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 -