Temporal Constraint Management in Artificial Intelligence

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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
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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
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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 computationall
y efficient
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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
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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!!!
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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
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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
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!
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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
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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
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!
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Survey (1/18)Types of temporal entities
- Time Points
- Time Intervals
- Sets of Time Points/Intervals
(repeated/periodic events)
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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 900 to 1133) - 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)
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Survey (3/18)Types of temporal constraints (2/4)
QUALITATIVE CONSTRAINTS on TIME POINTS
? Point Algebra Vilain Kautz, 87 - base
relations lt, , gt - composite relations (lt,),
(lt,gt), (,gt), (lt,,gt) Notice P1(r1,r2,rk)P2
means r1(P1,P2) ? r2(P1,P2) ? ? rk(P1,P2)
? Continuous Pointizable Algebra Vilain, Kautz,
VanBeek - base relations lt, , gt - composite
relations (lt,), (,gt), (lt,,gt)
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Survey (4/18)Types of temporal constraints (3/4)
QUALITATIVE CONSTRAINTS on TIME INTERVALS
? Interval Algebra Allen, 83 - 13 base
relations, 213 relations
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Survey (5/18)Types of temporal constraints (4/4)
gtgtgtgt QUANTITATIVE CONSTRAINTS see below
CONSTRAINTS on SETS OF INTERVALS (repeated/periodi
c 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
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Survey (6/18)Temporal Reasoning (1/5)
Mostly PATH-CONSISTENCY-based TR
C3NEW ? C3OLD ? (C1 _at_ C2)
Different instantiations, depending on the types
of constraints (and on the definitions of
intersection and composition)
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Survey (7/18)Temporal Reasoning (2/5)
E.g., path-consistency on quantitative
constraints between time points (STP framework
Dechter et al., 91)
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Survey (7/18)Temporal Reasoning (2/5)
E.g., path-consistency on quantitative
constraints between time points (STP framework
Dechter et al., 91)
IHNEW 10,30 ? (0,10?10,10) 10,20
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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
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Survey (9/18)Temporal Reasoning (4/5)
All-to-all shortest path algorithm
Floyd-Warshall
For k1 to N do For i1 to N do For j1 to
N do Mi,jMin(Mi,j,Mi,kMk,j)
Property Consistent iff no negative cycle
Complexity O(N3)
Property Correct complete for b.o.d.
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Survey (10/18)Temporal Reasoning (5/5)
Minimal Network (shortest path between each pair
of nodes)
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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 Maxi
mal tractable fragments Nebel Buckert, 95,
Drakengren Jonsson, 97
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Survey (12/18)Approaches Complexity (2/5)
QUANTITATIVE CONSTRAINTS
?? STP Dechter et al., 91 O(N3)
?? TCSP Dechter et al., 91 Exponential (many
optimizations)
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Survey (13/18)Approaches Complexity (3/5)
QUALITATIVEQUANTITATIVE 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
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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., P1ltP2 ?
0ltP2-P1
?? Some Interval Algebra relation e.g., I
(started-by,contains, finished-by,equal) J ? 0
? Start(J)-Start(I) ? 0 lt End(I)-End(J)
?? BUT NOT ALL RELATIONS e.g., P1(lt,gt)P2 ? 0
lt P1-P2 ? 0 lt P2-P1 (in TCST but not in
STP) e.g., I (before,after) J ? 0 lt
End(I)-Start(J) ? 0 lt End(J)-Start(I)
(neither in STP nor in TCSP)
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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
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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
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Survey (17/18)TRs Applications
MANY APPLICATIONS
? Scheduling ? Planning ? Natural Language
Understanding ? Diagnosis .. ? Multimedia
Presentations ? Clinical Guidelines
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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,
Intl 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.