Cognitive Aspects of Anticipation by the Klein Four-Group and the Elementary Pragmatic Model

In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. Whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the "universe of discourse" (UOD) (Boole, 1854/2003). According to Piaget, human adults normally know how to use properly classical propositional logic to manage their UOD. Piaget also showed that human propositional competence is realized via the integration of algebraic composition and relational ordering in formal logic based on the mathematical Klein group structure (KGS) (Inhelder & Piaget, 1955). In the last fifty years, many experiments made by psychologists of reasoning have often shown most adults commit logical fallacies in propositional inferences. They have so concluded, relying on many empirical evidences, that Piaget's claim about adults' competence in propositional logic was wrong and much too rationalist. In other words, according to experimental psychologists, Piaget was overestimating the logical capacities of average human adults in the use of classical propositional logical connectives. So, they abandoned his approach. Nevertheless, the KGS Piaget used can be reused to help us understand better what happens in spontaneous single human reasoning and in the production of fallacies. In fact, the KGS generates squares of opposition (SOO), and an important component of human rationality resides in the diagram of the SOO, as formal articulations of logical dependence between connectives. SOO are considered as important basic components of logical competence and of human predicative rationality (Beziau & Payette, 2012). The KGS captures all the fundamental transformations needed for the predicative proficiency of single human subject. But the formal rationality provided by the SOO is not spontaneous and therefore, should not be easy to learn for adults. By an abstract point of view, the Elementary Pragmatic Model (EPM) (De Giacomo et al., 2016) can be seen as the fundamental, logic description of two KGSs interacting with each other. In other words, EPM can model all the elementary interactions between two rational, interacting human subjects. Again, predicative competence for humans does not come for granted! This is the main reason why we need reliable and effective training tools to achieve full logic proficiency and competence, like EPM. EPM was developed in the late 1960s following Gregory Bateson's constructivist participant observer concept in the "second order cybernetics". Later it was applied to develop interactive psychotherapy strategies, online counseling and E-therapy. EPM is a quite flexible tool for mapping cross- inter- and trans- disciplinary expertise. Since the beginning of the new millennium its application area has been extended to other disciplines and even to engineering problems like user modeling, constraint requirements elicitation, software creativity and adaptive system design and development. EPM allows predictive, predicative computation that facilitates anticipatory behavior (Nadin, 2014). As a further example, the KGS can be even interpreted as the complete transformation mapping of the human perception of our outer and inner universe representations, where the encoding process is carried out by human affectors (our biological sensors) and the decoding process is done by human effectors (our biological actuators). In this way, the single observer encoding and decoding of the classic Rosen modeling relationship (Rosen, 1985) can be computationally formalized at operative level (De Giacomo & Fiorini, 2017). The information process describing the dynamics of reality to anticipation means to acknowledge that deterministic and non­deterministic processes are complementary. Therefore, it is possible to conceive a convenient EPM-based schema for Ontological Uncertainty Management (OUM) System as in Fiorini (2015). Following neurophysiological findings by LeDoux (2002), we focus on ontological uncertainty (Lane & Maxfield, 2005) as an emergent phenomenon from a complex system. A dynamic ontological perspective can be thought of as an emergent, natural cross- inter- trans- disciplinary reality level (TRL) (Nicolescu, 1992; 1996) from, at least, a dichotomy of two fundamental, coupled, irreducible, and complementary computational subsystems: (A) reliable unpredictability, and (B) reliable predictability subsystem respectively. From a Top-Down (TD) management perspective, the reliable predictability concept can be referred to the traditional system reactive approach (lag subsystem, closed logic, to learn and prosper) and operative management techniques. The reliable unpredictability concept can be associated with the system proactive approach (lead subsystem, open logic, to survive and grow) and strategic management techniques. In fact, to behave realistically, the system must guarantee both Logical Aperture (to survive and grow) and Logical Closure (to learn and prosper), both fed by environmental "noise" (better… from what human beings call "noise"). EPM coupled to EPM extension as "Evolutive Elementary Pragmatic Model" (E2PM) represents a different implementation of the same OUM system concept as presented in Fiorini (2015). Therefore, traditional EPM can be thought as a reliable starting subsystem (closed logic, operative management (B)) to initialize a process of continuous self-organizing and self-logic learning refinement by E2PM (open logic, strategic management subsystem (A)). This approach can capture natural logic dynamics behavior, as a function of specific unpredictable perturbance, unknown at system design level. It is an original contribution to current evolutive modeling and simulation, offering an example of new forms of system self-evolutive behavior by cross- inter- and trans-disciplinarity modeling (e.g. forecasting, strategic foresight, anticipation, uncertainty management, embracing the unknown, creativity, etc.) for the children of the Anthropocene Era.