Bias-Driven Revision of Logical Domain Theories

Search is one of the most important needs of problem solvers. Usually the problem solvers suffer from retracing conclusions. If a problem solver cached its inference, then it would not need to retrace conclusions that it had already derived earlier in the search. By caching the inferences, the problem solver avoid throwing away useful results and avoid wasting effort rediscovering the same things over and over. In this paper we present a belief revision system for logic programs that can work under the non-monotonic logic.

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence, 2017

In this paper we provide a general, unifying framework for probabilistic belief revision. We first introduce a probabilistic logic called p-logic that is capable of representing and reasoning with basic probabilistic information. With p-logic as the background logic, we define a revision function called p-revision that resembles partial meet revision in the AGM framework. We provide a representation theorem for p-revision which shows that it can be characterised by the set of basic AGM revision postulates. P-revision represents an "all purpose" method for revising probabilistic information that can be used for, but not limited to, the revision problems behind Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis's imaging. Importantly, p-revision subsumes all three approaches indicating that Bayesian conditionalisation, Jeffrey conditionalisation, and Lewis' imaging all obey the basic principles of AGM revision. As well our investigation sheds light on...

Proceedings of the 10th International Joint Conference on Knowledge Discovery, Knowledge Engineering and Knowledge Management, 2018

This paper aims to develop a domain-independent system for repairing faulty Datalog-like theories by combining three existing techniques: abduction, belief revision and conceptual change. Accordingly, the proposed system is named the ABC repair system. Given an observed assertion and a current theory, abduction adds axioms which represent the simplest and most likely explanation. Belief revision incorporates a new piece of information which conflicts with the input theory by deleting axioms. Conceptual change uses the reformation algorithm for blocking unwanted proofs or unblocking wanted proofs. The former two techniques change an axiom as a whole, while reformation changes the language in which the theory is written. These three techniques are complementary: abduction adds new axioms, belief revision deletes conflicting axioms, while reformation changes the language of the theory. But they have not previously been combined into one system. We are working on aligning these three techniques in the ABC repair system, which is capable of repairing logical theories with better quality than individual techniques. Datalog is used as the underlying logic of theories in this paper, but the proposed system has the potential to be adapted to theories in other logics.

The Journal of Symbolic Logic, 2001

A vast and interesting family of natural semantics for Belief Revision is defined. Suppose one is given a distance d between any two models. One may define the revision of a theory K by a formula a as the theory defined by the set of all those models of a that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.

We give a revision algorithm for monotone DNF formulas in the general revision model (additions and deletions of variables) that uses Ç´Ñ ¿ ÐÓ Òµ queries, where Ñ is the number of terms, the revision distance to the target formula, and Ò the number of variables. We also give an algorithm for revising 2-term unate DNF formulas in the same model, with a similar query bound. Lastly, we show that the earlier query bound on revising readonce formulas in the deletions-only model can be improved from Ç´ ÐÓ ¾ Òµ to Ç´ ÐÓ Òµ.

2004

Possible-world semantics are provided for Parikh's relevance-sensitive model for belief revision. Having Grove's system-of-spheres construction as a base, we consider additional constraints on measuring distance between possible worlds, and we prove that, in the presence of the AGM postulates, these constraints characterize precisely Parikh's axiom (P). These additional constraints essentially generalize a criterion of similarity that predates axiom (P) and was originally introduced in the context of Reasoning about Action. A by-product of our study is the identification of two possible readings of Parikh's axiom (P), which we call the strong and the weak versions of the axiom. An interesting feature of the strong version is that, unlike classical AGM belief revision, it makes associations between the revision policies of different theories.

Machine Learning, 2009

Theory revision systems are designed to improve the accuracy of an initial theory, producing more accurate and comprehensible theories than purely inductive methods. Such systems search for points where examples are misclassified and modify them using revision operators. This includes trying to add antecedents to clauses usually following a top-down approach, considering all the literals of the knowledge base. Such an approach leads to a huge search space which dominates the cost of the revision process. ILP Mode Directed Inverse Entailment systems restrict the search for antecedents to the literals of the bottom clause. In this work the bottom clause and mode declarations are introduced in a first-order logic theory revision system aiming to improve the efficiency of the antecedent addition operation and, consequently, also of the whole revision process. Experimental results compared to revision system FORTE show that the revision process is on average 55 times faster, generating more comprehensible theories and still not significantly decreasing the accuracies obtained by the original revision process. Moreover, the results show that when the initial theory is approximately correct, it is more efficient to revise it than learn from scratch, obtaining significantly better accuracies. They also show that using the proposed theory revision system to induce theories from scratch is faster and generates more compact theories than when the theory is induced using a traditional ILP system, obtaining competitive accuracies.