Synthese:1-30 (forthcoming)

Abilio Rodrigues
Federal University of Minas Gerais
Walter Carnielli
University of Campinas
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.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s11229-020-02571-w
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 51,756
External links

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

No references found.

Add more references

Citations of this work BETA

Add more citations

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 index

Total views
6 ( #1,030,954 of 2,333,950 )

Recent downloads (6 months)
6 ( #121,650 of 2,333,950 )

How can I increase my downloads?


My notes