Full Idea
Properties in semantic theory: functions from worlds to extensions ('Californian'), reference, as opposed to sense, of predicates (Frege), reference to universals (Russell), reference to situations (Barwise/Perry), and composition from context (Lewis).
Gist of Idea
There are five main semantic theories for properties
Source
Alex Oliver (The Metaphysics of Properties [1996], §02 n12)
Book Reference
-: 'Mind' [-], p.16
A Reaction
[compressed; 'Californian' refers to Carnap and Montague; the Lewis view is p,67 of Oliver]. Frege misses out singular terms, or tries to paraphrase them away. Barwise and Perry sound promising to me. Situations involve powers.