ONTOLOGIA ELEMENTARNA I KLASYCZNY RACHUNEK RELACJI

The notion of relation is one of the most important concepts present in our language. This study propose some extension of elementary ontology (OE) for relational variables and defining in his framework the concepts of the classical calculus of relations. Such enriched elementary ontology (OER) is a better tool for the analysis of natural language. It is shown that syllogistic with the negative terms enriched by so called oblique syllogisms (SNU with the axioms C1–C5) is a fragment of OER system (Theorem 1). The OER system is enriched next with individual variables (a,b,c) and by assuming the individual term referentiality (axiom A2) we obtain OER* system. The Proof that the classical calculus of relations (KRR) is a part of the system OER* (Theorem 2) is given.