(Last modified Tue Jan 22 22:41 2008)
In FOL an interpretation defines
many more kinds of things
than it does in PL.
An interpretation of a FOL language consists of:
- A value
true or false
for each
propositional variable
in the language
(as in a PL interpretation).
- A domain,
consisting of a set of objects or entities.
- For each name in the language,
a designation
(the domain object that the name refers to).
- A
function definition for each
function in the language,
assigning a domain object
to each tuple of objects that can be the function's arguments.
- A
characteristic function
for each
predicate
in the language,
assigning
true or false
to each tuple of objects that can be the predicate's arguments.
An interpretation does not define variables;
binding of variables is done only by a
quantifier.
Interpretations, satisfiability, validity;
implication; logical equivalence
We have already seen these defined for PL;
the definitions for FOL are the same,
substituting FOL interpretations for PL interpretations.
FOL
syntax
semantics
interpretation
