Logic and Mathematics on the occasion of His 85th Birthday. We propose to exploit certain of the milestone ideas created by this School and to apply them to data analysis in the framework of the rough set theory proposed by Professor Zdzisław Pawlak. To wit, we apply the idea of fractional truth states due to Jan Łukasiewicz, mereology created by Stanisław Leśniewski and the betweenness relation used by Alfred Tarski as one of primitive predicates in His axiomatization of Euclidean geometry. These ideas applied in problems of approximate reasoning permit us to formalize calculus of granules of knowledge and use it in preprocessing of data before applying a classification algorithm. Introduction of a mereological version of betweenness relation to data allows for partitioning of data into the kernel and the residuum, both sub-data sets providing a faithful representation of the whole data set and reducing the size of data without any essential loss of accuracy of classification. In the process of algorithmic construction of the partition of data into the kernel and the residuum, we exploit the Dual Indiscernibility Matrix which further allows us to introduce notions of a pair classifier and, more generally, k-classifier yet to be studied.

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Betweenness, Łukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper-granules and Conflict Resolution

Polkowski L. T., Nowak B.

Fundamenta Informaticae

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2016

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Vol. 147, nr 2/3

337--352

EN

In this work, we approach the problem of data analysis from a new angle: we investigate a relational method of separation of data into disjoint sub–data employing a modified betweenness relation, successfully applied by us in the area of behavioral robotics, and, we set a scheme for applications to be studied. The effect of the action by that relation on data is selection of a sub–data, say, ‘kernel’ with the property that each thing in it is a convex combination, in a sense explained below, of some other things in the kernel. One can say that kernel thus exhibited is ‘self–closed’. Algorithmically, this is achieved by means of a new construct, called by us a ‘dual indiscernibility matrix’. On the other hand, the complement to kernel consists of things in the data, which have some attribute values not met in any other thing. It is proper to call this complement to kernel the residuum. We examine both the kernel and the residuum from the point of view of quality of classification into decision classes for a few standard data sets from the UC Irvine Repository finding the results very satisfactory. Conceptually, our work is set in the framework of rough set theory and rough mereology and the main tool in inducing of the betweenness relation is the Łukasiewicz rough inclusion. Apart from the classification problem, we propose some strategies for conflict resolution based on concepts introduced in this work, and in this way we continue conflict analysis in rough set framework initiated by Zdzisław Pawlak.