Instead, our learning procedure is a general axiom exploshown to be very useful to reduce the search space explored through the addition of new axioms. This is done by evolved7 There are 19 dieren t induction rules that can be classied as most work in learning DLs does (see [5, 8] for example). ability nor Least Common Subsumer (LCS) computation [4], by a learning procedure. tion theory measures mentioned above. An initial theory is T0 YAYA learning procedure is not involved with PAC learnmainly into generalization, specialization, and general exploaxioms from axioms already existing in the theory.
Although there is no space to explain the whole 19 rules, we can sketch some of them to see how they work: designed to work with taxonomic knowledge. ration procedure that is heuristically guided by the informathe application of a set of induction rules that produce new ration In addition, some of these rules are specially rules8. iom 2 can be eÆciently computed [2]. These measures have maximize the amount of information provided by T with reterpretation can be directly represented as a set of boolean number of boolean variables necessary to represent I when whether 2 P The entropy of I is dened as the (d1; d2) I). are individual entities. ments 2 I we have another boolean variable (stating d1; d2 respect to I can be intuitively dened as the dierence beimum number of boolean variables necessary to represent I is intractable. Instead, some measures that provide an idea d 62 and for every role name P and every pair of ele- AI); I when no additional knowledge is available, and the the mintween the necessary number of boolean variables to represent Shannon information theory notions to DL domain. An inno additional knowledge is available. This is, in fact, a direct if T [ f g provides more information than T . spect to a training set. An axiom will be interesting for T we have a boolean variable (stating whether d 2 or AI used in the learning process are complete This diers models5. variables: for every concept name A and every element d 2 I The amount of information provided by a TBox T with Computing the amount of information provided by a TBox theory/TBox T from a set of models of T . So, the examples of the information added by an axiom 1 given another axfrom usual machine learning approaches in which examples when T is Then, the learning procedure has to available6. interpretation of Shannon information theory notions.
In order to dene what theory learning is, we rst adapt Theory learning is formalized as the process of determining a