We will also look at sentence schemas with more than one blank and use variables to label blanks in a consistent way. Variables allow us to specify more subtle subtitution schemas. The set of values that may be substituted for a predicate variable is called its domain . Different variables may have different domains. We are particularly interested the truth set of a predicate, that is, the set of those domain elements for which the predicate is true.
Truth sets define the logical meaning of a predicate.
The meaning of a predicate R that takes n arguments is the set of n -tuples Predicates are syntactic expressions and relations define their semantics . Different variables often range over different domains, in which case the above definitions need to be adjusted slightly. The two sentences Barry Cohen is teaching section 7 of CSE-113. Some student in CSE-113 drinks. All students in CSE- 113 drink.