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The Temporal Analysis of Chisholm's Paradox

AAAI Conferences

Box 1738 3000 DR Rotterdam, the Netherlands YTANQFAC.FBK.EUR..NL Abstract Deontic logic, the logic of obligations and permissions, is plagued by several paradoxes that have to be understood before deontic logic can be used as a knowledge representation language. In this paper we extend the temporal analysis of Chishohn's paradox using a deontic logic that combines temporal and preferential notions. Introduction Deontic logic is a modal logic in which Op is read as'p ought to be (done).' Deontic logic has traditionally been used by philosophers to analyze the structure of the normative use of language. In the eighties deontic logic had a revival, when it was discovered by computer scientists that this logic can be used for the formal specification and validation of a wide variety of topics in computer science (for an overview and further references see (Wieringa & Meyer 1993)). The advantage is that norms can be violated without creating an inconsistency in the formal specification, in contrast to violations of hard constraints. Another application is the use of deontic logic to represent legal reasoning in legal expert systems in artificial intelligence. Legal expert systems have to be able to reason about legal rules and documents such as for example a trade contract.


An Update Semantics for Defeasible Obligations

arXiv.org Artificial Intelligence

The deontic logic DUS is a Deontic Update Semantics for prescriptive obligations based on the update semantics of Veltman. In DUS the definition of logical validity of obligations is not based on static truth values but on dynamic action transitions. In this paper prescriptive defeasible obligations are formalized in update semantics and the diagnostic problem of defeasible deontic logic is discussed. Assume a defeasible obligation `normally A ought to be (done)' together withthe fact `A is not (done).' Is this an exception of the normality claim, or is it a violation of the obligation? In this paper we formalize the heuristic principle that it is a violation, unless there is a more specific overriding obligation. The underlying motivation from legal reasoning is that criminals should have as little opportunities as possible to excuse themselves by claiming that their behavior was exceptional rather than criminal.


Two Kinds of Conflicts Between Desires (and how to resolve them)

AAAI Conferences

Though sophisticated enough to handle many aspects of preferences (such as specificity, priority, or context-dependence), these approaches fail to represent conflicts in a suitable way. In this paper we start with conflicts in Boutilier's logic of qualitative decision, and our main claim is that the various types of conflicts can be clustered in two groups, respectively based on what we call utopian worlds and hidden uncertainty. We also sketch how Boutilier's logic can be relaxed to represent these two classes in a consistent way. M'" Introduction: what is a conflict? OtlVatlon Autonomous agents reason frequently about preferences such as desires and goals.


Modal Logics for Qualitative Possibility and Beliefs

arXiv.org Artificial Intelligence

Possibilistic logic has been proposed as a numerical formalism for reasoning with uncertainty. There has been interest in developing qualitative accounts of possibility, as well as an explanation of the relationship between possibility and modal logics. We present two modal logics that can be used to represent and reason with qualitative statements of possibility and necessity. Within this modal framework, we are able to identify interesting relationships between possibilistic logic, beliefs and conditionals. In particular, the most natural conditional definable via possibilistic means for default reasoning is identical to Pearl's conditional for e-semantics.


The Probability of a Possibility: Adding Uncertainty to Default Rules

arXiv.org Artificial Intelligence

We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A were believed, then B would be believed to degree p." This method of revision extends conditionalization by allowing meaningful revision by sentences whose probability is zero. This is achieved through the use of counterfactual probabilities. Thus, our system accounts for the best properties of qualitative methods of update (in particular, the AGM theory of revision) and probabilistic methods. We also show how our system can be viewed as a unification of probability theory and possibility theory, highlighting their orthogonality and providing a means for expressing the probability of a possibility. We also demonstrate the connection to Lewis's method of imaging.