Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
1.5 Predicate Prolog
Predicate prolog allows predicates that take one or more arguments, and it also gives a first glimpse of expressions
that depend on “context” for their interpretation. For example, we could have a 1-place predicate
mathematician which may be true of various individuals that have different names, as in the following axioms:
/*
* file: people.pl
*/
mathematician(frege).
mathematician(hilbert).
mathematician(turing).
mathematician(montague).
linguist(frege).
linguist(montague).
linguist(chomsky).
linguist(bresnan).
president(bush).
president(clinton).
sax_player(clinton).
piano_player(montague).
And using an initial uppercase letter or underscore to distinguish variables, we have expressions like
human(X) that have a truth value only relative to a “context” – an assignment of an individual to the variable.
In prolog, the variables of each definite clause are implicitly bound by universal quantifiers:
human(X) :- mathematician(X).
human(X) :- linguist(X).
human(X) :- sax_player(X).
human(X) :- piano_player(X).
sum(0,X,X).
sum(s(X),Y,s(Z)) :- sum(X,Y,Z).
self_identical(X).
socrates_is_mortal.
In this theory, we see 9 different predicates. Like 0-place predicates (=propositions), these predicates all begin
with lower case letters.
Besides predicates, a theory may contain terms, where a term is a variable, a name, or a function expression
that combines with some appropriate number of terms. Variables are distinguished by beginning with an
uppercase letter or an underscore. The theory above contains only the one variable X. Each axiom has all of its
variables “universally bound.” So for example, the axiom self_identical(X) says: for all X, X is identical to
itself. And the axiom before that one says: for all X, X is human if X is a piano player.
In this theory we see nine different names, which are either numerals or else begin with lower case letters:
frege, hilbert, turing, montague, chomsky, bresnan, bush, clinton, 0. Anamecanberegarded
as a 0-place function symbol. That is, it takes 0 arguments to yield an individual as its value.
In this theory we have one function symbol that takes arguments: the function symbol s appears in the two
axioms for sum. These are Peano’s famous axioms for the sum relation. The first of these axioms says that, for
all X, thesumof0and X is X. The second says that, for all X, Y and Z, the sum of the successor of X and Y is
the successor of Z where Z is the sum of X and Y. Sothesymbolsstands for the successor function. This is the
function which just adds one to its argument. So the successor of 0 is 1, s(0)=1, s(s(0))=2, ….Inthisway,
the successor function symbol takes 1 argument to yield an individual as its value. With this interpretation
of the symbol s, the two axioms for sum are correct. Remarkably, they are also the only axioms we need to
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