Belief Revision in Expressive Knowledge Representation Formalisms

We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence. In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences. The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach

An ABox Revision Algorithm for the Description Logic EL_bot

Abstract. Revision of knowledge bases (KBs) expressed in description logics (DLs) has gained a lot of attention lately. Existing revision algo-rithms can be divided into two groups: model-based approaches (MBAs) and formula-based approaches (FBAs). MBAs are fine-grained and in-dependent of the syntactical forms of KBs; however, they only work for some restricted forms of the DL-Lite family. FBAs can deal with more expressive DLs such as SHOIN, but they are syntax-dependent and not fine-grained. In this paper, we present a new method for instance-level revision of KBs. In our algorithm, a non-redundant depth-bounded model is firstly constructed for the KB to be revised; then a revision process based on justifications is carried out on this model by treating a model as a set of assertions; finally the resulting model is mapped back to a KB which will be returned by the algorithm. Our algorithm is syntax-independent and fine-grained, and works for the DL EL⊥.