- Wef the signature
`=`has an arrow expression`(s s)?k`then I_{=}must map D_{s}?D_{s}to D_{k}.

The effect of datatypes. If `dt` ? DTS, let LS_{dt} denote the lexical space of `dt`, VS_{dt} denote its value space, and L_{dt}: LS_{dt} > VS_{dt} the lexical-to-value-space mapping. Then the following must hold:

- VS
_{dt}? D; and - For each constant
`"lit"^^dt`such that`lit`? LS_{dt}, I_{C}(`"lit"^^dt`) = L_{dt}(`lit`).

RIF-FLD does not impose special requirements on I_{C} 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 VS_{dt} of a datatype `dt`.

## step three.5 Annotations and also the Certified Semantics

RIF-FLD annotations are stripped before the mappings that constitute RIF-FLD semantic structures are applied. Likewise, they are stripped before applying the specifics valuation, TVal_{I}, defined in the next section. Thus, identifiers and metadata have no effect on the formal semantics.

Note that in the event annotations associated with the RIF-FLD algorithms was overlooked because of the semantics, they truly are removed because of the XML equipment. Just like the annotations is illustrated by the physique words, they can be reasoned having because of the laws. The new physique terminology familiar with show metadata may then become given some other formulas, ergo enabling reason regarding metadata. not, RIF doesn’t define any real semantics to own metadata.

## step 3.six Translation from Non-document Formulas

This section defines how a semantic structure, I, determines the truth value TVal_{I}(`?`) 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, TVal_{I}, from the set of all non-document formulas to TV. Note that the definition implies that TVal_{I}(`?`) is defined only if the set DTS of the datatypes of I includes all the datatypes mentioned in `?`.

- I
_{truth}(I(`x = y`)) = t if I(`x`) = I(`y`) and I_{truth}(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`: glb_{t}(TVal_{I}(`c1 ## c2`), TVal_{I}(`c2 ## c3`)) ?_{t}TVal_{I}(`c1 ## c3`).

Note that this is a restriction on I_{truth} and the mapping I, which is expressed in a more succinct form using TVal_{I}.

To ensure that all members of 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`: glb_{t}(TVal_{I}(`o # cl`), TVal_{I}(`cl ## scl`)) ?_{t}TVal_{I}(`o # scl`).

Note that this is a restriction on I_{truth} and the mapping I, which is expressed in a more succinct form using TVal_{I}.

- TVal
_{I}(`o[a`) = glb_{1}->v_{1}. a_{k}->v_{k}]_{t}(TVal_{I}(`o[a`), . TVal_{1}->v_{1}]_{I}(`o[a`))._{k}->v_{k}]

Observe that this is a restriction on I_{truth} and the mapping I. For brevity, it is expressed in a more succinct form using TVal_{I}.

Note that, by definition, `External(t loc)` is well-formed only https://datingranking.net/benaughty-review/ 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 I_{truth} and the mapping I, which are expressed via TVal_{I}, 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 TVal_{I}(`Neg ?`) =