L. De Raedt and L. Dehaspe. Learning from satisfiability. In Proceedings of the Ninth Dutch Conference on Artificial Intelligence (NAIC'97), pages 303-312, 1997. Home/Search Document Details and Download
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From Propositional to First Order Logic in Machine Learning and.. - Van Laer (2002) (1 citation) (Correct)
....2.8 Consider Example 2.7: pAq p, pAq q, p pYq, qpYqandpAqpYq. On the other hand, p V: q and q V: p, sopandq are incomparable. The generality relation is reflexive and transitive on the hypothesis space of propositional formulas and is called a quasi order . As discussed in [Nienhuys Cheng and De Wolf, 1997], every quasi order can be transformed into a partial order (which is anti symmetric) on the set of equivalence classes. Two formulas P and Q are equivalent if P Q and Q P. P is strictly more general than Q (P Q) if P Q and Q P. If we restrict the hypothesis space to pure conjunctive ....
....exists a Pi such thatPi qj, i e ,Pi=qj iff Pl, Pn D ql, qm iff DG D DS. This means that the relation on queries and clauses coincides with the subset (C ) relation. As the subset relation is a lattice 9, the generality relation 5We use the definition as given in [Nienhuys Cheng and De Wolf, 1997]. In other text books, a quasi order is defined as an irrefiexive and transitive relation. ewe slightly abuse the notation by considering queries (and clauses) as set of literals. For instance, P1 k . k Pn C ql A . A qm means i1, Pn C ql, qm Because an inconsistent ....
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L. De Raedt and L. Dehaspe. Learning from satisfiability. In Proceedings of the Ninth Dutch Conference on Artificial Intelligence (NAIC'97), pages 303-312, 1997.
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