1. Knowledge Evolution Tools
KB development requires knowledge evolution
Debugging, refining, structuring, modularizing, …
Power tools are needed to support KB evolution
KB diagnosis
Bugs, omissions, heuristic warnings, architectural advice
KB merging
To enable interoperation of KBs with overlapping content
KB partitioning
To enable effective reasoning
To produce reusable KB building blocks
KSL is developing knowledge evolution tools
Knowledge Systems Laboratory, Stanford University

2. Partition-Based Logical Reasoning
Eyal Amir Sheila McIlraith
John McCarthy Richard Fikes
Formal Reasoning Group Knowledge Systems Laboratory
Stanford University
In collaboration with
Vinay Chaudhri, Mark Stickel, and Tomas Uribe
Artificial Intelligence Center
SRI International

3. Knowledge Systems Laboratory, Stanford University
Objective
The problem: How to reason effectively with common sense KBs created by multiple domain experts
Properties of these KBs:
Large-scale with significant internal structure
Overlapping content
Require multiple kinds of reasoners
What we are doing
Developing theory, algorithms, and implementations for
Query answering
More efficient propositional and first-order logical reasoning
that exploit KB structure
Supporting SRI in the application and evaluation of this work
Richard: I would just say here. “The RKF program is tasked with supporting domain experts in rapidly constructing KBs (rephrase)…but these KBs are of limited use unless we have ways to reason effectively with them, to extract the knowledge provided by these domain experts. The work we’ve been doing addresses precisely this problem, (providing a next-step in the reformulation of knowledge in support of knowledge formation for eventual extraction.)”
Knowledge Systems Laboratory, Stanford University

4. Knowledge Systems Laboratory, Stanford University
General Approach
Graph-based partitioning techniques exploiting structure:
Decompose
Convert to Tree
Original KB Graph Tree
Knowledge Systems Laboratory, Stanford University

5. Example Partitioned KB
 ok_pump   on_pump  water
 man_fill  water
 man_fill   on_pump
man_fill  on_pump A
 ok_pump   on_pump  water
 man_fill  water
 man_fill   on_pump
man_fill  on_pump
 water   ok_boiler   on_boiler
 steam
water   steam
on_boiler   steam
ok_boiler   steam
 steam   coffee  hot_drink
coffee  teabag
 steam   teabag  hot_drink
water A2
 water   ok_boiler   on_boiler
 steam
water   steam
on_boiler   steam
ok_boiler   steam
steam A3
 steam   coffee  hot_drink
coffee  teabag
 steam   teabag  hot_drink
Knowledge Systems Laboratory, Stanford University

6. Knowledge Systems Laboratory, Stanford University
General Approach
Graph-based partitioning techniques exploiting structure:
Decompose
Convert to Tree
Original Problem Graph Tree
Message-passing to realize global reasoning:
Inference done locally at each node
Information propagated between nodes to give global solution
 Inference is linear in the tree structure, worst-case exponential within the individual nodes.
Knowledge Systems Laboratory, Stanford University

7. Example Partitioned KB
 ok_pump   on_pump  water
 man_fill  water
 man_fill   on_pump
man_fill  on_pump A
 ok_pump   on_pump  water
 man_fill  water
 man_fill   on_pump
man_fill  on_pump
 water   ok_boiler   on_boiler
 steam
water   steam
on_boiler   steam
ok_boiler   steam
 steam   coffee  hot_drink
coffee  teabag
 steam   teabag  hot_drink
water A2
 water   ok_boiler   on_boiler
 steam
water   steam
on_boiler   steam
ok_boiler   steam
steam A3
 steam   coffee  hot_drink
coffee  teabag
 steam   teabag  hot_drink
Knowledge Systems Laboratory, Stanford University

8. Message Passing Algorithm (FMP)
Order partitions by distance from query
Concurrently:
Perform consequence finding in each partition
Consequences in the communication language of the link towards the query are added to the linked partition
If Q is proven, return YES 1 2 Q
Knowledge Systems Laboratory, Stanford University

9. Prove hot_drink, Given ok_pump, ok_boiler, on_boiler
FMP using Resolution (for example)
(1)  ok_pump   on_pump  water
(2)  man_fill  water
(3)  man_fill   on_pump
(4) man_fill  on_pump
(12) ok_pump assert
(13) on_pump  water (2,4)
(14)  ok_pump  water (13,1)
(13) water (14,12)
water
(5)  water   ok_boiler   on_boiler
 steam
(6) water   steam
(7) on_boiler   steam
(8) ok_boiler   steam
(14) ok_boiler assert
(15) on_boiler assert
(16)  ok_boiler   on_boiler  steam (13,5)
(17)  on_boiler  steam (16,14)
(18) steam (17,15)
steam
(9)  steam   coffee  hot_drink
(10) coffee  teabag
(11)  steam   teabag  hot_drink
(19)  steam  teabag  hot_drink (9,10)
(20)  steam  hot_drink (19,11)
(21) hot_drink (20,18)
Knowledge Systems Laboratory, Stanford University

10. Benefits of Partitioning
 ok_pump   on_pump  water
 man_fill  water
 man_fill   on_pump
man_fill  on_pump
 water   ok_boiler   on_boiler  steam
water   steam
on_boiler   steam
ok_boiler   steam
 steam   coffee  hot_drink
coffee  teabag
 steam   teabag  hot_drink
water
steam A1 A2 A3
Reduces
BETWEEN-partition
deduction
Enables parallel processing
Allows for different reasoners
in each partition
Knowledge Systems Laboratory, Stanford University

11. A New Refinement: Focused FMP
Order partitions by distance from query
Concurrently:
Perform consequence finding in the outbound communication language of each partition
Consequences in the communication language of the link towards the query are added to the linked partition
If Q is proven, return YES 1 2 Q
Knowledge Systems Laboratory, Stanford University

12. Prove hot_drink, Given ok_pump, ok_boiler, on_boiler
FMP using Resolution (for example)
(1)  ok_pump   on_pump  water
(2)  man_fill  water
(3)  man_fill   on_pump
(4) man_fill  on_pump
(12) ok_pump assert
(13) on_pump  water (2,4)
(14)  ok_pump  water (13,1)
(13) water (14,12)
water
(5)  water   ok_boiler   on_boiler
 steam
(6) water   steam
(7) on_boiler   steam
(8) ok_boiler   steam
(14) ok_boiler assert
(15) on_boiler assert
(16)  ok_boiler   on_boiler  steam (13,5)
(17)  on_boiler  steam (16,14)
(18) steam (17,15)
steam
(9)  steam   coffee  hot_drink
(10) coffee  teabag
(11)  steam   teabag  hot_drink
(19)  steam  teabag  hot_drink (9,10)
(20)  steam  hot_drink (19,11)
(21) hot_drink (20,18)
Knowledge Systems Laboratory, Stanford University

13. Benefits of Partitioning With Focused FMP
Reduces
WITHIN-partition
deduction A1
 ok_pump   on_pump  water
 man_fill  water
 man_fill   on_pump
man_fill  on_pump
 water   ok_boiler   on_boiler  steam
water   steam
on_boiler   steam
ok_boiler   steam
 steam   coffee  hot_drink
coffee  teabag
 steam   teabag  hot_drink
water
steam
Reduces
BETWEEN-partition
deduction A2
Enables parallel processing
Allows for different reasoners
in each partition A3
Knowledge Systems Laboratory, Stanford University

14. Accomplishments and Next Steps
Accomplishments and status
Theory developed
Algorithms designed, implemented, and tested
For both partitioning and reasoning with partitioned KBs
Evaluations being conducted on RKF KBs
By SRI with support from Stanford
Next steps
Complete evaluation of effectiveness on RKF KBs and tasks
Use RKF evaluation to determine high payoff next R&D steps
Incorporate into the RKF end-to-end systems
Embed in Chimaera as a knowledge evolution tool
Will enhance SME’s ability to produce useful KBs
Knowledge Systems Laboratory, Stanford University

15. Knowledge Systems Laboratory, Stanford University
Want to Learn More?
Papers
Amir, E. and McIlraith, S.; “Partition-Based Logical Reasoning for First-Order and Propositional Theories”; Submitted for Journal Publication.
McIlraith, S. and Amir, E.; “Theorem Proving with Structured Theories”; 17th International Conference on Artificial Intelligence (IJCAI-01); 2001.
Amir, E.; “Efficient Approximation for Triangulation of Minimum Tree Width”; 17th Conference on Uncertainty in Artificial Intelligence (UAI '01); 2001.
Amir, E. and McIlraith, S.; “Solving Satisfiability using Decomposition and the Most Constrained Subproblem”; Proceedings of SAT 2001; 2001.
Amir, E. and McIlraith, S.; “Partition-Based Logical Reasoning”; 7th International Conference on Principles of Knowledge Representation and Reasoning (KR'2000); 2000.
Software
Partitioning:
Partition-based SAT: By request. Contact Sheila McIlraith
Partition-based Theorem Proving: Contact SRI
Knowledge Systems Laboratory, Stanford University