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2013•arXiv (Cornell University)Open access

Probability as a Modal Operator

Alan M. Frisch, Peter Haddawy

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Abstract

This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to think of probability as a modal operator. Contrary to popular belief in AI, a probability ranging between 0 and 1 represents a continuum between impossibility and necessity, not between simple falsity and truth. The present work provides a clear semantics for quantification into the scope of the probability operator and for higher-order probabilities. Probability logic is a language for expressing both probabilistic and logical concepts.

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What this paper is about

This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to think of probability as a modal operator. Contrary to popular belief in AI, a probability ranging between 0 and 1 represents a continuum between impossibility and necessity, not between simple falsity and truth. The present work provides a clear semantics for quantification into the scope of the probability operator and for higher-order probabilities. Probability logic is a language for expressing both probabilistic and logical concepts.

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Available abstract

This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to think of probability as a modal operator. Contrary to popular belief in AI, a probability ranging between 0 and 1 represents a continuum between impossibility and necessity, not between simple falsity and truth. The present work provides a clear semantics for quantification into the scope of the probability operator and for higher-order probabilities. Probability logic is a language for expressing both probabilistic and logical concepts.

Key concepts: Imprecise probability, Modal logic, Normal modal logic, Modal operator, Probabilistic logic, Accessibility relation, Multimodal logic, Computer science

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