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28
Toward a Logic for Qualitative Decision Theory
 In Proceedings of the KR'94
, 1992
"... 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 proba ..."
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Cited by 207 (4 self)
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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.
On the Logic of Iterated Belief Revision
 Artificial intelligence
, 1996
"... We show in this paper that the AGM postulates are too week to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to ..."
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Cited by 180 (2 self)
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We show in this paper that the AGM postulates are too week to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a modelbased representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. Keywords: Iterated revision, AGM postulates, conditional beliefs, probabilistic conditioning, epistemic states, ...
Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study  Part 1: The flat case
"... This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A socalled argued consequence relation, taking into account the existence of consistent arguments in favour of a conclusion and the absence of consistent arguments in favour of its contrary, is partic ..."
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Cited by 76 (12 self)
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This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A socalled argued consequence relation, taking into account the existence of consistent arguments in favour of a conclusion and the absence of consistent arguments in favour of its contrary, is particularly investigated. Flat knowledge bases, i.e., without any priority between their elements, are studied under different inconsistencytolerant consequence relations, namely the socalled argumentative, free, universal, existential, cardinalitybased, and paraconsistent consequence relations. The syntaxsensitivity of these consequence relations is studied. A companion paper is devoted to the case where priorities exist between the pieces of information in the knowledge base. Key words: inconsistency, argumentation, nonmonotonic reasoning, syntaxsensitivity. * Some of the results contained in this paper were presented at the Ninth Conference on Uncertainty in Artificial Intelligence (UAI'...
A Probabilistic Calculus of Actions
, 1994
"... We present a symbolic machinery that admits both probabilistic and causal information about a given domain, and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P (yj ..."
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Cited by 31 (13 self)
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We present a symbolic machinery that admits both probabilistic and causal information about a given domain, and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of conditioning operators: ordinary Bayes conditioning, P (yjX = x), which represents the observation X = x, and causal conditioning, P (yjdo(X = x)), read: the probability of Y = y conditioned on holding X constant (at x) by deliberate action. Given a mixture of such observational and causal sentences, together with the topology of the causal graph, the calculus derives new conditional probabilities of both types, thus enabling one to quantify the effects of actions and observations. 1 Introduction Probabilistic methods, especially those based on graphical models have proven useful in tasks of predictions, abduction and belief revision [Pearl 1988, Heckerman 1990, Goldszmidt 1992, Darwiche 1993]. Their use in planning, however, remains less po...
Revision by Conditional Beliefs
 in Proceedings of the II th Natianl Conference on Artificial Intelligence (AAAI
, 1993
"... Both the dynamics of belief change and the process of reasoning by default can be based on the conditional belief set of an agent, represented as a set of “ifthen ” rules. In this paper we address the open problem of formalizing the dynamics of revising this conditional belief set by new ifthen ru ..."
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Cited by 29 (2 self)
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Both the dynamics of belief change and the process of reasoning by default can be based on the conditional belief set of an agent, represented as a set of “ifthen ” rules. In this paper we address the open problem of formalizing the dynamics of revising this conditional belief set by new ifthen rules, be they interpreted as new default rules or new revision policies. We start by providing a purely semantic characterization, based on the semantics of conditional rules, which induces logical constraints on any such revision process. We then introduce logical (syntaxindependent) and syntaxdependent techniques, and provide a precise characterization of the set of conditionals that hold after the revision. In addition to formalizing the dynamics of revising a default knowledge base, this work also provides some of the necessary formal tools for establishing the truth of nested conditionals, and attacking the problem of learning new defaults.
Query DAGs: A practical paradigm for implementing beliefnetwork inference
 In Proceedings of Twelfth Conference on Uncertainty in Artificial Intelligence
, 1997
"... We describe a new paradigm for implementing inference in belief networks, which consists of two steps: (1) compiling a belief network into an arithmetic expression called a Query DAG (QDAG); and (2) answering queries using a simple evaluation algorithm. Each nonleaf node of a QDAG represents a nu ..."
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Cited by 23 (4 self)
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We describe a new paradigm for implementing inference in belief networks, which consists of two steps: (1) compiling a belief network into an arithmetic expression called a Query DAG (QDAG); and (2) answering queries using a simple evaluation algorithm. Each nonleaf node of a QDAG represents a numeric operation, a number, or a symbol for evidence. Each leaf node of a QDAG represents the answer to a network query, that is, the probability of some event of interest. It appears that QDAGs can be generated using any of the standard algorithms for exact inference in belief networks  we show how they can be generated using the clustering algorithm. The time and space complexity of a QDAG generation algorithm is no worse than the time complexity of the inference algorithm on which it is based. The complexity of a QDAG evaluation algorithm is linear in the size of the QDAG, and such inference amounts to a standard evaluation of the arithmetic expression it represents. The main value...
Aspects Of Graphical Models Connected With Causality
, 1993
"... This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphica ..."
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Cited by 14 (10 self)
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This paper demonstrates the use of graphs as a mathematical tool for expressing independenices, and as a formal language for communicating and processing causal information in statistical analysis. We show how complex information about external interventions can be organized and represented graphically and, conversely, how the graphical representation can be used to facilitate quantitative predictions of the effects of interventions. We first review the Markovian account of causation and show that directed acyclic graphs (DAGs) offer an economical scheme for representing conditional independence assumptions and for deducing and displaying all the logical consequences of such assumptions. We then introduce the manipulative account of causation and show that any DAG defines a simple transformation which tells us how the probability distribution will change as a result of external interventions in the system. Using this transformation it is possible to quantify, from nonexperimental data...
A Calculus of Pragmatic Obligation
, 1993
"... We present a qualitative, decisiontheoretic account for statements of the form: "You ought to do A, if C". We show that adding a qualitative causal theory (in the form of a graph) as part of an epistemic state is sufficient to facilitate the analysis of action sequences, their consequenc ..."
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Cited by 10 (1 self)
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We present a qualitative, decisiontheoretic account for statements of the form: "You ought to do A, if C". We show that adding a qualitative causal theory (in the form of a graph) as part of an epistemic state is sufficient to facilitate the analysis of action sequences, their consequences, their interaction with observations, their expected utilities and, hence, the assertability of conditional "ought" statements. 1 Introduction Obligation statements, also called deontic statements, come in two varieties: obligations to act in accordance with peers' expectations or commitments to oneself, and obligations to act in the interest of one's survival, namely, to avoid danger and pursue safety. This paper develops a decision theoretic account of obligation statements of the second variety, using qualitative abstractions of probabilities and utilities. The idea is simple. A conditional obligation sentence of the form "You ought to do A if C" is interpreted as shorthand for a more elaborat...
Defining Normative Systems for Qualitative Argumentation
 Practical Reasoning, volume 1085 of Lecture Notes in Computer Science
"... . Inspired by two different approaches to providing a qualitative method for reasoning under uncertaintyqualitative probabilistic networks and systems of argumentationthis paper attempts to combine the advantages of both by defining systems of argumentation that have a probabilistic semantics. ..."
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Cited by 7 (4 self)
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. Inspired by two different approaches to providing a qualitative method for reasoning under uncertaintyqualitative probabilistic networks and systems of argumentationthis paper attempts to combine the advantages of both by defining systems of argumentation that have a probabilistic semantics. 1 Introduction In the last few years there have been a number of attempts to build systems for reasoning under uncertainty that are of a qualitative naturethat is they use qualitative rather than numerical values, dealing with concepts such as increases in belief and the relative magnitude of values. In particular, two types of qualitative system have become well established, namely qualitative probabilistic networks (QPNs) [4, 18], and systems of argumentation [8, 11, 12]. While the former are built as an abstraction of probabilistic networks where the links between nodes are only modelled in terms of the qualitative influence of the parents on the children, and therefore have an under...