A denotational semantics for CRUD operations on RDF datasets

RDF quads

Triples

S = I ∪ B

P = I

O = I ∪ B ∪ L

Graph names

G = I ∪ B

Global RDF dataset function/set

d : S × P × G → O

D = graph(d) = { (x, d(x)) : x ∈ S × P × G } = S × P × G × O

empty : D - empty dataset

Partial RDF dataset

R ⊆ D

Graph store functions

get : R × I → R

get(r, i) = (s, p, g, o) ∈ r : g = i

delete : R × I → R

delete(r, i) = r \ get(r, i)

post : R × R → R

post(r, r_request) = r ∪ r_request

put : R × R × I → R

put(r, r_request, i) = post(delete(r, i), r_request)

Quad store functions

get : R → R

get(r) = r

delete : R → R

delete(r) = r \ get(r) = empty

post : R × R → R

post(r, r_request) = r ∪ r_request

put : R × R × I → R

put(r, r_request) = post(delete(r), r_request)

Examples

Dataset

r ∈ R =

<s1> <p1> <o1> <g1>
<s1> <p2> <o2> <g1>
<s2> <p1> <o1> <g1>
<s2> <p2> <o2> <g1>
<s1> <p1> <o1> <g2>
<s1> <p2> <o2> <g2>
<s2> <p1> <o1> <g2>
<s2> <p2> <o2> <g2>

r_request ∈ R =

<s3> <p3> <o3> <g3>

Graph Store

get(r, g1) =

<s1> <p1> <o1> <g1>
<s1> <p2> <o2> <g1>
<s2> <p1> <o1> <g1>
<s2> <p2> <o2> <g1>

get(r, s1) = empty

delete(r, g1) =

<s1> <p1> <o1> <g2>
<s1> <p2> <o2> <g2>
<s2> <p1> <o1> <g2>
<s2> <p2> <o2> <g2>

post(r, r_request) =

<s1> <p1> <o1> <g1>
<s1> <p2> <o2> <g1>
<s2> <p1> <o1> <g1>
<s2> <p2> <o2> <g1>
<s1> <p1> <o1> <g2>
<s1> <p2> <o2> <g2>
<s2> <p1> <o1> <g2>
<s2> <p2> <o2> <g2>
<s3> <p3> <o3> <g3>

put(r, r_request, g1) =

<s1> <p1> <o1> <g2>
<s1> <p2> <o2> <g2>
<s2> <p1> <o1> <g2>
<s2> <p2> <o2> <g2>
<s3> <p3> <o3> <g3>

Quad Store

get(r) =

<s1> <p1> <o1> <g1>
<s1> <p2> <o2> <g1>
<s2> <p1> <o1> <g1>
<s2> <p2> <o2> <g1>
<s1> <p1> <o1> <g2>
<s1> <p2> <o2> <g2>
<s2> <p1> <o1> <g2>
<s2> <p2> <o2> <g2>

delete(r) = empty