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Logical Expressions for the Definition of Relations
- The definition of a relation is a logical expression defining the set of instances (n-ary tuples, if n is the arity of the relation) of the relation
- If the parameters are specified, the relation is represented by an n-ary predicate symbol with named arguments If R is the identifier denoting the relation, then the logical expression takes one of the following forms:
forAll ?v1,...,?vn ( R[p1 hasValue ?v1,...,pn hasValue ?vn] implies l-expr(?v1,...,?vn) )
forAll ?v1,...,?vn ( R[p1 hasValue ?v1,...,pn hasValue ?vn] impliedBy l-expr(?v1,...,?vn) )
forAll ?v1,...,?vn ( R[p1 hasValue ?v1,...,pn hasValue ?vn] equivalent l-expr(?v1,...,?vn) ) - If the parameters are not specified, then the relation is represented by a predicate symbol where the identifier of the relation is used as the name of the predicate symbol. If R is the identifier denoting the relation, then the logical expression takes one of the following forms:
forAll ?v1,...,?vn ( R(?v1,...,?vn) implies l-expr(?v1,...,?vn) )
forAll ?v1,...,?vn ( R(?v1,...,?vn) impliedBy l-expr(?v1,...,?vn) )
forAll ?v1,...,?vn ( R(?v1,...,?vn) equivalent l-expr(?v1,...,?vn) )
where l-expr(?v1,...,?vn) is a logical expression with precisely ?v1,...,?vn as its free variables and p1,...,pn are the names of the parameters of the relation
- If the parameters are specified, the relation is represented by an n-ary predicate symbol with named arguments If R is the identifier denoting the relation, then the logical expression takes one of the following forms:
Speaker notes:
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