Semgoodntic formations are often outlined with regards to a particular lay from datatypes, denoted because of the DTS

Semgoodntic formations are often outlined with regards to a <a href=""></a> particular lay from datatypes, denoted because of the DTS

A semantic structure, I, is a tuple of the form
  • a related place, known as value room, and you will
  • good mapping about lexical room of symbol area so you can the importance room, titled lexical-to-value-place mapping. ?

For the a concrete dialect, DTS usually has the datatypes backed by you to definitely dialect. Every RIF languages need to secure the datatypes which might be placed in Part Datatypes out-of [RIF-DTB]. Its really worth places together with lexical-to-value-room mappings of these datatypes was revealed in the same section.

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 1.dos and step one.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:decimal = step one.20^^xs:decimal is a RIF tautology. Likewise, RIF semantics for datatypes implies certain inequalities. For instance, abc^^xs:string ? 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:string.

3.cuatro Semantic Structures

This new central part of indicating a product-theoretic semantics to have a logic-created vocabulary are determining the idea of good semantic construction. Semantic structures are widely used to assign deends beliefs so you can RIF-FLD algorithms.

Definition (Semantic structure). C, IV, IF, INF, Ilist, Itail, Iframe, Isub, Iisa, I=, Iexternal, Iconnective, Itruth>. 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.
  • New disagreement to help you a phrase having named arguments is actually a small bag out of dispute/value pairs as opposed to a restricted ordered succession away from 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 a good->b). (However, p(a->b an effective->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->?A good a good->?B) becomes p(a->b an effective->b) if the variables ?A beneficial and ?B are both instantiated with the symbol b.

A semantic structure, I, is a tuple of the form
  • Ilist : D * > D
  • Itail : D + ?D > D

A semantic structure, I, is a tuple of the form
  • The function Ilist is injective (one-to-one).
  • The set Ilist(D * ), henceforth denoted Dlist , is disjoint from the value spaces of all data types in DTS.
  • Itail(a1, . ak, Ilist(ak+1, . ak+m)) = Ilist(a1, . ak, ak+1, . ak+yards).

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

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