Non-monotonic Reasoning with Various Kinds of Preferences in the Relational Data Model Framework

Abstract. The paper gives an overview of recent advances in the field of logic of preference and discusses their appli-cability in the frame of the relational data model. Namely, non-monotonic reasoning mechanisms with various kinds of preferences are reviewed in detail, and a way of suit-ing them to practical database applications is presented. These mechanisms enable to reason simultaneously about sixteen strict and non-strict kinds of preferences, includ-ing ceteris paribus preferences. To make the mechanisms useful for practical applications, the assumption of prefer-ence specification consistency has to be loosened. This is achieved in two steps: firstly, all the preference specifica-tions are generalized to permit uncertainty, and secondly, not a total pre-order on worlds but a partial pre-order on worlds is used in the semantics, which enables to indicate some kind of conflict among worlds by their incomparabil-ity. Most importantly, the semantics of set of preferences is related to that of a disjunctive logic program.