SLIDE 1
Incremental Event Calculus for Run-Time Reasoning Efthimis - - PowerPoint PPT Presentation
Incremental Event Calculus for Run-Time Reasoning Efthimis - - PowerPoint PPT Presentation
Incremental Event Calculus for Run-Time Reasoning Efthimis Tsilionis, Alexander Artikis, Georgios Paliouras NCSR Demokritos http://cer.iit.demokritos.gr/ 16 April 2019 Motivation for Incremental CER Motivation for Incremental CER Delayed
SLIDE 2
SLIDE 3
Motivation for Incremental CER
◮ Delayed events (e.g., satelite GPS messages)
SLIDE 4
Motivation for Incremental CER
◮ Delayed events (e.g., satelite GPS messages) ◮ Overlapping temporal windows
SLIDE 5
Motivation for Incremental CER
◮ Propagation of changes
drifting highSpeedNC withinArea trawlSpeed anchoredOrMoored movingSpeed tuggingSpeed changingSpeed trawlingMovement loitering gap sarSpeed pilotBoarding stopped sarMovement underWay rendezVous sar trawling lowSpeed tugging
SLIDE 6
Event Calculus
◮ A logic programming language for representing and reasoning
about events and their effects.
SLIDE 7
Event Calculus
◮ A logic programming language for representing and reasoning
about events and their effects.
◮ Key components:
◮ event (typically instantaneous). ◮ fluent: a property that may have different values at different
points in time.
SLIDE 8
Event Calculus
◮ A logic programming language for representing and reasoning
about events and their effects.
◮ Key components:
◮ event (typically instantaneous). ◮ fluent: a property that may have different values at different
points in time.
◮ Built-in representation of inertia:
◮ F = V holds at a particular time-point if F = V has been
initiated by an event at some earlier time-point, and not terminated by another event in the meantime.
SLIDE 9
Event Calculus
◮ A logic programming language for representing and reasoning
about events and their effects.
◮ Key components:
◮ event (typically instantaneous). ◮ fluent: a property that may have different values at different
points in time.
◮ Built-in representation of inertia:
◮ F = V holds at a particular time-point if F = V has been
initiated by an event at some earlier time-point, and not terminated by another event in the meantime.
◮ RTEC is a CER system based on the Event Calculus formalism
SLIDE 10
Problem Statement
time ω qi-1 - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ←
SLIDE 11
Problem Statement
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 12
Problem Statement
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 13
Problem Statement
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 14
Problem Statement: Inefficiency
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 15
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 16
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 17
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 18
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 19
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 20
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 21
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 22
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 23
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 24
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 25
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
SLIDE 26
Incremental RTEC
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T). happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
sF
Qi = sF Qi-1 + ΔsF(Qi-1,{ins,del}) qi-1
initiatedAt(F=V,T) ← initiatedAt(F=V,T) ←
◮ Two phases:
◮ Deletion phase ◮ Addition phase
SLIDE 27
Incremental RTEC - Deletion phase
time ω qi-1 - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ←
SLIDE 28
Incremental RTEC - Deletion phase
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1
initiatedAt(F=V,T) ←
SLIDE 29
Incremental RTEC - Deletion phase
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1 [happensAt(A,T)] del v [holdsAt(B=VB,T)] del v [happensAt(C,T)] ins v [holdsAt(D=VD,T)] ins .
initiatedAt(F=V,T) ←
[initiatedAt(F=V,T)]Qi-1 ←
SLIDE 30
Incremental RTEC - Deletion phase
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1 [happensAt(A,T)] del v [holdsAt(B=VB,T)] del v [happensAt(C,T)] ins v [holdsAt(D=VD,T)] ins .
initiatedAt(F=V,T) ←
[initiatedAt(F=V,T)]Qi-1 ←
SLIDE 31
Incremental RTEC - Deletion phase
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1 [happensAt(A,T)] del v [holdsAt(B=VB,T)] del v [happensAt(C,T)] ins v [holdsAt(D=VD,T)] ins .
initiatedAt(F=V,T) ←
[initiatedAt(F=V,T)]Qi-1 ←
SLIDE 32
Incremental RTEC - Deletion phase
time ω time ω qi qi-1 qi-1 - ω qi - ω
happensAt(A,T), holdsAt(B=VB,T), not happensAt(C,T), not holdsAt(D=VD,T).
qi-1 [happensAt(A,T)] del v [holdsAt(B=VB,T)] del v [happensAt(C,T)] ins v [holdsAt(D=VD,T)] ins .
initiatedAt(F=V,T) ←
[initiatedAt(F=V,T)]Qi-1 ←
SLIDE 33
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω
SLIDE 34
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 35
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 36
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 37
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 38
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 39
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 40
Incremental RTEC - Addition phase
time ω qi qi-1 qi - ω [happensAt(A,T)] ins , [holdsAt(B=VB,T)] Qi , [not happensAt(C,T)] Qi , [not holdsAt(D=VD,T)] Qi .
SLIDE 41
Incremental RTEC - Evaluation
◮ Delays up to 16 hours ◮ 17M position signals, 34K vessels ◮ European seas ◮ January 2016
SLIDE 42
Incremental RTEC - Evaluation
◮ Delays up to 16 hours ◮ 17M position signals, 34K vessels ◮ European seas ◮ January 2016
1h 2h 4h 8h 16h 1 2 3 4 5 6
Window(hours) Avg Time (in minutes)
Incremental RTEC RTEC
(Left) Average recognition time and (Right) average number of input and complex events. Sliding step of 1 hour
SLIDE 43
Summary
◮ Properties of the algorithm:
◮ Evaluation of small sets early ◮ Optimal rule rewriting ◮ Can handle retractions in the input
SLIDE 44
Summary
◮ Properties of the algorithm:
◮ Evaluation of small sets early ◮ Optimal rule rewriting ◮ Can handle retractions in the input
◮ We have performed a complexity analysis of the incremental
version and have discovered the conditions that lead to better performance
SLIDE 45
Summary
◮ Properties of the algorithm:
◮ Evaluation of small sets early ◮ Optimal rule rewriting ◮ Can handle retractions in the input
◮ We have performed a complexity analysis of the incremental
version and have discovered the conditions that lead to better performance
◮ Future work:
◮ Probabilistic version of the incremental algorithm