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Bags are employed here because the order of the attribute/value pairs in a frame is immaterial and the pairs may repeat. For instance, o[a->b a->b]. For instance, o[?A great->?B ?C->?D] becomes o[a->b an excellent->b] if variables ?A and ?C are instantiated with the symbol a and ?B, ?D with b. (We shall see later that o[a->b an excellent->b] is equivalent to o[a->b].)

The operator ## is required to be transitive, i.e., cstep one ## c2 and c2 ## c3 must imply c1 ## c3. This is ensured by a restriction in Section Interpretation of Formulas.

# and ## are required to have the usual property that all members of a subclass are also members of the superclass, i.e., o # cl and cl ## scl must imply o # scl. This is ensured by a restriction in Section Interpretation of Formulas.

For every outside schema, ?, associated with the language, I_external(?) is assumed to be specified externally in some document (hence the name external schema). ? is a schema of a RIF built-in predicate or function, I_external(?) is specified in [RIF-DTB] so that:

The newest relationship

• If ? is a schema of a built-in function then I_external(?) must be the function defined in the aforesaid document.
• If ? is a schema of a built-in predicate then I_knowledge? (I_external(?)) (the composition of I_truth and I_external(?), a truth-valued function) must be as specified in [RIF-DTB].

Further restrictions on the interaction of this function with I_truth will be imposed in order to ensure the intended semantics for each conjunctive and quantifier. For aggregates, I_connective maps them to functions D > D and additional restrictions are imposed on the mapping I defined below.

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Particularly, in the event the

I and define another identity-interpreting mapping on the well-shaped conditions, and that we signify using the same symbol I which is used for the semantic build alone. (más…)