Journal Article10.1109/21.328930
Conditional objects as nonmonotonic consequence relationships
Didier Dubois,Henri Prade +1 more
150
TL;DR: This paper investigates the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning, and proposes a logic of conditional objects that is more elementary and intuitive than the preferential semantics of Lehmann and colleagues and does not require probabilistic semantics.
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Abstract: This paper investigates the relationship between conditional objects obtained as a qualitative counterpart to conditional probabilities, and nonmonotonic reasoning. Viewed as an inference rule expressing a contextual belief, the conditional object is shown to possess all properties of a well-behaved nonmonotonic consequence relation when a suitable choice of connectives and deduction operation is made. Using previous results from Adams' conditional probabilistic logic, a logic of conditional objects is proposed. Its axioms and inference rules are those of preferential reasoning logic of Lehmann and colleagues. But the semantics relies on a three-valued truth valuation first suggested by De Finetti. It is more elementary and intuitive than the preferential semantics of Lehmann and colleagues and does not require probabilistic semantics. The analysis of a notion of consistency of a set of conditional objects is studied in the light of such a three-valued semantics and higher level counterparts of deduction theorem, modus ponens, resolution and refutation are suggested. Limitations of this logic are discussed. >
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Citations
What are fuzzy rules and how to use them
Didier Dubois,Henri Prade +1 more
TL;DR: A survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory.
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Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification
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TL;DR: This paper clarifies a pervasive confusion between possibility theory axioms and fuzzy set basic connectives by demonstrating that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool.
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Nonmonotonic reasoning, conditional objects and possibility theory
TL;DR: This short paper relates the conditional object-based and possibility theory-based approaches for reasoning with conditional statements pervaded with exceptions to other methods in nonmonotonic reasoning, showing Lehmann's preferential and rational closure entailments which obey normative postulates, the infinitesimal probability approach, and the conditional (modal) logics-based approach to be equivalent.
255
On bipolarity in argumentation frameworks
TL;DR: A survey of the use of bipolarity in argumentation frameworks can be found in this article, where the authors show that bipolarity can be used in each step of the argumentation process under different forms.
244
Representing partial ignorance
Didier Dubois,Henri Prade,Philippe Smets +2 more
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TL;DR: It is pointed out that within a numerical framework, two numbers are needed to account for partial ignorance about events, because on top of truth and falsity, the state of total ignorance must be encoded independently of the number of underlying alternatives.
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References
•Book
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Judea Pearl
- 01 Jan 1988
TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
17.6K
•Book
A mathematical theory of evidence
Glenn Shafer
- 01 Jan 1976
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
14.6K
Fuzzy sets as a basis for a theory of possibility
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
9.4K
Nonmonotonic reasoning, preferential models and cumulative logics
TL;DR: In this paper, a number of families of nonmonotonic consequence relations, defined in the style of Gentzen [13], are studied from both proof-theoretic and semantic points of view.
1.6K