A semantic structure, I, is a tuple of the form
- a connected set, known as worthy of area, alt coupon and
- a good mapping regarding lexical area of your symbol place so you can the importance space, named lexical-to-value-space mapping. ?
From inside the a real dialect, DTS usually includes the latest datatypes supported by you to definitely dialect. All the RIF dialects must keep the datatypes which can be placed in Point Datatypes out-of [RIF-DTB]. Their worthy of rooms as well as the lexical-to-value-area mappings for those datatypes are demonstrated 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, step 1.2^^xs:quantitative and step one.20^^xs:quantitative 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, 1.2^^xs:decimal = step 1.20^^xs:quantitative 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:sequence.
3.cuatro Semantic Formations
Brand new main step in indicating a product-theoretical semantics to have a reasoning-built words is defining the idea of a beneficial semantic structure. Semantic formations are acclimatized to designate specifics values so you’re able to 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.
- The fresh new disagreement so you can a phrase that have titled objections is a finite wallet away from disagreement/well worth pairs in lieu of a limited ordered series off simple 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 good->b). (However, p(a->b a beneficial->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 good->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 effective an effective->?B) becomes p(a->b an excellent->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+meters)) = Ilist(a1, . ak, ak+step one, . 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.
- a connected set, known as worthy of area, alt coupon and
- a good mapping regarding lexical area of your symbol place so you can the importance space, named lexical-to-value-space mapping. ?
From inside the a real dialect, DTS usually includes the latest datatypes supported by you to definitely dialect. All the RIF dialects must keep the datatypes which can be placed in Point Datatypes out-of [RIF-DTB]. Their worthy of rooms as well as the lexical-to-value-area mappings for those datatypes are demonstrated 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, step 1.2^^xs:quantitative and step one.20^^xs:quantitative 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, 1.2^^xs:decimal = step 1.20^^xs:quantitative 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:sequence.
3.cuatro Semantic Formations
Brand new main step in indicating a product-theoretical semantics to have a reasoning-built words is defining the idea of a beneficial semantic structure. Semantic formations are acclimatized to designate specifics values so you’re able to RIF-FLD algorithms.
Definition (Semantic structure).
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 fresh new disagreement so you can a phrase that have titled objections is a finite wallet away from disagreement/well worth pairs in lieu of a limited ordered series off simple 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 good->b). (However, p(a->b a beneficial->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 good->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 effective an effective->?B) becomes p(a->b an excellent->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+meters)) = Ilist(a1, . ak, ak+step one, . 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.
- 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 new disagreement so you can a phrase that have titled objections is a finite wallet away from disagreement/well worth pairs in lieu of a limited ordered series off simple 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 good->b). (However, p(a->b a beneficial->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 good->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 effective an effective->?B) becomes p(a->b an excellent->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+meters)) = Ilist(a1, . ak, ak+step one, . 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.
- 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+meters)) = Ilist(a1, . ak, ak+step one, . 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.
- 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+meters)) = Ilist(a1, . ak, ak+step one, . 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.
