Formalising Deductive Coherence: An Application to Norm Evaluation

This paper is a contribution to the formalisation of Thagard’s coherence theory. The term coherence is defined as the quality or the state of cohering, especially a logical, orderly, and aesthetically consistent relationship of parts. Cognitive coherence in particular is the coherence theory based explanation of the mind which evaluates the truth of a cognition in terms of it being a member of some suitably defined body of other cognitions: a body that is consistent, coherent, and possibly endowed with other virtues, provided these are not defined in terms of truth. Thus a coherent set is interdependent such that every element in it contributes to the coherence. We take the Thagard’s proposal of a coherence set as that of maximizing satisfaction of constraints between elements and explore its use in normative multiagent systems. In particular we show how it could be used as a mechanism to introduce true autonomy in agents particularly in a normative multi agent setting. We show, how an agent can deliberate on norm evaluation while also considering other factors such as sanctions and rewards. We first provide a general coherence framework with the necessary computing tools. Later we introduce a proof-theoretic characterization of a particular type of coherence namely the deductive coherence based on Thagard’s principles, and derive a mechanism to compute coherence values between elements in a deductive coherence graph, thus proposing a fully computational model of coherence. Our use of graded logic helps us to incorporate reasoning under uncertainty which is more realistic in the context of multiagent systems. We then explore a scenario where agents deliberate about norm evaluation in a multiagent system where there is competition for a common resource. We show how a coherence maximising agent decides to violate a norm guided by its coherence.