TY - GEN

T1 - Learning orthogonal F-Horn formulas

AU - Miyashiro, Akira

AU - Takimoto, Eiji

AU - Sakai, Yoshifumi

AU - Maruoka, Akira

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-60454-5_32

DO - 10.1007/3-540-60454-5_32

M3 - Conference contribution

AN - SCOPUS:84947931261

SN - 3540604545

SN - 9783540604549

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 110

EP - 122

BT - Algorithmic Learning Theory - 6th International Workshop, ALT 1995, Proceedings

A2 - Jantke, Klaus P.

A2 - Shinohara, Takeshi

A2 - Zeugmann, Thomas

PB - Springer Verlag

T2 - 6th International Workshop on Algorithmic Learning Theory, ALT 1995

Y2 - 18 October 1995 through 20 October 1995

ER -