AB AB C 1 2 TS Triples in the Window Entailments in the Window A C [11] [12] AB C 3 A C [11] [12] D [13] D B [12] [11] AB C 4 A C [12] D [13] D B [12] [11] E [14] x … … AB C 12 A C [12] D [13] D B [12] E [14] A C 13 A D [13] D E [14]

RDF Store Asserted Triples Entailed Triples Hash Table T of Asserted Triples Permanent Space T of Entailed Triples RDF Store Previous Materialization Hash Table T of Previous Materialization Working Space P[T], P [T] Ins P [T], P [T] - + Incremental Maintainer Rule EngineBuilt-ins P, P - + T of P, P - +

t0t0 t1t1 t2t2 T exp S stream derived T exp D T stay S D T in S

t0t0 t1t1 T exp S stream derived T exp D T stay S D T in S

T exp S stream T stay S T in S T exp S stream T stay S T in S More triples with different expiration time enter the window A triple already present in the window enters the window

(, e 0 ) (, e 1 ) (, e 2 ) e 0 ≤ e 1 ≤ e 2 (, e 0 )

t1t1 t 1-1 t 1-2 t 1-3 retweet reply retweet discuss