Deontic reasoning with incomplete trust (Q2904133)

This paper presents a framework of deontic logic for reasoning with situations of incomplete trust as when what an agent ought to do depends in part on the extent to which it trusts another agent to do something else, and even on the extent to which the agent trusts the other agent to trust it. The framework is a generalization of \textit{J. F. Horty's} account of the individual `ought-to-do' [Agency and deontic logic. Oxford: Oxford University Press (2001; Zbl 1119.03313)] that draws on the stit-theory of Belnap and others.NEWLINENEWLINE The language thus contains, in addition to a standard ought-to-be operator \(O\), formulas \([a_i\,\mathrm{cstit}]\phi\) that an agent \(a_i\) sees to it that \(\phi\), \(\bigodot[a_i\,\mathrm{cstit}]_n\phi\) that the agent ought to see to it that \(\phi\) with trust level \(n\), and \(\bigodot[a_i\,\mathrm{cstit}]\phi\) that the agent ought to see to it that \(\phi\), simpliciter.NEWLINENEWLINE This language is interpreted by way of utilitarian strategic models, containing a set of possible outcomes (think: worlds), a finite set of agents, a finite set of actions available to each agent, and a utility function weighing outcomes, as well as the usual valuation function from atomic propositions to sets of possible outcomes. Truth-conditions for complex formulas are defined, and numerous facts regarding ought-to-do operators established, including that they have standard properties familiar from deontic logic. This framework is illustrated with helpful examples.