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

• a connected lay, called the value room, and you may
• good mapping on the lexical place of your own icon place so you’re able to the value space, titled lexical-to-value-area mapping. ?

From inside the a concrete dialect, DTS constantly has this new datatypes supported by you to definitely dialect. The RIF languages must contain the datatypes which can be placed in Part Datatypes out of [RIF-DTB]. Its worth spaces together with lexical-to-value-space 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, step step 1.2^^xs:quantitative and step 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:decimal. However, these two constants are interpreted by the same element of the value space of the xs:quantitative type. Therefore, step 1.2^^xs:quantitative = step one.20^^xs:quantitative is a RIF tautology. Likewise, RIF semantics for datatypes implies certain inequalities. For instance, abc^^xs:sequence ? abcd^^xs:string 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.cuatro Semantic Formations

The fresh new central step in specifying an unit-theoretic semantics to have a reason-established vocabulary is identifying the very thought of an effective semantic construction. Semantic formations are acclimatized to assign insights philosophy so you can 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_additional, 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.
• This new disagreement in order to an expression having titled objections is a small bag from dispute/worth pairs as opposed to a finite ordered succession from simple issue.
• 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 good->b). (However, p(a->b a good->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 beneficial->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 beneficial good->?B) becomes p(a->b good->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+m)) = I_list(a₁, . a_k, a_{k+step one}, . a_k+yards).

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.