Contradictory Information: Too Much of a Good Thing [Book Review]
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 39 (4):425 - 452 (2010)
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|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Alan R. Anderson & Nuel D. Belnap (1975). Entailment: The Logic of Relevance and Neccessity, Vol. I. Princeton University Press.
Alan Ross Anderson, Nuel D. Belnap & J. Michael Dunn (1992). Entailment: The Logic of Relevance and Necessity, Vol. II. Princeton University Press.
F. G. Asenjo (1966). A Calculus for Antinomies. Notre Dame Journal of Formal Logic 16 (1):103-105.
F. G. Asenjo (1965). Dialectic Logic. Logique Et Analyse 8 (32):321-326.
N. D. Belnap (1977). A Useful Four-Valued Logic. In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Citations of this work BETA
No citations found.
Similar books and articles
John Horty (2007). Defaults with Priorities. Journal of Philosophical Logic 36 (4):367 - 413.
Andreas Pietz & Umberto Rivieccio (2013). Nothing but the Truth. Journal of Philosophical Logic 42 (1):125-135.
Heinrich Wansing (2012). A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity. Topoi 31 (1):93-100.
Fred Seymour Michael (2002). Entailment and Bivalence. Journal of Philosophical Logic 31 (4):289-300.
Barbara Osimani (2012). Risk Information Processing and Rational Ignoring in the Health Context. Journal of Socio-Economics 41:169-179.
James P. Delgrande, Abhaya C. Nayak & Maurice Pagnucco (2005). Gricean Belief Change. Studia Logica 79 (1):97 - 113.
Lloyd Humberstone (2003). False Though Partly True – an Experiment in Logic. Journal of Philosophical Logic 32 (6):613-665.
J. Michael Dunn (1979). A Theorem in 3-Valued Model Theory with Connections to Number Theory, Type Theory, and Relevant Logic. Studia Logica 38 (2):149 - 169.
Duccio Luchi & Franco Montagna (1999). An Operational Logic of Proofs with Positive and Negative Information. Studia Logica 63 (1):7-25.
Added to index2010-06-12
Total downloads60 ( #37,198 of 1,696,592 )
Recent downloads (6 months)2 ( #250,163 of 1,696,592 )
How can I increase my downloads?