A reduction of doxastic logic to action logic (Q1841011)

The aim of the present paper is to suggest a reduction of doxastic logic, the logic of belief, to the logic of concrete actions. The development of the proposed reduction is mainly conceptual and is based on a variant of doxastic voluntarism. The semantics would satisfy the following constraint: \((*)\) `\(\alpha\) believes that \(A\)' implies that at an earlier moment, \(\alpha\) voluntarily acquired the belief that \(A\). For this reduction to make sense, the semantic representation of ascriptions of voluntary belief acquisition and belief abandonment is given in terms of the `seeing-to-it-that' (stit) theory of agency (developed by Belnap, Perloff, and Xu in the nineties). Agentive sentences are represented using the deliberative-stit (d-stit) operator of von Kutschera (1986) and Horty (1989). The striking features of the resulting doxastic logic are derived from the agentive conception of belief acquisition and belief abandonment, together with the definition of belief operators; (1) failure of closure of belief under logical consequence, and (2) failure of closure of group belief under membership.