Formulation and Algebraic Treatment of Reasonings - 2. Notions of Existence, Occurrence, Conceivability.

The paper extends the method presented in Part 1 to arguments involving such fuzzy notions as ″some A or B″ , ″it may happen that AB″ , ″it is conceivable that AB″ etc. These notions are expressed in terms of so-called ″elementary variables″ . In a three-term (A, B, C) problem, there are eight potential elementary variables of existence. However, in a given argument, only part of them are used (for instance, in any given classical syllogism, only three or four of the eight potential elementary variables are used). Once the premises have been expressed in terms of these binary variables, the discovery of the conclusions is reduced to the preceding problem. The complexity of the arguments one can treat is limited only by the number of variables that can be accomodated in the search for the primary implicants of a function.