The complexity and generality of learning answer set programs

Abstract

Traditionally most of the work in the field of Inductive Logic Programming (ILP) has addressed the problem of learning Prolog programs. On the other hand, Answer Set Programming is increasingly being used as a powerful language for knowledge representation and reasoning, and is also gaining increasing attention in industry. Consequently, the research activity in ILP has widened to the area of Answer Set Programming, witnessing the proposal of several new learning frameworks that have extended ILP to learning answer set programs. In this paper, we investigate the theoretical properties of these existing frameworks for learning programs under the answer set semantics. Specifically, we present a detailed analysis of the computational complexity of each of these frameworks with respect to the two decision problems of deciding whether a hypothesis is a solution of a learning task and deciding whether a learning task has any solutions. We introduce a new notion of generality of a learning framework, which enables us to define a framework to be more general than another in terms of being able to distinguish one ASP hypothesis solution from a set of incorrect ASP programs. Based on this notion, we formally prove a generality relation over the set of existing frameworks for learning programs under answer set semantics. In particular, we show that our recently proposed framework, Context-dependent Learning from Ordered Answer Sets, is more general than brave induction, induction of stable models, and cautious induction, and maintains the same complexity as cautious induction, which has the highest complexity of these frameworks.

Representing and Learning Grammars in Answer Set Programming

“…A key observation to make is that the complexities for BV and BTS under propositional ASP are identical to the complexities for verification and satisfiability of ILP context LAS tasks (Law, Russo, and Broda 2018). These equivalences provided a strong hint that we could solve any ASG learning task by encoding it as an ILP context LAS task, and use the existing ILASP (Law, Russo, and Broda 2015a) system to solve the ASG learning task.…”

Inductive general game playing

“…By contrast, many ASP solvers disallow explicit lists, such as the popular Clingo system [26], and thus a direct comparison is difficult. Likewise, ASP-based systems can be used to learn non-deterministic specifications represented through choice rules and preferences modeled as weak constraints [48], which is not necessarily the case for Prolog-based systems. In addition, because many of the systems have learning parameters, it is often possible to show that there exist some parameter settings for which system X can perform better than Algorithm Y on a particular dataset.…”

Integrating Non-monotonic Logical Reasoning and Inductive Learning With Deep Learning for Explainable Visual Question Answering

“…Non-monotonic logic formalisms have been developed to address these limitations, e.g., Answer Set Prolog (ASP) has been used in cognitive robotics (Erdem and Patoglu, 2012 ) and other applications (Erdem et al, 2016 ). ASP has been combined with inductive learning to monotonically learn causal laws (Otero, 2003 ), and methods have been developed to learn and revise domain knowledge represented as ASP programs (Balduccini, 2007 ; Law et al, 2018 ). Cognitive architectures have also been developed to extract information from perceptual inputs to revise domain knowledge represented in first-order logic (Laird, 2012 ), and to combine logic and probabilistic representations to support reasoning and learning in robotics (Zhang et al, 2015 ; Sarathy and Scheutz, 2018 ).…”