Automating the repair of faulty logical theories

This thesis 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 (ABC). Given an observed assertion and a current theory, abduction adds axioms, or deletes preconditions, which explain that observation by making the corresponding assertion derivable from the expanded theory. Belief revision incorporates a new piece of information which conflicts with the input theory by deleting old 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. But they have not previously been combined into one system. We are working on aligning these three techniques in ABC, which is capable of repairing logical theories with better result than each individual technique alone. Datalog is used as the underlying logic of theories in this thesis, but the proposed system has the potential to be adapted to theories in other logics

Signature Entrenchment and Conceptual Changes in Automated Theory Repair

Human beliefs change, but so do the concepts that underpin them. The recent Abduction, Belief Revision and Conceptual Change (ABC) repair system combines several methods from automated theory repair to expand, contract, or reform logical structures representing conceptual knowledge in artificial agents. In this paper we focus on conceptual change: repair not only of the membership of logical concepts, such as what animals can fly, but also concepts themselves, such that birds may be divided into flightless and flying birds, by changing the signature of the logical theory used to represent them. We offer a method for automatically evaluating entrenchment in the signature of a Datalog theory, in order to constrain automated theory repair to succinct and intuitive outcomes. Formally, signature entrenchment measures the inferential contributions of every logical language element used to express conceptual knowledge, i.e., predicates and the arguments, ranking possible repairs to retain valuable logical concepts and reject redundant or implausible alternatives. This quantitative measurement of signature entrenchment offers a guide to the plausibility of conceptual changes, which we aim to contrast with human judgements of concept entrenchment in future work.Comment: Presented at The Ninth Advances in Cognitive Systems (ACS) Conference 2021 (arXiv:2201.06134