Updates and Subjunctive Queries

Abstract

A subjunctive query of the form φ > ψ, means "if φ were true in the knowledgebase, would ψ also necessarily be true?" We propose the following semantics for subjunctive queries: φ > ψ, will hold in the current knowledgebase T if ψ holds in the result of updating T with φ. This is known as the Ramsey test in philosophy. We adapt the model checking approach of Halpern and Vardi: A knowledgebase is a finite set of finite sets of positive facts interpreted in a closed world setting. We then use Winslett′s possible models approach to give semantics to knowledgebase updates, and we introduce a query language which is essentially propositional logic, augmented with a subjunctive conditional that has an intensional interpretation in our model. We show that query answering and update can be performed in time polynomial in the size of the knowledgebase. However, query equivalence is shown to be complete in polynomial space, and this is also the complexity of query answering as a function of query size. We give a sound axiomatization of query equivalence and show that the update operator satisfies the postulates for updates adapted by Katsuno and Mendelzon from the Alchourrón-Gärdenfors-Makinson belief revision postulates.