On Extending BDI Logics

Abstract

In this thesis we extend BDI logics, which are normal multimodal logics with an arbitrary set of normal modal operators, from three different perspectives. Firstly, based on some recent developments in modal logic, we examine BDI logics from a combining logic perspective and apply combination techniques like fibring/dovetailing for explaining them. The second perspective is to extend the underlying logics so as to include action constructs in an explicit way based on some recent action-related theories. The third perspective is to adopt a non-monotonic logic like defeasible logic to reason about intentions in BDI. As such, the research captured in this thesis is theoretical in nature and situated at the crossroads of various disciplines relevant to Artificial Intelligence (AI). More specifically this thesis makes the following contributions: 1. Combining BDI Logics through fibring/dovetailing: BDI systems modeling rational agents have a combined system of logics of belief, time and intention which in turn are basically combinations of well understood modal logics. The idea behind combining logics is to develop general techniques that allow to produce combinations of existing and well understood logics. To this end we adopt Gabbay's fibring/dovetailing technique to provide a general framework for the combinations of BDI logics. We show that the existing BDI framework is a dovetailed system. Further we give conditions on the fibring function to accommodate interaction axioms of the type G [superscript k,l,m,n] ([diamond][superscript k] [superscript l] [phi] [implies] [superscript m] [diamond][superscript n] [phi]) based on Catach's multimodal semantics. This is a major result when compared with other combining techniques like fusion which fails to accommodate axioms of the above type. 2. Extending the BDI framework to accommodate Composite Actions: Taking motivation from a recent work on BDI theory, we incorporate the notion of composite actions, [pi]-1; [pi]-2 (interpreted as [pi]-1 followed by [pi]-2), to the existing BDI framework. To this end we introduce two new constructs Result and Opportunity which helps in reasoning about the actual execution of such actions. We give a set of axioms that can accommodate the new constructs and analyse the set of commitment axioms as given in the original work in the background of the new framework. 3. Intention reasoning as Defeasible reasoning: We argue for a non-monotonic logic of intention in BDI as opposed to the usual normal modal logic one. Our argument is based on Bratman's policy-based intention. We show that policy-based intention has a defeasible/non-monotonic nature and hence the traditional normal modal logic approach to reason about such intentions fails. We give a formalisation of policy-based intention in the background of defeasible logic. The problem of logical omniscience which usually accompanies normal modal logics is avoided to a great extend through such an approach.