Modal Calculus of Names
Abstract
Sentences with the form: x is δ y, where δ is one of the modal operators (of the n/n category) is usually interpreted as rendering modalities of the de re type, as contrary to sentences included in the scheme: ΔP(x), where the modal operator Δ (of the s/s category) is semantically ambiguous (de re or de dicto). In literature treating modality as de dicto modality dominates. This results mainly from the fact that modal calculi are practiced mainly as sentential calculi, built over the classical sentential calculus, where – in the nature of things – the structure of sentences is not analyzed. We also have some extensions of elementary ontology (Lebedev’s) with the modal operator of the is-δ (s/nn) type as the primary operator.
In the article a construction is suggested, in which an operator of the δ (n/n) type is the primitive term. It is an elementary modal ontology that is an inferential extension of one of the mentioned systems, despite a formal simplification of its axioms.
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