We present a logic for representing and reasoning with qualitative statements of preference and normality and describe how these may interact in decision making under uncertainty. Our aim is to develop a logical calculus that employs the basic elements of classical decision theory, namely probabilities, utilities and actions, but exploits qualitative information about these elements directly for the derivation of goals. Preferences and judgements of normality are captured in a modal/conditional logic, and a simple model of action is incorporated. Without quantitative information, decision criteria other than maximum expected utility are pursued. We describe how techniques for conditional default reasoning can be used to complete information about both preferences and normality judgements, and we show how maximin and maximax strategies can be expressed in our logic.

this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based

. Deontic logic is characterized by the distinction between the actual and the ideal. In this article we discuss the situation where the actual deviates from the ideal, where obligations are violated. Nonmonotonic logics can be very helpful for the formalization of deontic reasoning, in particular to infer moral cues. It has been argued that the problems related to violated obligations, e.g. the Chisholm `Paradox', are just instances of problems of defeasible reasoning. We disagree with this claim since we will argue that there is a fundamental difference between a violated and a defeated obligation. In this article, we analyzeviolated obligations in Horty's nonmonotonic framework. We extend his definition of deontic consequence in such a way that it covers violated obligations and we give a solution to deal with conflicts between violability and defeasibility. 1 Introduction Deontic logic is characterized by the distinction between what is the case and what should be the case, betwee...

In this paper we give a general analysis of dyadic deontic logics that were introduced in the early seventies to formalize deontic reasoning about subideal behavior. Recently it was observed that they are closely related to nonmonotonic logics, theories of diagnosis and decision theories. In particular, we argue that two types of defeasibility must be distinguished in a defeasible deontic logic: overridden defeasibility that formalizes cancelling of an obligation by other conditional obligations and factual defeasibility that formalizes overshadowing of an obligation by a violating fact. We also show that this distinction is essential for an adequate analysis of notorious `paradoxes' of deontic logic such as the Chisholm and Forrester `Paradoxes'. 1 Introduction In recent years defeasible deontic logic has become increasingly popular as a tool to model legal reasoning in expert systems [ McCarty, 1992; Meyer and Wieringa, 1994; Jones and Sergot, 1994 ] , because defeasible reasoning i...

. In this paper we introduce Prohairetic Deontic Logic (PDL), a preference-based dyadic deontic logic. An obligation `ff should be (done) if fi is (done)' is true if (1) no :fffi state is as preferable as an fffi state and (2) the preferred fi states are ff states. We show that the different elements of this mixed representation solve different problems of deontic logic. The first part of the definition is used to formalize contrary-to-duty reasoning, that for example occurs in Chisholm's and Forrester's notorious paradoxes. The second part is used to make dilemmas inconsistent. PDL shares the intuitive semantics of preference-based deontic logics without introducing additional semantic machinery such as bi-ordering semantics or ceteris paribus preferences. 1 Introduction Deontic logic is a modal logic, in which absolute and conditional obligations are represented by the modal formulas Off and O(ffjfi), where the latter is read as `ff ought to be (done) if fi is (done).' It can be use...

In this paper, we will show how dynamic logic can be used to reason about so-called sub-ideal states, i.e. states in which some deontic constraint is violated. For this purpose we have to extend the definition of the deontic operators. Instead of only giving a postcondition with respect to violations for each action we will consider the complete state transition. In order to distinguish between different states of violation we will also index the violation predicates. The introduction of these two extensions makes it possible to reason in a flexible and natural way about sub-ideal states.

. In this paper we introduce the two-phase deontic logic 2dl. The preference-based semantics of 2dl is based on an explicit preference ordering between worlds, representing different degrees of ideality. The preference ordering can be used in two ways to evaluate formulas, which we call ordering and minimizing. Ordering uses all preference relations between relevant worlds, whereas minimizing uses the most preferred worlds only. We show that ordering corresponds to the inference pattern strengthening of the antecedent and the conjunction rule for the consequent, and minimizing to the inference pattern weakening of the consequent and the disjunction rule for the antecedent. Moreover, we show that in several problems like the notorious contrary-to-duty paradoxes ordering and minimizing have to be combined to obtain the desirable conclusions, and that in a dyadic deontic logic this can only be done in a so-called two-phase deontic logic. In the first phase the preference ordering is const...

In this paper we analyze the Chisholm paradox. We survey the paradox in Standard Deontic Logic, preference-based deontic logic, defeasible deontic logic and temporal deontic logic. We propose to combine preferential and temporal notions to analyze it. 1 Introduction The Chisholm set consists of the following four sentences. 1. `ff ought to be (done),' 2. `if ff is (done), then fi ought to be (done),' 3. `if ff is not (done), then fi ought not to be (done),' and 4. `ff is not (done).' The formalization of these sentences in Standard Deontic Logic is either inconsistent or the sentences are logically dependent. The Chisholm set is therefore called a paradox. Temporal deontic logic can consistently formalize the set 1'. `ff ought to be (done),' 2'. `if ff has been (done), then fi ought to be (done),' 3'. `if ff has not been (done), then fi ought not to be (done),' and 4'. `ff has not been (done).' For most ff and fi the first set can be transformed to the second one without changing ...

. Deontic logic is characterized by the distinction between the actual and the ideal. In this article we discuss the situation where the actual deviates from the ideal, where obligations are violated. Nonmonotonic logics can be very helpful for the formalization of deontic reasoning, in particular to infer moral cues. It has been argued that the problems related to violated obligations, e.g. the Chisholm `Paradox', are just instances of problems of defeasible reasoning. We disagree with this claim since wewill argue that there is a fundamental difference between a violated and a defeated obligation. In this article, we analyzeviolated obligations in Horty's nonmonotonic framework. We extend his definition of deontic consequence in such a way that it covers violated obligations and we give a solution to deal with conflicts between violability and defeasibility. 1 Introduction Deontic logic is characterized by the distinction between what is the case and what should be the case, betw...

In this paper we give a general analysis of dyadic deontic logics that were introduced in the early seventies to formalize deontic reasoning about subideal behavior. Recently it was observed that they are closely related to non-monotonic logics, theories of diagnosis and decision theories. In particular, we argue that twotypes of defeasibilitymust be distinguished in a defeasible deontic logic: overridden defeasibility that formalizes cancelling of an obligation by other conditional obligations and factual defeasibility that formalizes overshadowing of an obligation by a violation. We also show that this distinction is essential for an adequate analysis of notorious `paradoxes' of deontic logic such as the Chisholm and Forrester `Paradoxes'. Keywords: knowledge representation, defeasible deontic logic, non-monotonic logic, legal reasoning 1 Introduction In recentyears defeasible deontic logic has become increasingly popular as a tool to model legal reasoning in expert syste...