Inductive Learning for Possibilistic Logic Programs Under Stable Models
Hongbo Hu, Yisong Wang, Yi Huang, Kewen Wang
TL;DR
This work introduces a formal framework for inductive reasoning with possibilistic logic programs under stable-model semantics, defining induction tasks and proving properties about existence and minimality of induction solutions. It presents two algorithms, ilpsm and ilpsmmin, to compute solutions and identify minimal ones, and provides a constructive approach to build hypothesis programs from positive/negative examples using PPE and PNE constructs. An implemented prototype, ilsmmin, demonstrates that learning ordinary NLPs from stable models can outperform ILASP in both speed and memory on randomly generated tasks, validating the practical viability of the approach. The paper also explores variants, reductions to partial-stable-model and complete-stable-model scenarios, and situates the work within related literature on ASP induction and possibilistic learning, signaling promising avenues for extending the framework and improving scalability.
Abstract
Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive reasoning has not been investigated yet. This paper presents an approach to extracting poss-programs from a background program and examples (parts of intended possibilistic stable models). To this end, the notion of induction tasks is first formally defined, its properties are investigated and two algorithms ilpsm and ilpsmmin for computing induction solutions are presented. An implementation of ilpsmmin is also provided and experimental results show that when inputs are ordinary logic programs, the prototype outperforms a major inductive learning system for normal logic programs from stable models on the datasets that are randomly generated.