Brave induction: a logical framework for learning from incomplete information

This paper introduces a novel logical framework for concept-learning called brave induction. Brave induction uses brave inference for induction and is useful for learning from incomplete information. Brave induction is weaker than explanatory induction which is normally used in inductive logic programming, and is stronger than learning from satisfiability, a general setting of concept-learning in clausal logic. We first investigate formal properties of brave induction, then develop an algorithm for computing hypotheses in full clausal theories. Next we extend the framework to induction in nonmonotonic logic programs. We analyze computational complexity of decision problems for induction on propositional theories. Further, we provide examples of problem solving by brave induction in systems biology, requirement engineering, and multiagent negotiation.     

Logic programming in tensor spaces

Annals of Mathematics and Artificial Intelligence - This paper introduces a novel approach to computing logic programming semantics. First, a propositional Herbrand base is represented in a vector...     

Learning from interpretation transition

We propose a novel framework for learning normal logic programs from transitions of interpretations. Given a set of pairs of interpretations (I,J) such that J=T _P (I), where T _P is the immediate consequence operator, we infer the program P. The learning framework can be repeatedly applied for identifying Boolean networks from basins of attraction. Two algorithms have been implemented for this learning task, and are compared using examples from the biological literature. We also show how to incorporate background knowledge and inductive biases, then apply the framework to learning transition rules of cellular automata.     

Computing extended abduction through transaction programs

To explain observations from nonmonotonic background theories, one often needs removal of some hypotheses as well as addition of other hypotheses. Moreover, some observations should not be explained, while some are to be explained. In order to formalize these situations, extended abduction was introduced by Inoue and Sakama (1995) to generalize traditional abduction in the sense that it can compute negative explanations by removing hypotheses and anti‐explanations to unexplain negative observations. In this paper, we propose a computational mechanism for extended abduction. When a background theory is written in a normal logic program, we introduce its transaction program for computing extended abduction. A transaction program is a set of non‐deterministic production rules that declaratively specify addition and deletion of abductive hypotheses. Abductive explanations are then computed by the fixpoint of a transaction program using a bottom‐up model generation procedure. The correctness of the proposed procedure is shown for the class of acyclic covered abductive logic programs. In the context of deductive databases, a transaction program provides a declarative specification of database update. This revised version was published online in June 2006 with corrections to the Cover Date.