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In this work results of two experiments on application of rough set theory in land improvement sciences are included.

The discussions of the theory TSCL (B) of simple categorial languages, which is to be constructed in this chapter, will be concerned with an arbitrary but fixed language L of expression tokens which do not include variables bound by operators. The Language L, called here a simple categorial language of expression tokens, is determined by certain conditions imposed on its syntax in accordance with the idea of K.Ajdukiewicz’s categorial grammar 119351 and the conceptions of those researchers who referred to his ideas. (4)

The theory TSCL described languages which are poor in a certain sense. This is because most theorems formulated in mathematical theories are formulated in languages which include new expressions, not occurring in simple categorial languages, namely expressions with variables and operators that bind those variables. It seems, therefore, natural to modify TSCL - while retaining the main objectives described in Sec.IIA and observed when TSCL was constructed - so that it should cover the languages mentioned above. The syntactic analysis of expressions, correct from the point of view of the theory of syntactic category, should be respected, too.

Let us imagine the situation of a user of an ethnic language who wants to write a letter or the situation of a mathematician who wants to formulate theorems or to produce proofs in a formalized language. Both of them select ahd write out simple labels of’ a definite shape, combine them into more complex labels that follow one another, and -frequently reproduce them. Linguistic expressions used by a given language user are concrete, physical, sensorily perceivable objects, namely label tokens (in Latin (labels) in concreto, in English also label events; see Ch.S.Peirce [1931–19351; R.Carnap 119427). A precise explanation of the properties of those material objects encounters greater difficulties than those which we face when we establish the properties of ideal, abstract objects. We face such difficulties when we want to formulate an intuitive characteristic of a given language. (1)