Measuring evidence: a probabilistic approach to an extension of Belnap–Dunn logic

Synthese 198 (S22):5451-5480 (2020)
  Copy   BIBTEX


This paper introduces the logic of evidence and truth \ as an extension of the Belnap–Dunn four-valued logic \. \ is a slightly modified version of the logic \, presented in Carnielli and Rodrigues. While \ is equipped only with a classicality operator \, \ is equipped with a non-classicality operator \ as well, dual to \. Both \ and \ are logics of formal inconsistency and undeterminedness in which the operator \ recovers classical logic for propositions in its scope. Evidence is a notion weaker than truth in the sense that there may be evidence for a proposition \ even if \ is not true. As well as \, \ is able to express preservation of evidence and preservation of truth. The primary aim of this paper is to propose a probabilistic semantics for \ where statements \\) and \\) express, respectively, the amount of evidence available for \ and the degree to which the evidence for \ is expected to behave classically—or non-classically for \ \). A probabilistic scenario is paracomplete when \ + P 1\), and in both cases, \ < 1\). If \ = 1\), or \ = 0\), classical probability is recovered for \. The proposition \, a theorem of \, partitions what we call the information space, and thus allows us to obtain some new versions of known results of standard probability theory.



    Upload a copy of this work     Papers currently archived: 92,953

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A Gentzen Calculus for Nothing but the Truth.Stefan Wintein & Reinhard Muskens - 2016 - Journal of Philosophical Logic 45 (4):451-465.
A probabilistic extension of intuitionistic logic.Z. Ognjanovic & Z. Markovic - 2003 - Mathematical Logic Quarterly 49 (4):415.
Models & Proofs: LFIs Without a Canonical Interpretations.Eduardo Alejandro Barrio - 2018 - Principia: An International Journal of Epistemology 22 (1):87-112.
Remarks on the Epistemic Interpretation of Paraconsistent Logic.Nicolás Lo Guercio & Damian Szmuc - 2018 - Principia: An International Journal of Epistemology 22 (1):153-170.
Contradictory Information: Too Much of a Good Thing. [REVIEW]J. Michael Dunn - 2010 - Journal of Philosophical Logic 39 (4):425 - 452.


Added to PP

32 (#515,304)

6 months
14 (#200,889)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Walter Carnielli
University of Campinas
Abilio Rodrigues
Federal University of Minas Gerais

References found in this work

A Mathematical Theory of Evidence.Glenn Shafer - 1976 - Princeton University Press.
A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
Evidence.Thomas Kelly - 2006 - Philosophy Compass.

View all 25 references / Add more references