Constructing lambda terms
For this exercise, you should already know something about semantic construction. In particular, you should be familiar with lambda calculus. The second week course on computational semantics by Koller, Burchardt and Walter will start at this point: they will tell you about semantic construction using lambda calculus and how to do it in Prolog.
We can use the same mechanism that we used for constructing parse trees to build lambda terms representing the semantics of the parsed expression.
Here is a way of representing lambda terms as Prolog terms:
-
Let's use a two place complex term with the functor
lfor representing lambda abstraction. That is, we representλx.Formula asl(X,Formula). For example, the semantics associated with the verb kills, i.e., the lambda termλx.λy.kill(y,x) , would look like this in our Prolog representation:l(X,l(Y,kill(Y,X))) -
Let's use a two place complex term with the functor
'@'to represent functional application. That is,λx.λy.kill(y,x)(bill) is'@'(l(X,l(Y,kill(Y,X))), bill)in our representation.
First, use this simple grammar
and add a semantic representation to all lexical entries.
Solution
Second, extend the rules so that the semantics representation is
build while processing the input phrase. The mechanism is
exactly the same as the one that we used for building the parse
tree. Use the '@' symbol to express that one
expression is applied to another. That means, the output will be
a lambda term which is not beta-reduced. For example, the lambda
representation for the sentence
[the,nurse,whistles] is '@'('@'(l(R,l(S,
exists(X,'@'(R,X),'@'(S,X)))),l(Y,nurse(Y))),l(Z,whistles(Z))).
Solution