that A, then it's not obligatory that A. FA, meaning it is forbidden that A, can be defined (equivalently) as or . There are two main extensions of SDL that are usually considered. The first results by adding an alethic modal operator in order to express the Kantian claim that "ought implies can": where . It is generally assumed that is at least a KT operator, but most commonly it is taken to be an S5 operator. In practical situations, obligations are usually assigned in anticipation of future events, in which case alethic possibilities can be hard to judge; Therefore, obligation assignments may be performed under the assumption of different conditions on different branches of timelines in the future, and past obligation assignments may be updated due to unforeseen developments that happened along the timeline. The other main extension results by adding a "conditional obligation" operator O(A/B) read "It is obligatory that A given (or conditional on) B". Motivation for a conditional operator is given by considering the following ("Good Samaritan") case. It seems true that the starving and poor ought to be fed. But that the starving and poor are fed implies that there are starving and poor. By basic principles of SDL we can infer that there ought to be starving and poor! The argument is due to the basic K axiom of SDL together with the following principle valid in any normal modal logic: If we introduce an intensional conditional operator then we can say that the starving ought to be fed only on the condition that there are in fact starving: in symbols O(A/B). But then the following argument fails on the usual (e.g. Lewis 73) semantics for conditionals: from O(A/B) and that A implies B, infer OB. Indeed, one might define the unary operator O in terms of the binary conditional one O(A/B) as , where stands for an arbitrary tautology of the underlying logic (which, in the case of SDL, is classical). Semantics of standard deontic logic The accessibility relation between possible world is interpreted as acceptability relations: is an acceptable world (viz. ) if and only if all the obligations in are fulfilled in (viz. ). Anderson's deontic logic Alan R. Anderson (1959) shows how to define in terms of the alethic operator and a deontic constant (i.e. 0-ary modal operator) standing for some sanction (i.e. bad thing, prohibition, etc.): . Intuitively, the