- Wef the signature = has an arrow expression (s s)?k then I= must map Ds?Ds to Dk.
The effect of datatypes. If dt ? DTS, let LSdt denote the lexical space of dt, VSdt denote its value space, and Ldt: LSdt > VSdt the lexical-to-value-space mapping. Then the following must hold:
- VSdt ? D; and
- For each constant "illuminated"^^dt such that lit ? LSdt, IC("lit"^^dt) = Ldt(lit).
RIF-FLD does not impose special requirements on IC for constants in the symbol spaces that do not correspond to the identifiers of the datatypes in DTS. Dialects ple of such a restriction could be a requirement that no constant in a particular symbol space (such as rif:regional) can be mapped to VSdt of a datatype dt.
step three.5 Annotations in addition to Official Semantics
RIF-FLD annotations are stripped before the mappings that constitute RIF-FLD semantic structures are applied. Likewise, they are stripped before applying the details valuation, TValI, defined in the next section. Thus, identifiers and metadata have no effect on the formal semantics.
Note that even in the event annotations in the RIF-FLD formulas was forgotten by the semantics, they are extracted of the XML units. Once the annotations is actually illustrated from the physique terminology, they may be reasoned having by regulations. The new frame terminology used to portray metadata can then getting fed some other formulas, therefore enabling need from the metadata. Yet not, RIF will not define any real semantics to possess metadata.
step three.6 Translation out-of Low-document Algorithms
This section defines how a semantic structure, I, determines the truth value TValI(?) of a RIF-FLD formula, ?, where ? is any formula other than a document formula or a remote formula. Truth valuation of document formulas is defined in the next section.
To this end, we define a mapping, TValI, from the set of all non-document formulas to TV. Note that the definition implies that TValI(?) is defined only if the set DTS of the datatypes of I includes all the datatypes mentioned in ?.
- Itruth(I(x = y)) = t if I(x) = I(y) and Itruth(I(x = y)) = f otherwise.
To ensure that the operator ## is transitive, i.e., cstep one ## c2 and c2 ## c3 imply c1 ## c3, the following is required:
- For all well-formed terms c1, c2, c3: glbt(TValI(c1 ## c2), TValI(c2 ## c3)) ?tTValI(c1 ## c3).
Note that this is a restriction on Itruth and the mapping I, which is expressed in a more succinct form using TValI.
To ensure that all members of BBWCupid support a subclass are also members of the superclass, i.e., o # cl and cl ## scl imply o # scl, the following is required:
- For all well-formed terms o, cl, scl: glbt(TValI(o # cl), TValI(cl ## scl)) ?tTValI(o # scl).
Note that this is a restriction on Itruth and the mapping I, which is expressed in a more succinct form using TValI.
- TValI(o[a1->v1 . ak->vk]) = glbt(TValI(o[a1->v1]), . TValI(o[ak->vk])).
Observe that this is a restriction on Itruth and the mapping I. For brevity, it is expressed in a more succinct form using TValI.
Note that, by definition, External(t loc) is well-formed only if it is an instantiation of an external schema. Furthermore, by the definition of coherent sets of external schemas, it can be an instantiation of at most one external schema, so I(External(t loc)) is well-defined.
To ensure the intended semantics for the RIF-FLD reserved connectives and quantifiers, the following restrictions are imposed (observe that all these are restrictions on Itruth and the mapping I, which are expressed via TValI, for brevity):
The symmetric negation, Neg, is sufficiently general to capture many different kinds of such negation. For instance, classical negation would, in addition, require TValI(Neg ?) =