1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
|
package rsacomb
import tech.oxfordsemantic.jrdfox.logic.Datatype
import tech.oxfordsemantic.jrdfox.logic.expression.{Literal, IRI}
sealed trait SkolemStrategy
object SkolemStrategy {
// TODO: might want to use something else other than `hashCode` as a
// function to generate a fresh function/constant
/* No skolemization at all.
*
* From
* ∃R.A ⊑ B
* to
* R(x,y), B(y) -> B(x)
*/
case object None extends SkolemStrategy
/* Functional skolemization
*
* From
* A ⊑ ∃R.B
* to
* A(x) -> R(x,f(x)), B(f(x))
* for f, fresh function associated with the input axiom
*
* In RDFox this can represented combining the BIND operator with the
* SKOLEM operator as such:
* A(x), BIND(y, SKOLEM("f", x)) -> R(x,y), B(y)
* The first argument of a SKOLEM call is a literal string (ideally
* identifing the simulated function name).
*
* NOTE: this requirement for the SKOLEM operator is not enforced by
* RDFox, that will fail silently if omitted.
*/
case class Standard(func: Literal) extends SkolemStrategy
object Standard {
def apply(axiom: String) =
new Standard(
Literal.create(genFunctionString(axiom), Datatype.XSD_STRING)
)
def genFunctionString(str: String) = "f_" ++ str.hashCode.toString
}
/* Constant skolemization
*
* From
* A ⊑ ∃R.B
* to
* A(y) -> R(x,c), B(c)
* for c, fresh constant associated with the input axiom
*/
case class Constant(const: IRI) extends SkolemStrategy
object Constant {
def apply(axiom: String) =
new Constant(IRI.create(genConstantString(axiom)))
def genConstantString(str: String) = "c_" ++ str.hashCode.toString
}
/* (RSA) Constant skolemization
* This is a special skolemization option to introduce additional atoms for RSA
* checking algorithm.
*
* From
* A ⊑ ∃R.B
* to
* A(y) -> R(x,c), PE(x,c), B(c)
* for c, fresh constant associated with the input axiom and PE an internal predicate.
*/
case class ConstantRSA(const: IRI) extends SkolemStrategy
object ConstantRSA {
def apply(axiom: String) =
new ConstantRSA(IRI.create(genConstantString(axiom)))
def genConstantString(str: String) = "c_" ++ str.hashCode.toString
}
}
|
