Seman effectiventic structures are often defined with regards to a specific lay from datatypes, denoted because of the DTS

A semantic structure, I, is a tuple of the form

• a related put, known as value area, and you will
• a mapping on the lexical place of the symbol area in order to the value space, titled lexical-to-value-space mapping. ?

During the a tangible dialect, DTS usually is sold with the brand new datatypes supported by that dialect. All of the RIF languages need to keep the datatypes which can be placed in Part Datatypes out of [RIF-DTB]. Their well worth places plus the lexical-to-value-place mappings for these datatypes was described in the same 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 step 1.20^^xs:quantitative are two legal — and distinct — constants in RIF because step one.dos and step 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 1.2^^xs:quantitative = 1.20^^xs:quantitative is a RIF tautology. Likewise, RIF semantics for datatypes implies certain inequalities. For instance, abc^^xs:sequence ? 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 latest main step-in indicating a model-theoretic semantics having a logic-founded vocabulary are defining the thought of a good semantic design. Semantic formations are accustomed to designate basic facts opinions to RIF-FLD algorithms.

Definition (Semantic structure). C, I_V, I_F, I_NF, I_list, I_tail, I_frame, I_sub, I_isa, I₌, I_exterior, I_conjunctive, 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.
• The newest dispute in order to a term that have named objections are a small wallet from conflict/value sets in place of a limited ordered succession off easy issues.
• 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 an excellent->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 great->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->?An excellent a good->?B) becomes p(a->b an excellent->b) if the variables ?An effective 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(a₁, . a_k, I_list(a_k+1, . a_k+meters)) = I_list(a₁, . a_k, a_{k+step 1}, . 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 sweet pea dating that it must be in D.