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Title: Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets

Abstract

Over the years a number of generalizations of recursion theory have been introduced and studied. In this dissertation the author presents yet another such generalization. Based on the concept of a weakly recursively presented Boolean algebra, he defines Boolean-valued sets, Boolean-valued recursive sets, and Boolean-valued recursively enumerable sets and discuss the basic relationships between a Boolean-valued set, its principal part, and its support. Then he generalizes many elementary concepts and results about recursive and recursively enumerable sets such as the s-m-n theorem, the recursion theorem, and the projection theorem, etc. to Boolean valued sets. By using finite and infinite injury arguments, he generalizes the Friedberg-Muchnik theorem, the theorem about nonrecursive low r.e. sets, the minimal pair theorem, and other results. Finally, he discusses the possible application of Boolean-valued logic in artificial intelligence, and gives an implementation of a parser for the four-valued Boolean logic.

Authors:
Publication Date:
Research Org.:
California Univ., Berkeley, CA (USA)
OSTI Identifier:
6309943
Resource Type:
Miscellaneous
Resource Relation:
Other Information: Thesis (Ph.D)
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ARTIFICIAL INTELLIGENCE; ALGORITHMS; PROGRAMMING; ALGEBRA; CONTROL THEORY; RECURSION RELATIONS; MATHEMATICAL LOGIC; MATHEMATICS; 990200* - Mathematics & Computers

Citation Formats

Cai, Maohua. Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets. United States: N. p., 1989. Web.
Cai, Maohua. Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets. United States.
Cai, Maohua. 1989. "Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets". United States.
@article{osti_6309943,
title = {Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets},
author = {Cai, Maohua},
abstractNote = {Over the years a number of generalizations of recursion theory have been introduced and studied. In this dissertation the author presents yet another such generalization. Based on the concept of a weakly recursively presented Boolean algebra, he defines Boolean-valued sets, Boolean-valued recursive sets, and Boolean-valued recursively enumerable sets and discuss the basic relationships between a Boolean-valued set, its principal part, and its support. Then he generalizes many elementary concepts and results about recursive and recursively enumerable sets such as the s-m-n theorem, the recursion theorem, and the projection theorem, etc. to Boolean valued sets. By using finite and infinite injury arguments, he generalizes the Friedberg-Muchnik theorem, the theorem about nonrecursive low r.e. sets, the minimal pair theorem, and other results. Finally, he discusses the possible application of Boolean-valued logic in artificial intelligence, and gives an implementation of a parser for the four-valued Boolean logic.},
doi = {},
url = {https://www.osti.gov/biblio/6309943}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 1989},
month = {Sun Jan 01 00:00:00 EST 1989}
}

Miscellaneous:
Other availability
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