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Temporal Constraint Management in Artificial Intelligence Paolo Terenziani Dipartimento di Informatica Universita’ del Piemonte Orientale, Alessandria, Italy TEMPORAL CONSTRAINT - Introduction: time & temporal constraints - The problem - Survey of AI approaches to temporal constraints Introduction (1/3) 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 Time has a “peculiar” semantics, so that it deserves a specific attention 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 Introduction (3/3) “Specialised” approaches IDEA: modularity: Building efficient solutions to well-defined parts of the whole problem NOTICE: general (not ad-hoc) solutions to a slice of temporal phenomena 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 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!!! 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 Temporal Constraint Managers: the Problem (3/5) (1.1) the end of A is equal to the start of B (1.2) the end of B is equal to the start of C (1.3) the duration of A is between 10 and 20 m (1.4) the duration of B is between 10 and 20 m (1.5) the duration of C is between 10 and 20 m A 10-20 B 10-20 C 10-20 Implied constraint (temporal reasoning): (1.6) C ends between 30 and 60 m after the start of A 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! 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 Temporal Constraint Managers: the Problem (5/5) (1.1) the end of A is equal to the start of B (1.2) the end of B is equal to the start of C (1.3) the duration of A is between 10 and 20 m (1.4) the duration of B is between 10 and 20 m (1.5) the duration of C is between 10 and 20 m A 10-20 B 10-20 C 10-20 Implied constraint (temporal reasoning): (1.6) C ends between 30 and 60 m after the start of A 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! Survey (1/18) Types of temporal entities - Time Points - Time Intervals - Sets of Time Points/Intervals (repeated/periodic events) 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) 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(r1,r2,…rk)P2 means r1(P1,P2) r2(P1,P2) … rk(P1,P2) Continuous Pointizable Algebra [Vilain, Kautz, VanBeek] - base relations: <, =, > - composite relations: (<,=), (=,>), (<,=,>) Survey (4/18) Types of temporal constraints (3/4) QUALITATIVE CONSTRAINTS on TIME INTERVALS Interval Algebra [Allen, 83] - 13 base relations, 213 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 contains J (J during I) I equal J I started-by J (J starts I) Survey (5/18) Types of temporal constraints (4/4) >>>> QUANTITATIVE CONSTRAINTS: see below 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 Survey (6/18) Temporal Reasoning (1/5) Mostly: PATH-CONSISTENCY-based TR I C1 J C2 K C3? C3NEW C3OLD (C1 @ C2) Different instantiations, depending on the types of constraints (and on the definitions of intersection and composition) Survey (7/18) Temporal Reasoning (2/5) E.g., path-consistency on quantitative constraints between time points (STP framework [Dechter et al., 91]) [0,10] I J [10,10] H [10,30] [10,20] K [10,20] Survey (7/18) Temporal Reasoning (2/5) E.g., path-consistency on quantitative constraints between time points (STP framework [Dechter et al., 91]) [0,10] I J [10,10] H [10,20] [10,20] K [10,20] IHNEW= [10,30] ([0,10][10,10]) = [10,20] 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 i [c,d] 0 J-I 10 10 K-I 20 10 H-I 30 10 H-J 10 10 H-K 20 - < K-J < + j d -c i c j-i d j I J K H I 0 10 20 30 J 0 0 + 10 K -10 + 0 20 H -10 -10 -10 0 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(N3) Property: Correct & complete for b.o.d. Survey (10/18) Temporal Reasoning (5/5) I I J 0 J -10 K -10 H -20 K H 10 10 20 0 0 10 0 -10 0 -10 10 0 [10,10] J [10,10] [0,0] I H [20,20] [10,10] K [10,10] Minimal Network (shortest path between each pair of nodes) Survey (11/18) Approaches & Complexity (1/5) QUALITATIVE CONSTRAINTS Continuous Pointizable Algebra [Vilain, Kautz, VanBeek, 89] O(N3) Point Algebra [Vilain & Kautz, 87] O(N4) Interval Algebra [Allen, 83] Exponential Maximal tractable fragments [Nebel & Buckert, 95], [Drakengren & Jonsson, 97] Survey (12/18) Approaches & Complexity (2/5) QUANTITATIVE CONSTRAINTS STP [Dechter et al., 91] O(N3) TCSP [Dechter et al., 91] Exponential (many optimizations) [10,20][30,35] I J 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 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) 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 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] Survey (17/18) TRs & Applications MANY APPLICATIONS ….. Scheduling Planning Natural Language Understanding Diagnosis Multimedia Presentations Clinical Guidelines 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.