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 #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 #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 #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 #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 #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 #1153786 has the title `Updates and Counterfactuals  
` and the 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. 
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Question: Which category should Paper #1153786 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1153786 has the title `Updates and Counterfactuals  
` and the 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. 
`.
Question: Which category should Paper #1153786 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