# Sema beneficialntic formations are often outlined when it comes to a particular put of datatypes, denoted because of the DTS

## A semantic structure, I, is a tuple of the form <TV, DTS, D, I

- an associated place, known as well worth area, and
- a mapping on the lexical room of the symbol room to help you the significance room, entitled lexical-to-value-area mapping. ?

Inside the a concrete dialect, DTS usually has brand new datatypes supported by that dialect. All of the RIF languages have to keep the datatypes that will be checklisted in Part Datatypes away from [RIF-DTB]. Its value spaces together with lexical-to-value-room mappings for those datatypes are explained in identical point.

Although the lexical and the value spaces might sometimes look similar, one should not confuse them. Lexical spaces define the syntax of the constant symbols in the RIF language. Value spaces define the meaning of the constants. The lexical and the value spaces are often not even isomorphic. For example, `1.2^^xs:quantitative` and `1.20^^xs:decimal` are two legal — and distinct — constants in RIF because `step 1.2` and `step one.20` belong to the lexical space of `xs:decimal`. However, these two constants are interpreted by the same element of the value space of the `xs:decimal` type. Therefore, `step 1.2^^xs:quantitative = step 1.20^^xs:decimal` is a RIF tautology. Likewise, RIF semantics for datatypes implies certain inequalities. For instance, `abc^^xs:string` ? `abcd^^xs:sequence` is a tautology, since the lexical-to-value-space mapping of the `xs:sequence` type maps these two constants into distinct elements in the value space of `xs:string`.

## step 3.4 Semantic Structures

The newest central help specifying an unit-theoretical semantics having a logic-depending words try defining the very thought of a semantic body typework. Semantic structures are acclimatized to assign facts thinking to RIF-FLD formulas.

Definition (Semantic structure). _{C}, I_{V}, I_{F}, I_{NF}, I_{list}, I_{tail}, I_{frame}, I_{sub}, I_{isa}, I_{=}, I_{external}, I_{connective}, I_{truth}>. Here D is a non-empty set of elements called the domain of I. We will continue to use `Const` to refer to the set of all constant symbols and `Var` to refer to the set of all variable symbols. TV denotes the set of truth values that the semantic structure uses and DTS is a set of identifiers for datatypes.

## A semantic structure, I, is a tuple of the form <TV, DTS, D, I

- Each pair <
`s,v`> ?`ArgNames`? D represents an argument/value pair instead of just a value in the case of a positional term. - The fresh conflict to a phrase which have entitled objections is a restricted bag away from argument/well worth pairs as opposed to a limited ordered succession off easy aspects.
- Bags are used here because the order of the argument/value pairs in a term with named arguments is immaterial and the pairs may repeat:
`p(a->b an excellent->b)`. (However,`p(a->b a great->b)`is not equivalent to`p(a->b)`, as we shall see later.)

To see why such repetition can occur, note that argument names may repeat: `p(a->b an effective->c)`. This can be understood as treating `a` as a bag-valued argument. Identical argument/value pairs can then arise as a result of a substitution. For instance, `p(a->?Good a beneficial->?B)` becomes `p(a->b a good->b)` if the variables `?A` and `?B` are both instantiated with the symbol https://www.datingranking.net/adventist-singles-review `b`.

## A semantic structure, I, is a tuple of the form <TV, DTS, D, I

- I
_{list}: D * > D - I
_{tail}: D + ?D > D

## A semantic structure, I, is a tuple of the form <TV, DTS, D, I

- The function I
_{list}is injective (one-to-one). - The set I
_{list}(D * ), henceforth denoted D_{list}, is disjoint from the value spaces of all data types in DTS. - I
_{tail}(`a`_{1}, .`a`_{k}, I_{list}(`a`_{k+step 1}, .`a`_{k+yards})) = I_{list}(`a`_{1}, .`a`_{k},`a`_{k+step one}, .`a`_{k+meters}).

Note that the last condition above restricts I_{tail} only when its last argument is in D_{list}. If the last argument of I_{tail} is not in D_{list}, then the list is a general open one and there are no restrictions on the value of I_{tail} except that it must be in D.