Predicate Abstraction
Get Predicate Abstraction essential facts below. View Videos or join the Predicate Abstraction discussion. Add Predicate Abstraction to your topic list for future reference or share this resource on social media.
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 (?y.Q), where ? is an abstraction operator and in which every occurrence of y occurs bound by ? in (?y.Q). The resultant predicate (?x.Q(x)) is a monadic predicate capable of taking a term t as argument as in (?x.Q(x))(t), which says that the object denoted by 't' has the property of being such that Q.

The law of abstraction states ( ?x.Q(x) )(t) ? Q(t/x) where Q(t/x) 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: (i) when t is irreferential and (ii) when Q contains modal operators.

In modal logic the "de re / de dicto distinction" is stated as

1. (DE DICTO):

2. (DE RE): .

In (1) the modal operator applies to the formula A(t) and the term t is within the scope of the modal operator. In (2) t is not within the scope of the modal operator.


For the semantics and further philosophical developments of predicate abstraction see Fitting and Mendelsohn, First-order Modal Logic, Springer, 1999.

  This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.



Music Scenes