Finite Approximations of Predicate Circumscription
Summary :
Predicate Circumscription is a fundamental formalization of common sense reasoning. In this paper, we study a new approximation formula of it. In our previous works, we investigated Lifschitz's pointwise circumscription and its generalization, which functions as a finite approximation to predicate circumscription in the first-order framework. In this paper, at first, we study the ability of the generalized pointwise circumscription more closely, and give a simple example which shows that it cannot be complete even when a minimized predicate has only finite extension on the minimal models. Next, we introduce a new approximation formula, called finite constructive circumscription, in order to overcome that limitation. Finally, we compare expressive power of the two approximation methods with of predicate circumscription schema, and propose a open problem that should be solved to clarify that the completeness of predicate circumscription schema with respect to minimal model semantics.
- Publication
- IEICE TRANSACTIONS on Information Vol.E82-D No.2 pp.475-479
- Publication Date
- 1999/02/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Artificial Intelligence and Cognitive Science
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Kazuhiko OOTA, Koji IWANUMA, "Finite Approximations of Predicate Circumscription" in IEICE TRANSACTIONS on Information,
vol. E82-D, no. 2, pp. 475-479, February 1999, doi: .
Abstract: Predicate Circumscription is a fundamental formalization of common sense reasoning. In this paper, we study a new approximation formula of it. In our previous works, we investigated Lifschitz's pointwise circumscription and its generalization, which functions as a finite approximation to predicate circumscription in the first-order framework. In this paper, at first, we study the ability of the generalized pointwise circumscription more closely, and give a simple example which shows that it cannot be complete even when a minimized predicate has only finite extension on the minimal models. Next, we introduce a new approximation formula, called finite constructive circumscription, in order to overcome that limitation. Finally, we compare expressive power of the two approximation methods with of predicate circumscription schema, and propose a open problem that should be solved to clarify that the completeness of predicate circumscription schema with respect to minimal model semantics.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_2_475/_p
Copy
@ARTICLE{e82-d_2_475,
author={Kazuhiko OOTA, Koji IWANUMA, },
journal={IEICE TRANSACTIONS on Information},
title={Finite Approximations of Predicate Circumscription},
year={1999},
volume={E82-D},
number={2},
pages={475-479},
abstract={Predicate Circumscription is a fundamental formalization of common sense reasoning. In this paper, we study a new approximation formula of it. In our previous works, we investigated Lifschitz's pointwise circumscription and its generalization, which functions as a finite approximation to predicate circumscription in the first-order framework. In this paper, at first, we study the ability of the generalized pointwise circumscription more closely, and give a simple example which shows that it cannot be complete even when a minimized predicate has only finite extension on the minimal models. Next, we introduce a new approximation formula, called finite constructive circumscription, in order to overcome that limitation. Finally, we compare expressive power of the two approximation methods with of predicate circumscription schema, and propose a open problem that should be solved to clarify that the completeness of predicate circumscription schema with respect to minimal model semantics.},
keywords={},
doi={},
ISSN={},
month={February},}
Copy
TY - JOUR
TI - Finite Approximations of Predicate Circumscription
T2 - IEICE TRANSACTIONS on Information
SP - 475
EP - 479
AU - Kazuhiko OOTA
AU - Koji IWANUMA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 1999
AB - Predicate Circumscription is a fundamental formalization of common sense reasoning. In this paper, we study a new approximation formula of it. In our previous works, we investigated Lifschitz's pointwise circumscription and its generalization, which functions as a finite approximation to predicate circumscription in the first-order framework. In this paper, at first, we study the ability of the generalized pointwise circumscription more closely, and give a simple example which shows that it cannot be complete even when a minimized predicate has only finite extension on the minimal models. Next, we introduce a new approximation formula, called finite constructive circumscription, in order to overcome that limitation. Finally, we compare expressive power of the two approximation methods with of predicate circumscription schema, and propose a open problem that should be solved to clarify that the completeness of predicate circumscription schema with respect to minimal model semantics.
ER -
English
