The Logic of Knowledge Based Obligation

Abstract

Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty.