TY - JOUR
T1 - Induction by enumeration
AU - Martin, Eric
AU - Osherson, Daniel
N1 - Funding Information:
1We offer warm thanks to two generous referees for their constructive remarks on an earlier draft, particularly, for spotting an error in the original proofs of Propositions 28 and 72. The work was supported by the Australian Research Council Grant A49803051.
PY - 2001/11/25
Y1 - 2001/11/25
N2 - Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i.e., the one pioneered by E. M. Gold (1967, Inform. and Control 10, 447-474)). The concept is less easily interpreted within the first-order paradigm discussed by K. T. Kelly (1996, "The Logic of Reliable Inquiry," Oxford Univ. Press, New York) and E. Martin and D. Osherson (1998, "Elements of Scientific Inquiry," MIT Press, Cambridge, MA), in which the scientist's data amount to the basic diagram of a structure. We formulate two kinds of enumerative induction that are appropriate to the first-order paradigm and analyze their potential for discovery. Among other results, it is shown that one form of enumerative induction achieves maximum inductive competence.
AB - Induction by enumeration has a clear interpretation within the numerical paradigm of inductive discovery (i.e., the one pioneered by E. M. Gold (1967, Inform. and Control 10, 447-474)). The concept is less easily interpreted within the first-order paradigm discussed by K. T. Kelly (1996, "The Logic of Reliable Inquiry," Oxford Univ. Press, New York) and E. Martin and D. Osherson (1998, "Elements of Scientific Inquiry," MIT Press, Cambridge, MA), in which the scientist's data amount to the basic diagram of a structure. We formulate two kinds of enumerative induction that are appropriate to the first-order paradigm and analyze their potential for discovery. Among other results, it is shown that one form of enumerative induction achieves maximum inductive competence.
UR - http://www.scopus.com/inward/record.url?scp=0035951019&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035951019&partnerID=8YFLogxK
U2 - 10.1006/inco.2001.2910
DO - 10.1006/inco.2001.2910
M3 - Article
AN - SCOPUS:0035951019
VL - 171
SP - 50
EP - 68
JO - Information and Computation
JF - Information and Computation
SN - 0890-5401
IS - 1
ER -