Probability, fuzziness and borderline cases

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An integrated approach to truth-gaps and epistemic uncertainty is described, based on probability distributions defined over a set of three-valued truth models. This combines the explicit representation of borderline cases with both semantic and stochastic uncertainty, in order to define measures of subjective belief in vague propositions. Within this framework we investigate bridges between probability theory and fuzziness in a propositional logic setting. In particular, when the underlying truth model is from Kleene's three-valued logic then we provide a complete characterisation of compositional min–max fuzzy truth degrees. For classical and supervaluationist truth models we find partial bridges, with min and max combination rules only recoverable on a fragment of the language. Across all of these different types of truth valuations, min–max operators are resultant in those cases in which there is only uncertainty about the relative sharpness or vagueness of the interpretation of the language.
Original languageEnglish
Pages (from-to)1164–1184
Number of pages20
JournalInternational Journal of Approximate Reasoning
Issue number5
Early online date28 Jan 2014
Publication statusPublished - Jul 2014

Bibliographical note

Date of Acceptance: 22/01/2014


  • Vagueness
  • Truth-gaps
  • Probability
  • Fuzziness


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