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

Modeling of Phenomena and Dynamic Logic of Phenomena

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, problem or theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models

Sketched Answer Set Programming

Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models is not trivial. We propose a novel method, called Sketched Answer Set Programming (SkASP), aiming at supporting the user in resolving this issue. The user writes an ASP program while marking uncertain parts open with question marks. In addition, the user provides a number of positive and negative examples of the desired program behaviour. The sketched model is rewritten into another ASP program, which is solved by traditional methods. As a result, the user obtains a functional and reusable ASP program modelling her problem. We evaluate our approach on 21 well known puzzles and combinatorial problems inspired by Karp's 21 NP-complete problems and demonstrate a use-case for a database application based on ASP.Comment: 15 pages, 11 figures; to appear in ICTAI 201

A Multimedia Interactive Environment Using Program Archetypes: Divide-and-Conquer

As networks and distributed systems that can exploit parallel computing become more widespread, the need for ways to teach parallel programming effectively grows as well. Even though many colleges and universities provide courses on parallel programming [1], most of those courses are reserved for graduate students and advanced undergraduates. There is a demand for ways to teach fundamental parallel programming concepts to people with just a working knowledge of programming. By using the idea of a software archetype, and providing a learning environment that teaches both concept and coding, we hope to satisfy this need. This paper presents an overview of the multimedia approach we took in teaching parallel programming and offers Divide-and-Conquer as an example of its use

Complexity of Equivalence and Learning for Multiplicity Tree Automata

We consider the complexity of equivalence and learning for multiplicity tree automata, i.e., weighted tree automata over a field. We first show that the equivalence problem is logspace equivalent to polynomial identity testing, the complexity of which is a longstanding open problem. Secondly, we derive lower bounds on the number of queries needed to learn multiplicity tree automata in Angluin's exact learning model, over both arbitrary and fixed fields. Habrard and Oncina (2006) give an exact learning algorithm for multiplicity tree automata, in which the number of queries is proportional to the size of the target automaton and the size of a largest counterexample, represented as a tree, that is returned by the Teacher. However, the smallest tree-counterexample may be exponential in the size of the target automaton. Thus the above algorithm does not run in time polynomial in the size of the target automaton, and has query complexity exponential in the lower bound. Assuming a Teacher that returns minimal DAG representations of counterexamples, we give a new exact learning algorithm whose query complexity is quadratic in the target automaton size, almost matching the lower bound, and improving the best previously-known algorithm by an exponential factor