A predicate is a verb phrase template that describes a property of objects, or a relationship among objects represented by the variables.
For example, the sentences "The car Tom is driving is blue", "The sky is blue", and
"The cover of this book is blue" come from the template "is blue"
by placing an
appropriate noun/noun phrase in front of it.
The phrase "is blue" is
a predicate and it describes the property of being blue. Predicates are often
given a name. For example any of "is_blue", "Blue" or "B" can be used to
represent the predicate "is blue" among others. If we adopt B as the name
for the predicate "is_blue", sentences that assert an object is blue can be
represented as "B(x)", where x represents an arbitrary object. B(x) reads as "x is blue".
Similarly the sentences "John gives the book to Mary", "Jim gives a loaf of bread to Tom", and "Jane gives a lecture to Mary" are obtained by substituting an appropriate object for variables x, y, and z in the sentence "x gives y to z". The template "... gives ... to ..." is a predicate and it describes a relationship among three objects. This predicate can be represented by Give( x, y, z ) or G( x, y, z ), for example.
Note: The sentence "John gives the book to Mary" can also be represented by another predicate such as "gives a book to". Thus if we use B( x, y ) to denote this predicate, "John gives the book to Mary" becomes B( John, Mary ). In that case, the other sentences, "Jim gives a loaf of bread to Tom", and "Jane gives a lecture to Mary", must be expressed with other predicates.