Contradictory Information: Too Much of a Good Thing [Book Review]

Journal of Philosophical Logic 39 (4):425 - 452 (2010)
Abstract
Both I and Belnap, motivated the "Belnap-Dunn 4-valued Logic" by talk of the reasoner being simply "told true" (T) and simply "told false" (F), which leaves the options of being neither "told true" nor "told false" (N), and being both "told true" and "told false" (B). Belnap motivated these notions by consideration of unstructured databases that allow for negative information as well as positive information (even when they conflict). We now experience this on a daily basis with the Web. But the 4-valued logic is deductive in nature, and its matrix is discrete: there are just four values. In this paper I investigate embedding the 4-valued logic into a context of probability. Jøsang's Subjective Logic introduced uncertainty to allow for degrees of belief, disbelief, and uncertainty. We extend this so as to allow for two kinds of uncertainty— that in which the reasoner has too little information (ignorance) and that in which the reasoner has too much information (conflicted). Jøsang's "Opinion Triangle" becomes an "Opinion Tetrahedron" and the 4-values can be seen as its vertices. I make/prove various observations concerning the relation of non-classical "probability" to non-classical logic
Keywords Subjective Logic  De Morgan lattices  Probability  Paraconsistent  Information  Relevance logic  Entailment  Contradictions
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DOI 10.1007/s10992-010-9134-6
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The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Truth and Probability.F. P. Ramsey - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
Knowledge and Belief.Jaakko Hintikka - 1962 - Ithaca: Cornell University Press.

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