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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

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