Cs792 Notes Logical Relations

4. R(ConstA(c), ConstB(c)) for every typed constant c : σ of Σ. For λ we drop the rule for × and for extensions of λ there is another rule for each type form. The essential property for λ is that two functions are related iff they take related arguments to related results. The intuition is that a logical relation, relates the meaning of a term in one model to its meaning in another model. The conditions are to assure that the meanings are consistent under introduction and elimination, of × and → in this case. Logical relations can be generalized to be n-ary rather than binary. The unary case is called a logical predicate. Taking the obvious definition for logical predicates, it can be seen that a binary logical relation R ⊆ A× B is nothing more than a logical predicate over the applicative structure A× B.