## A semantic structure, I, is a tuple of the form
- a connected lay, known as value area, and you can
- an effective mapping regarding the lexical room of the symbol area so you’re able to the importance place, entitled lexical-to-value-space mapping. ?

Within the a tangible dialect, DTS always includes the fresh datatypes backed by one dialect. The RIF languages have to hold the datatypes that are placed in Point Datatypes out of [RIF-DTB]. Its well worth spaces in addition to lexical-to-value-place mappings for those datatypes are discussed in the same part.

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:decimal` and `1.20^^xs:quantitative` are two legal — and distinct — constants in RIF because `step 1.dos` and `1.20` belong to the lexical space of `xs:quantitative`. However, these two constants are interpreted by the same element of the value space of the `xs:decimal` type. Therefore, `step one.2^^xs:decimal = 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:sequence`.

## 3.4 Semantic Structures

The brand new main help indicating a model-theoretical semantics for a logic-situated words try identifying the thought of a beneficial semantic physical staturework. Semantic formations are acclimatized to assign information values so you’re able 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
- Each pair <
`s,v`> ? `ArgNames` ? D represents an argument/value pair instead of just a value in the case of a positional term.
- Brand new argument so you can a term that have entitled arguments try a small wallet from dispute/worth sets as opposed to a finite purchased succession out-of easy facets.
- 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 effective->b)`. (However, `p(a->b a->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 a->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->?A good an effective->?B)` becomes `p(a->b a->b)` if the variables `?A good` and `?B` are both instantiated with the symbol `b`.

## A semantic structure, I, is a tuple of the form
- I
_{list} : D * > D
- I
_{tail} : D + ?D > D

## A semantic structure, I, is a tuple of the form
- 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 one}, . `a`_{k+meters})) = I_{list}(`a`_{1}, . `a`_{k}, `a`_{k+step one}, . `a`_{k+m}).

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.

- a connected lay, known as value area, and you can
- an effective mapping regarding the lexical room of the symbol area so you’re able to the importance place, entitled lexical-to-value-space mapping. ?

Within the a tangible dialect, DTS always includes the fresh datatypes backed by one dialect. The RIF languages have to hold the datatypes that are placed in Point Datatypes out of [RIF-DTB]. Its well worth spaces in addition to lexical-to-value-place mappings for those datatypes are discussed in the same part.

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:decimal` and `1.20^^xs:quantitative` are two legal — and distinct — constants in RIF because `step 1.dos` and `1.20` belong to the lexical space of `xs:quantitative`. However, these two constants are interpreted by the same element of the value space of the `xs:decimal` type. Therefore, `step one.2^^xs:decimal = 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:sequence`.

## 3.4 Semantic Structures

The brand new main help indicating a model-theoretical semantics for a logic-situated words try identifying the thought of a beneficial semantic physical staturework. Semantic formations are acclimatized to assign information values so you’re able to RIF-FLD formulas.

Definition (Semantic structure). _{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
- Each pair <
`s,v`> ? `ArgNames` ? D represents an argument/value pair instead of just a value in the case of a positional term.
- Brand new argument so you can a term that have entitled arguments try a small wallet from dispute/worth sets as opposed to a finite purchased succession out-of easy facets.
- 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 effective->b)`. (However, `p(a->b a->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 a->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->?A good an effective->?B)` becomes `p(a->b a->b)` if the variables `?A good` and `?B` are both instantiated with the symbol `b`.

## A semantic structure, I, is a tuple of the form
- I
_{list} : D * > D
- I
_{tail} : D + ?D > D

## A semantic structure, I, is a tuple of the form
- 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 one}, . `a`_{k+meters})) = I_{list}(`a`_{1}, . `a`_{k}, `a`_{k+step one}, . `a`_{k+m}).

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.

- Each pair <
`s,v`> ?`ArgNames`? D represents an argument/value pair instead of just a value in the case of a positional term. - Brand new argument so you can a term that have entitled arguments try a small wallet from dispute/worth sets as opposed to a finite purchased succession out-of easy facets.
- 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 effective->b)`. (However,`p(a->b a->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 a->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->?A good an effective->?B)` becomes `p(a->b a->b)` if the variables `?A good` and `?B` are both instantiated with the symbol `b`.

## A semantic structure, I, is a tuple of the form
- I
_{list} : D * > D
- I
_{tail} : D + ?D > D

## A semantic structure, I, is a tuple of the form
- 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 one}, . `a`_{k+meters})) = I_{list}(`a`_{1}, . `a`_{k}, `a`_{k+step one}, . `a`_{k+m}).

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.

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

## A semantic structure, I, is a tuple of the form
- 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 one}, . `a`_{k+meters})) = I_{list}(`a`_{1}, . `a`_{k}, `a`_{k+step one}, . `a`_{k+m}).

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.

- 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 one}, .`a`_{k+meters})) = I_{list}(`a`_{1}, .`a`_{k},`a`_{k+step one}, .`a`_{k+m}).

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.