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Intuitionistic epistemic logic, Kripke models and Fitch's paradox

Proietti, Carlo LU (2012) In Journal of Philosophical Logic 41(5). p.877-900
Abstract
The present work is motivated by two questions.

(1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it?

In what follows we outline an answer to (2) and give a model-theoretic definition of the operator $K$. This will shed some light also on (1), since it turns out that $K$, defined as we do, fulfills the properties of a necessity operator for a normal modal logic.

The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon's proposal of formulating the... (More)
The present work is motivated by two questions.

(1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it?

In what follows we outline an answer to (2) and give a model-theoretic definition of the operator $K$. This will shed some light also on (1), since it turns out that $K$, defined as we do, fulfills the properties of a necessity operator for a normal modal logic.

The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon's proposal of formulating the verification thesis as $\phi \rightarrow \neg \neg K\phi$. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Epistemic logic, Intuitionistic logic, Fitch's paradox, Kripke models
in
Journal of Philosophical Logic
volume
41
issue
5
pages
877 - 900
publisher
Springer
external identifiers
  • wos:000308871700004
  • scopus:84866497020
ISSN
0022-3611
DOI
10.1007/s10992-011-9207-1
language
English
LU publication?
yes
id
9ab4cf52-fceb-473e-9331-e3744b949f69 (old id 1969292)
date added to LUP
2011-05-25 16:42:24
date last changed
2017-06-04 03:20:25
@article{9ab4cf52-fceb-473e-9331-e3744b949f69,
  abstract     = {The present work is motivated by two questions.<br/><br>
(1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? <br/><br>
In what follows we outline an answer to (2) and give a model-theoretic definition of the operator $K$. This will shed some light also on (1), since it turns out that $K$, defined as we do, fulfills the properties of a necessity operator for a normal modal logic.<br/><br>
The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon's proposal of formulating the verification thesis as $\phi \rightarrow \neg \neg K\phi$. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models.},
  author       = {Proietti, Carlo},
  issn         = {0022-3611},
  keyword      = {Epistemic logic,Intuitionistic logic,Fitch's paradox,Kripke models},
  language     = {eng},
  number       = {5},
  pages        = {877--900},
  publisher    = {Springer},
  series       = {Journal of Philosophical Logic},
  title        = {Intuitionistic epistemic logic, Kripke models and Fitch's paradox},
  url          = {http://dx.doi.org/10.1007/s10992-011-9207-1},
  volume       = {41},
  year         = {2012},
}