Temporal Constraint Networks Chapter12培训课件.ppt

Minimal Network Light Room Switch {o, m} {b, m, mi, a} {o, s, d} Light Room Switch {o, m} {b, m} {o, s} Constraint Tightening A unique network equivalent to original network All constraints are subsets of original constraints Provides a more explicit representation Useful in answering many types of queries IA: Path Consistency Intersection Composition (a table like 12.5 page 342) QPC-1 (page 342) Tighten every pair of constraints using Until minimal network or inconsistency detected IA: Path Consistency Composition table (page 12.5) QPC-1, in some cases, guaranteed to generate minimal network (exact) But, minimal network is not guaranteed Global consistent Backtrack free Solution: combine, at each node, backtracking scheme with path-consistency look-ahead engine Backtracking scheme with path-consistency look-ahead engine Dual graph representation Use constraints as variables Use common variables as edges Light Room Switch {o, m} {b, m} {o, s, d} {o, m} {o, s, d} {b, m, mi, a} Light Room Switch A minimal network Backtracking Path-consistency look-ahead Point Algebra [Vilain Kautz 1986] Each variable represents a time point Domain are real numbers Constraint express relative positions of 2 points Three basic relations: PQ, P=Q, PQ Constraints are PA elements {, , =} Cheaper than IA: reasoning tasks are polynomial O(n3) Point Algebra: Example Story: Fred put the paper down and drank the last of his coffee IA: Paper { s, d, f, = } Coffee PA: Paper=[x, y], Coffee=[z, t] Constraints: xy, zt, xt, x=z, y=t, yz Coffee Coffee Coffee Coffee paper paper paper paper PA: Path Consistency Algorithm is basically the same as IA Composition table (Table 12.2 page 343) ? means universal constraint Path-consistent ? minimal ? decomposable (globally consistent) Convex PA (CPA) network Only have {, =, =, =, } Exclude ? PA: Consistency Inference Theorem 12.1.10 Path-consistency decides the consistency in O(n3) Consistency and solu