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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

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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

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@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},}

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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 -