Abstract
This paper studies learning inference by induction. We first consider the problem of learning logical inference rules. Given a set S of propositional formulas and their logical consequences T, the goal is to find deductive inference rules that produce T from S. We show that an induction algorithm LF1T, which learns logic programs from interpretation transitions, successfully produces deductive inference rules from input transitions. Next we consider the problem of learning non-logical inference rules. We address three case studies for learning abductive inference, frame axioms and conversational implicature by induction. The current study provides a preliminary approach to the problem of learning inference to which little attention has been paid in machine learning and ILP.
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Notes
- 1.
The result is shown for normal logic programs and is applied to their subclass of programs.
- 2.
The experimental archive is found at http://www.wakayama-u.ac.jp/~sakama/ILP2015-short/.
- 3.
An atom A occurring in b(R) is redundant if \(b(R)\setminus \{A\}\equiv _\theta b(R)\) where \(\equiv _\theta \) is equivalence under \(\theta \)-subsumption \(\le _\theta \), i.e., \(R_1\le _\theta R_2\) iff \(h(R_1\theta )=h(R_2)\) and \(b(R_1\theta )\subseteq b(R_2)\) for some substitution \(\theta \).
- 4.
Here we assume the existence of a state constraint : \(\forall x\forall y\, [hold(on(x,t))\wedge hold(on(x,y))\rightarrow y=t\,]\) asserting that if an object x is on a table t and x is on y then y is t.
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Sakama, C., Ribeiro, T., Inoue, K. (2016). Learning Inference by Induction. In: Inoue, K., Ohwada, H., Yamamoto, A. (eds) Inductive Logic Programming. ILP 2015. Lecture Notes in Computer Science(), vol 9575. Springer, Cham. https://doi.org/10.1007/978-3-319-40566-7_13
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