In this study the author aims to solve the question of the ontological context of the semeiological status of the algorithmic description of the objective process taking place in nature, in society and in thinking. Using the explanatory function of Ogden and Richards’ reference triangle we can say that the syntax of the language of the algorithm is in the sense of the Leninist theory of reflection a “rational reconstruction” of those thinking operations which are the basis of the logical model of end processes and purposeful action in systems of living organisms, thinking and machines. In this respect we consider the algorithm as an instrument, a method and a process of rational orientation in a reality and as one of the logical forms of “objective dialectics of nature”. A great number of respective examples can be found in bionomics and cybernetics. The reflection of the objective, ontological algorithmic process in cognition and psychology form just that psychic context of the language of the text of the algorithm, and that the language of the algorithm can then be explained as the expression of this context or the so-called psychic state of the cognizing subject. In the outlined process of investigation we draw attention to the necessity of studying the logic of thinking and its possible algorithmic description which will enable us to build algorithmic processes of programming a selected part of the teaching material in such a way that the teaching text will become a semantic model of the logic of the algorithmic process of thinking. A great number of possibilities in this respect are provided by systems of logical calculations. Their interpretation in individual sciences is, in this case, the creation of the semantic models of these calculations and thereby also a possibility of making use of the algorithm in programming the teaching material of a given scientific branch. In conclusion it is pointed out that special didactics, or the so-called methodologies of subjects are in substance metatheories of the given theoretical disciplines, and are, above all, rational, logical reconstructions of their conceptual and expressional construction. In this sense we underline the necessity of studying modern mathematical logic, semeiotics and general systemology. These disciplines are regarded as fundamental theoretical pre-requisites for building scientific theories of special didactics "