The paper represents a transcription of the lecture delivered at the Mathematics Department of the University of Malaya, Kuala Lumpur (Malaysia). The problem of modelling heuristic activities in problem solving using different forms of logic is studied. The process of thinking itself is taken as an object of investigation rather than the result of this process. Classical logical theories (from Aristotle to Boole), Brouwer’s and Heyting’s Intuitionism, Kolmogoroff’s ‘Logic of Problems’, modal logic and Polya’s theory of plausible reasoning are considered as possible sources of models. One example of problem solving is presented to illustrate an application of Kolmogoroff’s axioms and shows that only few of them are natural for modelling mental activities. Sequential logic is considered to represent temporal reference. Logical basics of reasoning are also discussed. Some limitations of the presented logical models in applications for problem solving activities modelling are discussed.
It is concluded that heuristic and problem solving activities cannot be precisely modelled by any of the considered logical models. Classical logical theories are considered as rough models of thinking as they cannot represent all mental activities. Some difficulties appear when it is necessary to model logically nonlinear flows of actions and feedback elements. It is because thinking as problem solving activity involves meta-logical, meta-cognitive and non-logical elements and operations. The classical concept of negation function has also to be redefined to be able to distinguish between ‘not doing’ and ‘doing in opposite way’.
Future results are anticipated using applications of contemporary theory of synergetic and neurophysiology.