2 research outputs found
The complexity and generality of learning answer set programs
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
Inductive learning of answer set programs
The goal of Inductive Logic Programming (ILP) is to find a hypothesis that
explains a set of examples in the context of some pre-existing background
knowledge. Until recently, most research on ILP targeted learning definite
logic programs. This thesis constitutes the first comprehensive work on
learning answer set programs, introducing new learning frameworks, theoretical
results on the complexity and generality of these frameworks, algorithms for
learning ASP programs, and an extensive evaluation of these algorithms.
Although there is previous work on learning ASP programs, existing learning
frameworks are either brave -- where examples should be explained by at
least one answer set -- or cautious where examples should be explained
by all answer sets. There are cases where brave induction is too weak and
cautious induction is too strong. Our proposed frameworks combine brave and
cautious learning and can learn ASP programs containing choice rules and
constraints. Many applications of ASP use weak constraints to express a
preference ordering over the answer sets of a program. Learning weak
constraints corresponds to preference learning, which we achieve by
introducing ordering examples. We then explore the generality of our
frameworks, investigating what it means for a framework to be general enough to
distinguish one hypothesis from another. We show that our frameworks are more
general than both brave and cautious induction.
We also present a new family of algorithms, called ILASP (Inductive Learning of
Answer Set Programs), which we prove to be sound and complete. This work
concerns learning from both non-noisy and noisy examples. In the latter case,
ILASP returns a hypothesis that maximises the coverage of examples while
minimising the length of the hypothesis. In our evaluation, we show that ILASP
scales to tasks with large numbers of examples finding accurate hypotheses
even in the presence of high proportions of noisy examples.Open Acces