Predicate abstraction
In logic, predicate abstraction is the result of creating a predicate from a sentence. If Q is any formula then the predicate abstract formed from that sentence is, where λ is an abstraction operator and in which every occurrence of y occurs bound by λ in. The resultant predicate is a monadic predicate capable of taking a term t as argument as in, which says that the object denoted by 't' has the property of being such that Q.
The law of abstraction states ≡ Q where Q is the result of replacing all free occurrences of x in Q by t. This law is shown to fail in general in at least two cases: when t is irreferential and when Q contains modal operators.
In modal logic the "de re / de dicto distinction" is stated as
1. :
2. :.
In the modal operator applies to the formula A and the term t is within the scope of the modal operator. In t is not within the scope of the modal operator.
