Learning orthogonal F-Horn formulas

Akira Miyashiro, Eiji Takimoto, Yoshifumi Sakai, Akira Maruoka

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the PAC-learning, or the query learning model, it has been an important open problem to decide whether the class of DNF and CNF formulas is learnable. Recently, it was pointed out that the problem of PAC-learning for these classes with membership queries can be reduced to that of query learning for the class of A:-quasi Horn formulas with membership and equivalence queries. A k-quasi Horn formula is a CNF formula with each clause containing at most k unnegated literals. In this paper, notions of .F-Horn formulas and l-F-Horn formulas, which are extensions of k-quasi formulas, are introduced, and it is shown that the problem of PAC-learning for DNF and CNF formulas with membership queries can be reduced to that of query learning for l-F-Horn formulas with membership and equivalence queries for an appropriate choice of P. It is shown that under some condi­tion, the class of orthogonal F-Horn formulas is learnable with membership, equivalence and subset queries. Moreover, it is shown that under some condi­tion the class of orthogonal l-F-Horn formulas is learnable with membership and equivalence queries.

Original languageEnglish
Title of host publicationAlgorithmic Learning Theory - 6th International Workshop, ALT 1995, Proceedings
EditorsKlaus P. Jantke, Thomas Zeugmann, Takeshi Shinohara
PublisherSpringer Verlag
Pages110-122
Number of pages13
ISBN (Print)3540604545, 9783540604549
Publication statusPublished - Jan 1 1995
Externally publishedYes
Event6th International Workshop on Algorithmic Learning Theory, ALT 1995 - Fukuoka, Japan
Duration: Oct 18 1995Oct 20 1995

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume997
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Workshop on Algorithmic Learning Theory, ALT 1995
CountryJapan
CityFukuoka
Period10/18/9510/20/95

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All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Miyashiro, A., Takimoto, E., Sakai, Y., & Maruoka, A. (1995). Learning orthogonal F-Horn formulas. In K. P. Jantke, T. Zeugmann, & T. Shinohara (Eds.), Algorithmic Learning Theory - 6th International Workshop, ALT 1995, Proceedings (pp. 110-122). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 997). Springer Verlag.