A Logic of Objective and Subjective Oughts

A Deontic Stit Logic Based on Beliefs and Expected Utility

“…In principle, if an agent does not know how to fulfill an obligation, it should be excused for not having done so. The mentioned [21], [13], and [1] all extend Horty's stit theory of act utilitarian ought-to-do with knowledge operators and explore the relation between uncertainty and obligation. In turn, here we will be extending the logics of [13] and [1] with modalities for belief.…”

“…The mentioned [21], [13], and [1] all extend Horty's stit theory of act utilitarian ought-to-do with knowledge operators and explore the relation between uncertainty and obligation. In turn, here we will be extending the logics of [13] and [1] with modalities for belief. 1 Definition 1 (Language) Given a finite set Ags of agent names, a countable set of propositions P such that p ∈ P and α ∈ Ags, the grammar for the formal language L KO is given by:…”

“…In turn, here we will be extending the logics of [13] and [1] with modalities for belief. 1 Definition 1 (Language) Given a finite set Ags of agent names, a countable set of propositions P such that p ∈ P and α ∈ Ags, the grammar for the formal language L KO is given by:…”

“…Horty's idea of optimality is undeniably inspired by solution concepts from game theory, particularly by dominance of strategies. Following this idea, the recent works [21] and [1] introduce epistemic (resp. subjective) ought-to-do's to account for the relation between knowledge and obligation.…”

“…Thus, we propose that at a given index of evaluation an agent had the doxastic obligation to see to it that ϕ if ϕ is a consequence of all the actions that maximized expected (deontic) utility at such index, where this utility is identified with the deontic value of the index just as in [23]. The basic aspects of the logic that we develop here, then, can be summarized in this way: we extend the basic stit language with (a) epistemic and doxastic operators, (b) objective and subjective ought-to-do operators (whose logic was developed in [1]), and (c) a doxastic ought-to-do operator, meant to build up formulas to characterize the effects of those actions that agents' belief-systems render as optimal-i.e., the effects of rational best responses (see [8]).…”