Akinori Abe

Abstract

If a knowledge base does not have all of the necessary clauses for reasoning, ordinary hypothetical reasoning systems are unable to explain observations. In this case, it is necessary to explain such observations by abductive reasoning, supplemental reasoning, or approximate reasoning. In fact, it is somewhat difficult to find clauses to explain an observation without hints being given.
Therefore, I use an abductive strategy (CMS) to find missing clauses, and to generate plausible hypotheses to explain an observation from these clauses while referring to other clauses in the knowledge base. In this page, I show two types of inferences and combines them. One is a type of approximate inference that explains an observation using clauses that are analogous to abduced clauses without which the inference would fail. The other is a type of exact inference that explains an observation by generating clauses that are analogous to clauses in the knowledge base.

Abductive Analogical Reasoning

Preparations...

Inference

A knowledge base does not always have all of the necessary clauses for reasoning. When this is the case, ordinary inference systems can not make correct inferences. Inferences will stop before returning answers or wrong answers will be returned. Recently, therefore, it has become important to make inferences with incomplete knowledge. If inferences are made with an incomplete knowledge base, however, it is necessary to make abductive inferences, supplemental inferences or approximate inferences.
This page shows the inference that uses an abductive strategy to find missing clauses, and to generate plausible hypotheses to explain an observation from these clauses while referring to other clauses in the knowledge base.
In general, it is slightly difficult to find the analogical supplemental clauses to explain an observation without any hints. Therefore, I adopted the following method:

  1. to derive a clause set () that can derive analogical clause of abduced missing clause (),
  2. to transform a clause set to a clause set () by using reverse mapping of [ -> ] to explain an observation.

Basically, AAR's inference is abduction and its inference manner is as follows:
I adopted the framework of CMS as abduction that may produce new hypotheses.

  1. An observation C is given from the user. sends the clause C to .
  2. If C can not be explained by the current knowledge base (a clause set Σ), returns minimal support clause with respect to clause set Σ. The negation of minimal support clause can be a minimal hypothesis to explain an observation . However, it is not derived from the current knowledge base (). Therefore, a justification of can not be guaranteed.
  3. is send to (Partial Analogical Derivation System), derives a clause set () that can derive an analogical clause of from the knowledge base.

    ()

  4. Furthermore, is transformed by using the reverse mapping of [] to . The geneated clause set seems to be the same type as minimal support clause. It is send to .
    ()
  5. The observation is explained by as a hypothesis.
I explained the inference algorithm of AAR. By using the above inference algorithm, even if the knowledge that is necesary to explain a observation is missing, an observation can be explained by generating a necessary clause as hypothesis to explain the observation by referring to clauses in the knowledge base.
Moerover, the justification of the generated clause can be guaranteed, bacause it is generated by referring to the clauses in the knowledge base.

Fig. 1: Inference manner

Since the relation between concepts is represented like these pictures:

,

By the inference shown in the right picture, the above can be generated.
Click the right picture, you can see the inference animation!!

Fig. 2: Phase I

By the inference shown in the right picture, the above can be generated.
Click the right picture, you can see the inference animation!!

Fig. 3: Phase II

The relation between CMS and AAR is presented as follows:

CMS AAR
given
inference


( )

( )
hypotheses

Fig. 4: CMS vs AAR

Fig. 5: Inference manner

Click the above picture, then you can see the inference animation!!

Furtermore......

References:

  1. Abe A.: Abduction + Analogical Reasoning = Supplemental Reasoning -> Abduce, IPSJ SIG Notes, 95-AI-101-8-1, pp. 49--50 (1995) (in Japanese).
  2. Abe A.: Abductive Analogical Reasoning, presented in WAL96 (1996) (in Japanese).
  3. Abe A.: Abductive Analogical Reasoning, Proc, of Annal Conf. of JSAI, S6-04, pp. (123)--(126) (1996) (in Japanese).
  4. Abe A.: Abductive Analogical Reasoning, Trans. of the IEICE vol. J81-D-II, No. 6, pp. 1285--1292 (1998) (in Japanese)
  5. Abe A.: Applications of Abduction, Proc. of ECAI98 Workshop on Abduction and Induction in AI (1998)
  6. Abe A.: Two-sided Hypotheses Generation for Abductive Analogical Reasoning, Proc. of ICTAI99, pp. 145--152 (1999)
  7. Abe A. and Fujimoto K.: Multi-agentized Reasoning as Reasoning with Incomplete Knowledge base, MACC99 (1999)
  8. Abe A.: Abductive Analogical Reasoning, Systems and Computers in Japan, Vol. 31, No. 1, pp. 11--19 (2000)
  9. Fujimoto K., Kazawa H., Sato H., Abe A., Matsuzawa K.: DSIU systems: Decision Support for Internet Usres , J. of JSAI, Vol. 15, No. 1, pp. 61--64 (2000)
  10. Ha N. V., Ishikawa T. and Abe A.: A Mechanism for Inferring Approxiamate Solutions under Incomplete Knowledge based on Rule Similarity, Proc. of AISTA2000 (2000)
  11. Ha N. V., Ishikawa T. and Abe A.: An Inference Mechanism under Incomplete Knowledge based on Rule Similarity Considering Viewpoint, Proc. of KES2000 (2000)
  12. Abe A.: The Role of Abduction in Internet-based Applications, Proc. of PRICAI2000, pp. 831 (2000)
  13. Abe A. and Fujimoto K.: Selection of preferable abductive hypotheses, Proc. of IJCAI Workshop on Abductive Reasoning, pp. 1--6 (2001)
  14. Abe A.: The role of abduction in Chance Discovery, Proc. of SCI2001, Vol. VIII, pp. 400-405 (2001)
  15. Viet Ha Nguyen, Tsutomu Ishikawa and Akinori Abe: A mechanism for inferring approximate solutions under incomplete knowledge based on rule similarity, Systems and Computers in Japan, Vol. 33, No. 9, pp. 78--89 (2002)
  16. Abe A.: The role of abduction in Chance Discovery, New Generation Computing, Vol.21, No.1, pp. 61-71 (2003)
  17. Abe A.: Abduction and Analogy in Chance Discovery, in Chance Discovery (Osawa Y. and McBurney P. eds.), Chap. 16, pp. 231-248, Springer (2003)
  18. Abe A., Kogure K. and Hagita N.: Determination of A Chance in Nursing Risk Management, Proc. of ECAI2004 Workshop on Chance Discovery, pp. 222-231 (2004)
  19. Abe A., Kogure K. and Hagita N.: Nursing Risk Prediction as Chance Discovery, Proc. of KES2004 Vol. II, pp. 815--822 (2004).
  20. Abe A., Naya F., Ozaku H.I., Kuwahara N., and Kogure K.: Scenario Violation in Nursing Activities, Proc. of the ICML05 4th Int'l Workshop on Chance Discovery, pp. 102--109 (2005)
  21. Abe A., Ozaku H.I., Kuwahara N., and Kogure K.: Scenario Violation in Nursing Activities --- Nursing Risk Management from the viewpoint of Chance Discovery, Soft Computing Journal, Springer (2006) to appear
  22. Abe A., Ozaku H.I., Kuwahara N., and Kogure K.: Scenario-base Construction for Abductive Nursing Risk Management, Proc. of IPUM2006, pp. 206--213 (2006)
  23. Abe A., Ozaku H.I., Kuwahara N., and Kogure K.: What Should be Abducible in Abductive Nursing Risk Management?, Proc. of KES2006 (LNAI4253), Vol III, pp. 22--29 (2006) to appear
  24. Abe A., Ozaku H.I., Kuwahara N., and Kogure K.: Relation between Abductive and Inductive Nursing Risk Managements, Proc. of RM2006 (JSAI2006), pp. 121--132 (2006)
  25. Ohsawa Y., Abe A., and Nakamura J.: Chance Discovery as Analogy based Value Sensing, International Journal of Organizational and Collective Intelligence, Vol. 1, No. 1 (2010) to appear