A sense-based, process model of belief

Abstract

A process-oriented model of belief is presented which permits the representation of nested propositional attitudes within first-order logic. The model (NIM, for ‘nested intensional model’) is axiomatized, sense-based (via intensions), and sanctions inferences involving nested epistemic attitudes, with different agents and different times. Because NIM is grounded upon senses, it provides a framework in which agents may reason about the beliefs of another agent while remaining neutral with respect to the syntactic forms used to express the latter agent's beliefs. Moreover, NIM provides agents with a conceptual map, interrelating the concepts of ‘knowledge’, ‘belief’, ‘truth’, and a number of cognate concepts, such as ‘infers’, ‘retracts’, and ‘questions’. The broad scope of NIM arises in part from the fact that its axioms are represented in a novel extension of first-order logic, ℐ-FOL (presented herein). ℐ-FOL simultaneously permits the representation of truth ascriptions, implicit self-reference, and arbitrarily embedded sentences within a first-order setting. Through the combined use of principles derived from Frege, Montague, and Kripke, together with context-sensitive semantic conventions, ℐ-FOL captures the logic of truth inferences, while avoiding the inconsistencies exhibited by Tarski. Applications of ℐ-FOL and NIM to interagent reasoning are described and the soundness and completeness of ℐ-FOL are established herein.