![]() B |/= E+ī and H logically implies E+ i.e. B and H and E- |/= ī does not logically imply E+ i.e. B and E- |/= ī and H and E- is satisfiable i.e. the followingī and E- is satisfiable i.e. With these theĪbductive step is to find a set of clauses H, s.t. ILP systems for prediction are given a set of clauses as backgroundī, positive examples E+ and negative examples E. Most ILP systems do this by finding Fs that subsume G. The hypothesis formation problem in this setting is then to find F, Generalisation in ILP For ILP systems, the word "generalisation" has a particular Ideas from probability or information theory. Selecting the best hypothesis amongst all those that satisfy Of induction, namely justification, is concerned with Logical consequence and logical subsumption. Obtaining hypotheses from specific cases is tied in with: ILP systems form hypotheses in first-order logic. Induction = Hypothesis Formation + Justification The process of constructing some general hypothesisĪnd then providing a justification for why it should be trueĬan be viewed (controversially) as a form of "induction". In some sense, all the clauses made redun-ĭant by this clause are special cases of this clause. Universal quantification on the variables of the clause This is not surprising, when you consider the With some background knowledge B, L_l is redundantī and C is logically equivalent to B and C1ī and C |= B and C1 and B and C1 |= B and C It is straightforwards to show that L_l is redundant in C iff:Ī Note on Generalisation You can see from the previous sections that definitions like: Remember, for definite clauses, only one of ![]() are the variables in C, C1 and C1 is C with Consider (in clausal form):Ĭ : (Forall X,Y,Z.) L_1 or L_2 or. We will first look at redundant literals in a clause. Remains unaffected if the new clause is added and these oth-Įr clauses are removed). Moved (that is, the things that the program can prove A clause constructed may make other clauses thatĪre already present unnecessary. Safely (that is, the things the clause can prove remains Redundancy ILP programs typically look to remove redundancy in two ways:ġ.When constructing a clause, some literals in theĬlause may be unnecessary, and therefore can be removed
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