Inexpensive CostOptimized Measurement Proposal for Sequential ModelBased Diagnosis

Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis DX’ 17 Patrick Rodler, Wolfgang Schmid, Konstantin Schekotihin

Agenda • Addressed Problem • Novel Approach (Overview and Ideas) • Experiments + Results • Conclusions DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 2

Addressed Problem • DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 3

Example (Queries and q-Partitions) • 1 0 1 1 0 positive negative DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis !! 4

Generic Sequential Diagnosis System Optimize output, make computations more efficient Minimize Expensive! DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 5

Novel Approach: Properties + Placement Uses reasoner as a black-box (BB) (reasoner is used as-is, as an oracle for answering consistency/entailment queries) As opposed to glass-box (GB) approaches (rely on internal modifications of reasoner to effect more efficient computations relevant to diagnostic problem) • Evaluations (Kalyanpur, 2006; Horridge, 2011) evidenced – often slight performance gain of GB over BB – that BB also often outperforms GB – possible exponential blow-up of GB realized by bookkeeping (cf. ATMS (de. Kleer, 1986)) Consequences: • General applicability, i. e. independent of – the (monotonic+decidable) KR language modeling the system to be diagnosed, and – the used (sound+complete) reasoner • Can directly benefit from latest improvements in reasoning systems • Can switch to specialized reasoners for sublanguages of logics “for free“ Examples: – Horn Logic (polytime) vs. Propositional Logic (NP-complete) – OWL EL (polytime) vs. OWL 2 (N 2 EXPTIME-complete) • Better robustness, less error-prone (because simpler) DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 6

Novel Approach: Properties + Placement Can efficiently handle implicit query spaces (IQS) (enumeration of possible queries is intractable) As opposed to explicit query spaces (EQS) (enumeration of possible queries in polytime in size of system description) • Examples – Digital circuit EQS (possible queries = wires; extractable from system model) – KB system IQS (possible queries = entailments; (intractable) inference needed) Problems of existing systems applied to IQS: • Exploration of unnecessary and duplicate query candidates • Are incomplete and hence not optimal • Often use reasoner extensively • Are dependent (e. g. in terms of completeness) on particular output of used reasoner • Are not scalable New Approach • Solves all these problems • While achieving orders of magnitude less time and better query quality DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 7

Novel Approach: Properties + Placement Overall: Approach preserves maximal generality Is broadly applicable across different MBD application domains DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 8

Novel Approach • DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 9

Relationship between query and q-partition (QP) Search space relevant for QCM MECE (Mutually Exclusive and Collectively Exhaustive) QP is a function of query optimize QP (i. e. QSM) first! Search space relevant for QSM DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 10

Phase P 1 (QSM Optimization) • ? ? Strongly conjectured empty DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 11

Once the QP is fixed… Run Phase P 1 QP Optimization Query Optimization no reasoner calls! poly number of reasoner calls! instantaneous! reasonably fast! DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 12

Phase P 2 (QCM optimization, restricted search space) • DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 13

Phase P 3 (QCM optimization, full search space) • DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 14

Phase P 3 (QCM optimization, full search space) • DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 15

Example (Phases P 1+P 2+P 3) • 1 0 1 1 0 DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 16

Experiments • DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 17

Results – (Comprehensive) Diagnoses Computation vs. Query Computation DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 18

Results – (Comprehensive) Query Computation vs. System Reaction Time DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 19

Results – (Comprehensive) Search Space Size vs. Computation Times DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 20

Results – (Scalability) Scalability Tests DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 21

Results – (Comparative) Comparative (Brute Force) Tests of method (NEW) with approach (OLD) not applying the new theory DX‘ 17, Inexpensive Cost-Optimized Measurement Proposal for Sequential Model-Based Diagnosis 22