Above are papers related to the following paper: [Paper_ID] Paper #1110209. 	[Title] Defining Relative Likelihood in Partially-Ordered Preferential Structures [Abstract] 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. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1117920. 	[Title] Plausibility Measures: A User's Guide [Abstract] We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. The lack of structure in a plausibility measure makes it easy for us to add structure on an as needed basis, letting us examine what is required to ensure that a plausibility measure has certain properties of interest. This gives us insight into the essential features of the properties in question, while allowing us to prove general results that apply to many approaches to reasoning about uncertainty. Plausibility measures have already proved useful in analyzing default reasoning. In this paper, we examine their algebraic properties, analogues to the use of + and fi in probability theory. An understanding of such properties will be essential if plausibility measures are to be used in practice as a representation tool. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #65057. 	[Title] Abduction as Belief Revision [Abstract] We propose a model of abduction based on the revision of the epistemic state of an agent. Explanations must be sufficient to induce belief in the sentence to be explained (for instance, some observation), or ensure its consistency with other beliefs, in a manner that adequately accounts for factual and hypothetical sentences. Our model will generate explanations that nonmonotonically predict an observation, thus generalizing most current accounts, which require some deductive relationship between explanation and observation. It also provides a natural preference ordering on explanations, defined in terms of normality or plausibility. To illustrate the generality of our approach, we reconstruct two of the key paradigms for model-based diagnosis, abductive and consistency-based diagnosis, within our framework. This reconstruction provides an alternative semantics for both and extends these systems to accommodate our predictive explanations and semantic preferences on explanations. It also illustrates how more general information can be incorporated in a principled manner. fl Some parts of this paper appeared in preliminary form as Abduction as Belief Revision: A Model of Preferred Explanations, Proc. of Eleventh National Conf. on Artificial Intelligence (AAAI-93), Washington, DC, pp.642-648 (1993). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #134307. 	[Title] Generalized Update: Belief Change in Dynamic Settings [Abstract] Belief revision and belief update have been proposed as two types of belief change serving different purposes. Belief revision is intended to capture changes of an agent's belief state reflecting new information about a static world. Belief update is intended to capture changes of belief in response to a changing world. We argue that both belief revision and belief update are too restrictive; routine belief change involves elements of both. We present a model for generalized update that allows updates in response to external changes to inform the agent about its prior beliefs. This model of update combines aspects of revision and update, providing a more realistic characterization of belief change. We show that, under certain assumptions, the original update postulates are satisfied. We also demonstrate that plain revision and plain update are special cases of our model, in a way that formally verifies the intuition that revision is suitable for static belief change. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #89416. 	[Title] Rational Belief Revision (Preliminary Report) [Abstract] Theories of rational belief revision recently proposed by Alchourron, Gardenfors, Makin-son, and Nebel illuminate many important issues but impose unnecessarily strong standards for correct revisions and make strong assumptions about what information is available to guide revisions. We reconstruct these theories according to an economic standard of rationality in which preferences are used to select among alternative possible revisions. By permitting multiple partial specifications of preferences in ways closely related to preference-based nonmonotonic logics, the reconstructed theory employs information closer to that available in practice and offers more flexible ways of selecting revisions. We formally compare this new conception of rational belief revision with the original theories, adapt results about universal default theories to prove that there is unlikely to be any universal method of rational belief revision, and examine formally how different limitations on rationality affect belief revision. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #137130. 	[Title] On the Semantics of Belief Revision Systems [Abstract] We consider belief revision operators that satisfy the Alchourron-Gardenfors-Makinson postulates, and present an epistemic logic in which, for any such revision operator, the result of a revision can be described by a sentence in the logic. In our logic, the fact that the agent's set of beliefs is is represented by the sentence O, where O is Levesque's `only know' operator. Intuitively, O is read as ` is all that is believed.' The fact that the agent believes is represented by the sentence B , read in the usual way as ` is believed'. The connective represents update as defined by Katsuno and Mendelzon. The revised beliefs are represented by the sentence O B . We show that for every revision operator that satisfies the AGM postulates, there is a model for our epistemic logic such that the beliefs implied by the sentence O B in this model correspond exactly to the sentences implied by the theory that results from revising by . This means that reasoning about changes in the agent's beliefs reduces to model checking of certain epistemic sentences. The negative result in the paper is that this type of formal account of revision cannot be extended to the situation where the agent is able to reason about its beliefs. A fully introspective agent cannot use our construction to reason about the results of its own revisions, on pain of triviality. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #74698. 	[Title] Abduction to Plausible Causes: An Event-based Model of Belief Update [Abstract] The Katsuno and Mendelzon (KM) theory of belief update has been proposed as a reasonable model for revising beliefs about a changing world. However, the semantics of update relies on information which is not readily available. We describe an alternative semantical view of update in which observations are incorporated into a belief set by: a) explaining the observation in terms of a set of plausible events that might have caused that observation; and b) predicting further consequences of those explanations. We also allow the possibility of conditional explanations. We show that this picture naturally induces an update operator conforming to the KM postulates under certain assumptions. However, we argue that these assumptions are not always reasonable, and they restrict our ability to integrate update with other forms of revision when reasoning about action. fl Some parts of this report appeared in preliminary form as An Event-Based Abductive Model of Update, Proc. of Tenth Canadian Conf. on in AI, Banff, Alta., (1994). Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #134316. 	[Title] A Qualitative Markov Assumption and Its Implications for Belief Change [Abstract] The study of belief change has been an active area in philosophy and AI. In recent years, two special cases of belief change, belief revision and belief update, have been studied in detail. Roughly speaking, revision treats a surprising observation as a sign that previous beliefs were wrong, while update treats a surprising observation as an indication that the world has changed. In general, we would expect that an agent making an observation may both want to revise some earlier beliefs and assume that some change has occurred in the world. We define a novel approach to belief change that allows us to do this, by applying ideas from probability theory in a qualitative settings. The key idea is to use a qualitative Markov assumption, which says that state transitions are independent. We show that a recent approach to modeling qualitative uncertainty using plausibility measures allows us to make such a qualitative Markov assumption in a relatively straightforward way, and show how the Markov assumption can be used to provide an attractive belief-change model. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #87915. 	[Title] On the Complexity of Conditional Logics [Abstract] Conditional logics, introduced by Lewis and Stalnaker, have been utilized in artificial intelligence to capture a broad range of phenomena. In this paper we examine the complexity of several variants discussed in the literature. We show that, in general, deciding satisfiability is PSPACE-complete for formulas with arbitrary conditional nesting and NP-complete for formulas with bounded nesting of conditionals. However, we provide several exceptions to this rule. Of particular note are results showing that (a) when assuming uniformity (i.e., that all worlds agree on what worlds are possible), the decision problem becomes EXPTIME-complete even for formulas with bounded nesting, and (b) when assuming absoluteness (i.e., that all worlds agree on all conditional statements), the decision problem is NP-complete for for mulas with arbitrary nesting. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #142268. 	[Title] Plausibility Measures and Default Reasoning [Abstract] We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility measures. We focus on one application of plausibility measures in this paper: default reasoning. In recent years, a number of different semantics for defaults have been proposed, such as preferential structures, *-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. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #65074. 	[Title] Rank-based systems: A simple approach to belief revision, belief update, and reasoning about evidence and actions. [Abstract] We describe a ranked-model semantics for if-then rules admitting exceptions, which provides a coherent framework for many facets of evidential and causal reasoning. Rule priorities are automatically extracted form the knowledge base to facilitate the construction and retraction of plausible beliefs. To represent causation, the formalism incorporates the principle of Markov shielding which imposes a stratified set of independence constraints on rankings of interpretations. We show how this formalism resolves some classical problems associated with specificity, prediction and abduction, and how it offers a natural way of unifying belief revision, belief update, and reasoning about actions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153786. 	[Title] Updates and Counterfactuals [Abstract] We study the problem of combining updates |a special instance of theory change| and counterfactual conditionals in propositional knowledgebases. Intuitively, an update means that the world described by the knowledgebase has changed. This is opposed to revisions |another instance of theory change| where our knowledge about a static world changes. A counterfactual implication is a statement of the form `If A were the case, then B would also be the case', where the negation of A may be derivable from our current knowledge. We present a decidable logic, called VCU 2 , that has both update and counterfactual implication as connectives in the object language. Our update operator is a generalization of operators previously proposed and studied in the literature. We show that our operator satisfies certain postulates set forth for any reasonable update. The logic VCU 2 is an extension of D. K. Lewis' logic VCU for counterfactual conditionals. The semantics of VCU 2 is that of a multimodal propositional calculus, and is based on possible worlds. The infamous Ramsey Rule becomes a derivation rule in our sound and complete axiomatization. We then show that Gardenfors' Triviality Theorem, about the impossibility to combine theory change and counterfactual conditionals via the Ramsey Rule, does not hold in our logic. It is thus seen that the Triviality Theorem applies only to revision operators, not to updates. fl A preliminary version of this paper was presented at the Second International Conference on Principles of Knowledge Representation and Reasoning, Cambridge, Massachusetts, April 22-25, 1991. The work was partially performed while the author was visiting the Department of Computer Science at the University of Toronto. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #714748. 	[Title] CAUSATION, ACTION, AND COUNTERFACTUALS [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #23070. 	[Title] A Knowledge-Based Framework for Belief Change Part I: Foundations [Abstract] We propose a general framework in which to study belief change. We begin by defining belief in terms of knowledge and plausibility: an agent believes ' if he knows that ' is true in all the worlds he considers most plausible. We then consider some properties defining the interaction between knowledge and plausibility, and show how these properties affect the properties of belief. In particular, we show that by assuming two of the most natural properties, belief becomes a KD45 operator. Finally, we add time to the picture. This gives us a framework in which we can talk about knowledge, plausibility (and hence belief), and time, which extends the framework of Halpern and Fagin [HF89] for modeling knowledge in multi-agent systems. We show that our framework is quite expressive and lets us model in a natural way a number of different scenarios for belief change. For example, we show how we can capture an analogue to prior probabilities, which can be updated by "conditioning". In a related paper, we show how the two best studied scenarios, belief revision and belief update, fit into the framework. Please summarise all the given information.

Paper #1110209 has the title `Defining Relative Likelihood in Partially-Ordered Preferential Structures  
` and the abstract `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.
`.
Question: Which category should Paper #1110209 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1110209 has the title `Defining Relative Likelihood in Partially-Ordered Preferential Structures  
` and the abstract `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.
`.
Question: Which category should Paper #1110209 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Probabilistic_Methods