1. Temporal Constraint Management in Artificial Intelligence - Introduction: time & temporal constraints - The problem - Survey of AI approaches to temporal constraints Paolo Terenziani Dipartimento di Informatica Universita’ del Piemonte Orientale, Alessandria, Italy TEMPORAL CONSTRAINT

2. Introduction (1/3) Time has a “peculiar” semantics, so that it deserves a specific attention The world evolves in time: time is an intrinsic part of human way of approaching reality  Time has to be taken into account in each approach modeling (evolving) parts of the world

3. Introduction (2/3) Many different approaches in the literature, e.g., -simulation-based approaches (Petri Nets, Markov Models, Workflows,...) -…. -logical approaches (dynamic l., temporal l., nonmonotonic l., semantic nets, ….) A MAIN DISTINCTION: “general purpose”: modeling both (part of) the world and its temporal phenomena +generality, homogeneous framework to deal with phenomena -computationally not efficient VS. “specialised”: dealing only with some temporal phenomena -generality +computationally efficient

4. Introduction (3/3) “Specialised” approaches IDEA: modularity: Building efficient solutions to well-defined parts of the whole problem IN AI: “Knowledge Servers” [Brachman & Levesque] to be paired with other systems/problem solvers Trade-off between expressiveness and computational complexity of (correct & complete) inferential mechanisms NOTICE: general (not ad-hoc) solutions to a slice of temporal phenomena

5. Temporal Constraint Managers: the Problem (1/5) Temporal Constraint (TC): a part of the problem that can be isolated e.g., A before B & B before C  A before C REGARDLESS of the description of the events A, B, C (1) Which constraints (representation language)? (2) Which inferences? Trade-off!!!

6. Temporal Constraint Managers: the Problem (2/5) Digression Intended vs. supported SEMANTICS Temporal Constraints without Temporal Reasoning (constraint propagation) -are useless -clash with users’ intuitions/expectations

7. Temporal Constraint Managers: the Problem (3/5) Implied constraint (temporal reasoning): (1.6) C ends between 30 and 60 m after the start of A ABC 10-20 Correct (consistent) assertion: (1.7) C ends between 30 and 50 m after the start of A Not correct (inconsistent) assertion: (1.8) C ends more than 70 m. after the start of A However: Temporal Reasoning is NEEDED in order to support such an intended semantics!

8. Temporal Constraint Managers: the Problem (4/5) DESIDERATA for Temporal Reasoning Algorithms - tractability  “reasonable” response time (important for Knowledge servers!) - correctness  no wrong inferences - completeness  reliable answers

9. Temporal Constraint Managers: the Problem (5/5) Implied constraint (temporal reasoning): (1.6) C ends between 30 and 60 m after the start of A ABC 10-20 Suppose that temporal reasoning is NOT complete, so that (1.6) is not inferred The answer to query (Q1) might be: YES (Q1) Is it possible that C ends more than 70 m. after the start of A? Complete Temporal Reasoning is NEEDED in order to grant correct answers to queries!

10. Survey (1/18) Types of temporal entities -Time Points -Time Intervals -Sets of Time Points/Intervals (repeated/periodic events)

11. Survey (2/18) Types of temporal constraints (1/4) -Qualitative: relative positions of entities (e.g., A during B) -Quantitative: metric time -dates (A on 1/1/2003 from 9:00 to 11:33) -duration (A lasted between 3 and 4 hours) -delays (B started between 5 and 10 minutes after A) -Periodicity/repetition -based (qualitative and/or quantitative)

12. Survey (3/18) Types of temporal constraints (2/4) QUALITATIVE CONSTRAINTS on TIME POINTS  Point Algebra [Vilain & Kautz, 87] -base relations: -composite relations: ( ), (=,>), ( ) Notice: P1(r 1,r 2,…r k )P2 means r 1 (P1,P2)  r 2 (P1,P2)  …  r k (P1,P2)  Continuous Pointizable Algebra [Vilain, Kautz, VanBeek] -base relations: -composite relations: ( ), ( )

13. Survey (4/18) Types of temporal constraints (3/4) QUALITATIVE CONSTRAINTS on TIME INTERVALS  Interval Algebra [Allen, 83] -13 base relations, 2 13 relations I before J (J after I) I meets J (J met-by I) I overlaps J (J overlapped-by I) I finished-by J (J finishes I) I equal J I contains J (J during I) I started-by J (J starts I)

14. Survey (5/18) Types of temporal constraints (4/4) CONSTRAINTS on SETS OF INTERVALS (repeated/periodic events)  Periodicity-dependent durations [Loganantharaj & Gimbrone, 95] e.g.On Mondays John goes to work in 40-45 minutes On Tuesdays John goes to work in 30-55 minutes  “Absolute” qualitative constraints on repeated events [Morris et al., 93] e.g.Meetings always precede Lunches  Periodicity-dependent qualitative constraints on repeated events [Terenziani, 95] e.g.From 10/1/2003 to 31/3/2003, twice each Monday, two units of Math precede one unit of Physics >>>> QUANTITATIVE CONSTRAINTS: see below

15. Survey (6/18) Temporal Reasoning (1/5) Mostly: PATH-CONSISTENCY-based TR C3 NEW  C3 OLD  (C1 @ C2) Different instantiations, depending on the types of constraints (and on the definitions of intersection and composition) IJK C3? C2C1

16. Survey (7/18) Temporal Reasoning (2/5) E.g., path-consistency on quantitative constraints between time points (STP framework [Dechter et al., 91]) I J K [0,10] H [10,20] [10,30] [10,20] [10,10]

17. Survey (7/18) Temporal Reasoning (2/5) E.g., path-consistency on quantitative constraints between time points (STP framework [Dechter et al., 91]) I J K [0,10] H [10,20] [10,10] IH NEW = [10,30]  ([0,10]  [10,10]) = [10,20]

18. Survey (8/18) Temporal Reasoning (3/5) STP (Simple Temporal Problem) framework [Dechter et al., 91]) Conjunction of Bounds on Difference (b.o.d.) constraints 0  J-I  10 10  H-I  30 10  K-I  20 10  H-K  20 10  H-J  10 -  < K-J < +  I I J JK K H H 0 0 0 0 10 0 -1020 ++ -10 10 3020 ++ ij [c,d] ij d -c  c  j-i  d

19. Survey (9/18) Temporal Reasoning (4/5) All-to-all shortest path algorithm [Floyd-Warshall] For k:=1 to N do For i:=1 to N do For j:=1 to N do M[i,j]=Min(M[i,j],M[i,k]+M[k,j]) Property: Consistent iff no negative cycle Complexity: O(N 3 ) Property: Correct & complete for b.o.d.

20. Survey (10/18) Temporal Reasoning (5/5) I J K [10,10] H [20,20] [10,10] [0,0] Minimal Network (shortest path between each pair of nodes) I I J JK K H H 0 0 0 0 10 -10 100 -10 -20 10 2010 0

21. Survey (11/18) Approaches & Complexity (1/5) QUALITATIVE CONSTRAINTS  Continuous Pointizable Algebra [Vilain, Kautz, VanBeek, 89] O(N 3 )  Point Algebra [Vilain & Kautz, 87] O(N 4 )  Interval Algebra [Allen, 83] Exponential Maximal tractable fragments [Nebel & Buckert, 95], [Drakengren & Jonsson, 97]

22. Survey (12/18) Approaches & Complexity (2/5) QUANTITATIVE CONSTRAINTS  STP [Dechter et al., 91] O(N 3 )  TCSP [Dechter et al., 91] Exponential (many optimizations) IJ [10,20]  [30,35]

23. Survey (13/18) Approaches & Complexity (3/5) QUALITATIVE+QUANTITATIVE CONSTRAINTS  [Vilain & Kautz, 91] Combining two TRs Does the exchange of constraints between TRs end?  [Meiri, 91] “two sorted” formalism + mapping operators  [Brusoni, Terenziani et al., 95] mapping onto STP

24. Survey (14/18) Approaches & Complexity (4/5) STP (and TCSP) and QUALITATIVE CONSTRAINTS STP (and TCSP) can also represent (a subset of) qualitative constraints  Continuous Poitizable relations e.g., P1<P2  0<P2-P1  Some Interval Algebra relation e.g., I (started-by,contains, finished-by,equal) J  0  Start(J)-Start(I)  0 < End(I)-End(J)  BUT NOT ALL RELATIONS e.g., P1( )P2  0 < P1-P2  0 < P2-P1 (in TCST but not in STP) e.g., I (before,after) J  0 < End(I)-Start(J)  0 < End(J)-Start(I) (neither in STP nor in TCSP)

25. Survey (15/18) Approaches & Complexity (5/5) SURVEY NOT EXHAUSTIVE !!! E.g., relative duration E.g., “A lasted more than B”  [Pujary & Sattar, 99]  [Jonsson & Backstrom, 98] homogeneous approach based on linear programming

26. Survey (16/18) TRs & Applications MANY TRs (knowledge servers) in AI  TMM [Dean & McDermott, 87]  Timelogic [Koomen, 89]  MATS [Kautz & Ladkin, 91]  Timegraph Gerevini & Schubert, 95]  …..  Later [Brusoni, Terenziani et al., 95] Comparison of several systems in [Allen & Yampratoom, 93]

27. Survey (17/18) TRs & Applications MANY APPLICATIONS  Scheduling  Planning  Natural Language Understanding  Diagnosis …..  Multimedia Presentations  Clinical Guidelines

28. Survey (18/18) TRs & Applications REFERENCES TO SURVEYS  M. Vilain, H. Kautz, and P. VanBeek. "Constraint Propagation Algorithms for temporal reasoning: a Revised Report", D.S. Weld, J. deKleer, eds., Readings in Qualitative Reasoning about Physical Systems. Morgan Kaufmann, 373-381, 1990.  J. Allen, “Time and Time Again: The Many Ways to Represent Time”, Int’l Journal of Intelligent Systems 6(4), 341-355, 1991.  E. Yampratoom, J. Allen, “Performance of Temporal reasoning Systems”, Sigart Bull. 4(3), 26-29, 1993.  L. Vila. 1994, "A Survey on Temporal Reasoning in Artificial Intelligence", AI Communications 7(1):4-28, 1994. …..  P. Terenziani, “Reasoning about time”, Encyclopedia of Cognitive Science, Macmillan Reference Ltd, Vo.3, 869-874, 2003.