Intuitionistic epistemic logic, Kripke models and Fitch's paradox
(2012) In Journal of Philosophical Logic 41(5). p.877900 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 Kripkemodel for it?
In what follows we outline an answer to (2) and give a modeltheoretic 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 Kripkemodel for it?
In what follows we outline an answer to (2) and give a modeltheoretic 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1969292
 author
 Proietti, Carlo ^{LU}
 organization
 publishing date
 2012
 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
 00223611
 DOI
 10.1007/s1099201192071
 language
 English
 LU publication?
 yes
 id
 9ab4cf52fceb473e9331e3744b949f69 (old id 1969292)
 date added to LUP
 20110525 16:42:24
 date last changed
 20180114 03:15:29
@article{9ab4cf52fceb473e9331e3744b949f69, 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 Kripkemodel for it? <br/><br> In what follows we outline an answer to (2) and give a modeltheoretic 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 = {00223611}, keyword = {Epistemic logic,Intuitionistic logic,Fitch's paradox,Kripke models}, language = {eng}, number = {5}, pages = {877900}, publisher = {Springer}, series = {Journal of Philosophical Logic}, title = {Intuitionistic epistemic logic, Kripke models and Fitch's paradox}, url = {http://dx.doi.org/10.1007/s1099201192071}, volume = {41}, year = {2012}, }