Studia Logica 105 (6):1149-1166 (2017)

Authors
Melvin Fitting
CUNY Graduate Center
Abstract
In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which \ can be read as asserting there is implicit evidence for X, where we understand evidence to permit contradictions. We show BLE embeds into KX4 in the same way that Intuitionistic logic embeds into S4. Then we formulate a new justification logic, JX4, in which the implicit evidence motivating KX4 is made explicit. KX4 embeds into JX4 via a realization theorem. Thus BLE has both implicit and explicit possibly contradictory evidence interpretations in a formal sense.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s11225-017-9714-3
Options
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: 70,079
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

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
Explicit Provability and Constructive Semantics.Sergei N. Artemov - 2001 - Bulletin of Symbolic Logic 7 (1):1-36.
The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
Modal Logics, Justification Logics, and Realization.Melvin Fitting - 2016 - Annals of Pure and Applied Logic 167 (8):615-648.

Add more references

Citations of this work BETA

Models & Proofs: LFIs Without a Canonical Interpretations.Eduardo Alejandro Barrio - 2018 - Principia: An International Journal of Epistemology 22 (1):87-112.
Tracking Reasons with Extensions of Relevant Logics.Shawn Standefer - 2019 - Logic Journal of the IGPL 27 (4):543-569.

View all 12 citations / Add more citations

Similar books and articles

Axioms for Classical, Intuitionistic, and Paraconsistent Hybrid Logic.Torben Braüner - 2006 - Journal of Logic, Language and Information 15 (3):179-194.
The Logic of Justification.Sergei Artemov - 2008 - Review of Symbolic Logic 1 (4):477-513.
Relating Logics of Justification and Evidence.Igor Sedlár - 2014 - In Vít Punčochář & Michal Dančák (eds.), The Logica Yearbook 2013. College Publications. pp. 207-222.
Evidence and Justification.David Kelley - 1991 - Reason Papers 16:165-179.
Paraconsistent Logic and Weakening of Intuitionistic Negation.Zoran Majkić - 2012 - Journal of Intelligent Systems 21 (3):255-270.
Paraconsistency Everywhere.Greg Restall - 2002 - Notre Dame Journal of Formal Logic 43 (3):147-156.
The Logic of Uncertain Justifications.Robert S. Milnikel - 2014 - Annals of Pure and Applied Logic 165 (1):305-315.
A Quantified Logic of Evidence.Melvin Fitting - 2008 - Annals of Pure and Applied Logic 152 (1):67-83.

Analytics

Added to PP index
2017-02-23

Total views
26 ( #438,854 of 2,506,017 )

Recent downloads (6 months)
1 ( #416,828 of 2,506,017 )

How can I increase my downloads?

Downloads

My notes