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: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, ffl-semantics, possibilistic structures, and -rankings, that have been shown to be characterized by the same set of axioms, known as the KLM properties. While this was viewed as a surprise, we show here that it is almost inevitable. In the framework of plausibility measures, we can give a necessary condition for the KLM axioms to be sound, and an additional condition necessary and sufficient to ensure that the KLM axioms are complete. This additional condition is so weak that it is almost always met whenever the axioms are sound. In particular, it is easily seen to hold for all the proposals made in the literature. Categories and Subject Descriptors: F.4.1 [Mathematical Logic and Formal Languages]:

We propose a model

The notion of preference occurs across many areas, including the philosophy of action, decision theory, optimality theory, and game theory. In these settings, individual preferences between worlds or actions can be used to predict behavior by rational agents. In a more abstract sense, the notion of preference also

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

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a “virtual” manner, using uniterated revision.

In this paper we propose a semantics for dyadic deontic logic with an explicit preference ordering between worlds, representing different degrees of ideality. We argue that this ideality 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 strengthening of the antecedent, and minimizing to weakening of the consequent. Moreover, we show that in some cases ordering and minimizing have to be combined to obtain certain desirable conclusions, and that this can only be done in a so-called twophase deontic logic. In the first phase, the preference ordering is constructed, and in the second phase the ordering is used for minimization. If these two phases are not distinguished, then counterintuitive conclusions follow. 1 Introduction Preference-based deontic logics are deontic logics of which the se...

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...

Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the context of studying counterfactuals, but he assumed a total preference order on worlds. Complications arise when examining partial orders that are not present for total orders. There are subtleties involving the exact approach to lifting the order on worlds to an order on sets of worlds. In addition, the axiomatization of the logic of relative likelihood in the case of partial orders gives insight into the connection between relative likelihood and default reasoning. 1. Introduction A preference order on a set W of worlds is a reflexive, transitive relation on W . Various readings have been given to the relation in the literature; u v has been interpreted as "u at least as preferred or desirable as v" (Kraus, Lehmann, & Magidor, 1990; Doyle, Shoham, & ...

ABSTRACT. We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations.