### Abstract

Cost-based Hypothetical Reasoning is an important framework for knowledge-based systems; however it is a form of non-monotonic reasoning and thus an NP-hard problem. To find a near-optimal solution in polynomial time with respect to problem size, some algorithms have been developed so far using optimization techniques. In this paper, we show two major ways of transforming prepositional clauses in the hypothetical reasoning problems into constraints. One transforms the clauses into linear inequalities and is good at getting a low-cost solution, while the other transforms them into non-linear equalities and is good at finding a feasible solution. We them show a method of integrating these two transformations by using augmented Lagrangian method. Here, each variable and constraint is regarded as a processor and the searh is realized by their interaction. Two kinds of processors are derived from the two transformations; the structure of these processors are changed dynamically during the search. The cooperation of these two processors allows to obtain better near-optimal solutions than by our previous SL method. This effect is shown in the experiments using two problems with different problem structures.

Original language | English |
---|---|

Pages (from-to) | 400-407 |

Number of pages | 8 |

Journal | Transactions of the Japanese Society for Artificial Intelligence |

Volume | 16 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Augmented lagrangian method
- Hypothetical reasoning
- Near-optimal solution
- Optimization

### ASJC Scopus subject areas

- Artificial Intelligence

### Cite this

**Tranformation of cost-based hypothetical reasoning into two continuous optimization problems and a reasoning method with their collaboration.** / Matsuo, Yutaka; Ishizuka, Mitsuru.

Research output: Contribution to journal › Article

*Transactions of the Japanese Society for Artificial Intelligence*, vol. 16, no. 5, pp. 400-407. https://doi.org/10.1527/tjsai.16.400

}

TY - JOUR

T1 - Tranformation of cost-based hypothetical reasoning into two continuous optimization problems and a reasoning method with their collaboration

AU - Matsuo, Yutaka

AU - Ishizuka, Mitsuru

PY - 2001

Y1 - 2001

N2 - Cost-based Hypothetical Reasoning is an important framework for knowledge-based systems; however it is a form of non-monotonic reasoning and thus an NP-hard problem. To find a near-optimal solution in polynomial time with respect to problem size, some algorithms have been developed so far using optimization techniques. In this paper, we show two major ways of transforming prepositional clauses in the hypothetical reasoning problems into constraints. One transforms the clauses into linear inequalities and is good at getting a low-cost solution, while the other transforms them into non-linear equalities and is good at finding a feasible solution. We them show a method of integrating these two transformations by using augmented Lagrangian method. Here, each variable and constraint is regarded as a processor and the searh is realized by their interaction. Two kinds of processors are derived from the two transformations; the structure of these processors are changed dynamically during the search. The cooperation of these two processors allows to obtain better near-optimal solutions than by our previous SL method. This effect is shown in the experiments using two problems with different problem structures.

AB - Cost-based Hypothetical Reasoning is an important framework for knowledge-based systems; however it is a form of non-monotonic reasoning and thus an NP-hard problem. To find a near-optimal solution in polynomial time with respect to problem size, some algorithms have been developed so far using optimization techniques. In this paper, we show two major ways of transforming prepositional clauses in the hypothetical reasoning problems into constraints. One transforms the clauses into linear inequalities and is good at getting a low-cost solution, while the other transforms them into non-linear equalities and is good at finding a feasible solution. We them show a method of integrating these two transformations by using augmented Lagrangian method. Here, each variable and constraint is regarded as a processor and the searh is realized by their interaction. Two kinds of processors are derived from the two transformations; the structure of these processors are changed dynamically during the search. The cooperation of these two processors allows to obtain better near-optimal solutions than by our previous SL method. This effect is shown in the experiments using two problems with different problem structures.

KW - Augmented lagrangian method

KW - Hypothetical reasoning

KW - Near-optimal solution

KW - Optimization

UR - http://www.scopus.com/inward/record.url?scp=18444406873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18444406873&partnerID=8YFLogxK

U2 - 10.1527/tjsai.16.400

DO - 10.1527/tjsai.16.400

M3 - Article

AN - SCOPUS:18444406873

VL - 16

SP - 400

EP - 407

JO - Transactions of the Japanese Society for Artificial Intelligence

JF - Transactions of the Japanese Society for Artificial Intelligence

SN - 1346-0714

IS - 5

ER -