Complex predicates and logics for properties and relations (Q1267085)

A logic is introduced for dealing with predicates and relations and their deontations. This is a standard first-order language, with the addition of an operator \(\lambda\) that forms predicates from formulas. This language is interpreted over what the author calls intensional relational structures\(\). An intensional relational structure is an ordered quadruple \(\langle{\mathcal D}_{\mathcal I},{\mathcal D}_{\mathcal R},{\mathcal O},\text{ext} \rangle\) where the first two terms comprise a domain of individuals and a domain of primitive relations, the third contains a number of ``relation building'' operations, and the last represents an extension assignment that maps each relation into an extension. Distinct relations may be mapped into the same extension. In this logic some complex predicates have denotations, while some may not. The approach is simple, and throws considerable light on some philosophical issues concerning predicates and relations. The author shows how various philosophical assumptions about the denotata of relations give rise to significant algebras of relations.