By Luc De Raedt (auth.), Jacques Calmet, Jan Plaza (eds.)
This publication constitutes the refereed lawsuits of the foreign convention on synthetic Intelligence and Symbolic Computation, AISC'98, held in Plattsburgh, big apple, in September 1998.
The 24 revised complete papers offered have been rigorously chosen for inclusion within the ebook. The papers handle numerous points of symbolic computation and formal reasoning similar to inductive good judgment programming, context reasoning, machine algebra, facts conception and theorem proving, time period rewriting, algebraic manipulation, formal verification, constraint fixing, and information discovery.
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S. Muggleton and L. De Racdt. Inductive logic programming : Theory and methods. Journal of Logic Programming, 19,20:629-679, 1994. 21. J. Ross Quinlan. 5: Programs for Machine Learning. Morgan Kaufmann series in machine learning. Morgan Kaufmann, 1993. 22. R. Quinlan. Learning logical definitions from relations. Machine Learning, 5:239-266, 1990. 23. G. Sablon, L. De Raedt, and M. Bruynooghe. Iterative versionspaces. Artificial Intelligence, 69:393-409, 1994. 24. W. Shen, K. Ong, B. Mitbander, and C.
A/I, F IFv X A Y if and only if 3,t, F IFv X and 2M, F IFv Y (and similarly for the other Boolean connectives). 3. M , F IFv 9 if and only if M , A IFv X for every A E ~ such that FT-r (and similarly for (}). 4. All, F IFv (Vx)~ if and only if A4, F IFv, ~ for every valuation v I that is like v except that v' is some arbitrary member of ~D(F) (and similarly for ~). 5. ~)(t). 6. ~}(t) if and only if Ad, F IFv, ~ where v I is like v except that v~(x) is what t designates at F. Item 4 makes explicit the idea that quantifiers quantify over what actually exists--over the domain of the particular possible world only.
When analysing the above algorithm, the glb, lub, rags and msg operators can be straightforwardly and efficiently implemented. However, the key implementation issue is how to compute the S set for the case of frequency(Q, K, D, F), F > f. Similar questions arise for F < and the use of covers. In the data mining literature, a lot of attention has been devoted to this, resulting in algorithms such as APRIORI 2. We can find the S set for this case in two different manners, that correspond to traversing the space in two dual methods.