Author: Alexandru DRAGOMIR
Abstract : 1) We will begin by offering a short introduction to Epistemic Logic
and presenting Fitch’s paradox in an epistemic‑modal logic. (2) Then, we will
proceed to presenting three Epistemic Temporal logical frameworks creat‑
ed by Hoshi (2009) : TPAL (Temporal Public Announcement Logic), TAPAL
(Temporal Arbitrary Public Announcement Logic) and TPAL+P ! (Temporal
Public Announcement Logic with Labeled Past Operators). We will show how
Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze
his argument on why this version of it is immune from paradox. (3) Edgington
(1985) offered an interpretation of the Verificationist Thesis that blocks Fitch’s
paradox and we will propose a way to formulate it in a TAPAL‑based lan‑
guage. The language we will use is a combination of TAPAL and TPAL+P ! with
an Indefinite (Unlabeled) Past Operator (TAPAL+P !+P). Using indexed satisfi‑
ability relations (as introduced in (Wang 2010 ; 2011)) we will offer a prospec ‑
tive semantics for this language. We will investigate whether the tentative re‑
formulation of Edgington’s Verificationist Thesis in TAPAL+P !+P is free from
paradox and adequate to Edgington’s ideas on how „all truths are knowable“
should be interpreted.
Keywords : Fitch’s paradox, knowability, dynamic epistemic logic, epistemic
logic, epistemic temporal logic, protocols
References
1. Ågotnes, T., P. Balbiani, H. van Ditmarsch, P. Seban. 2010. Group an‑
nouncement logic, Journal of Applied Logic, Volume 8, Issue 1, March 2010,
pp. 62‑81, ISSN 1570‑8683, http ://dx.doi.org/10.1016/j.jal.2008.12.002.
2. Balbiani, P., A. Baltag, H. van Ditmarsch, A. Herzig, T. Hoshi, and T. de
Lima. 2007. What can we achieve by arbitrary announcements ? A dy‑
namic take on Fitch’s knowability. In Proceedings of the 11th conference
on Theoretical aspects of rationality and knowledge (TARK ‚07). ACM, New
York, NY, USA, pp. 42‑51. DOI=10.1145/1324249.1324259 http ://doi.acm.org/10.1145/1324249.1324259
3. van Benthem, J. 2004. „What One May Come to Know“. Analysis,
64(2) :95‑105, 2004.
4. Blackburn, P., M. de Rijke and Y. Venema. 2002. Modal Logic. Cambridge
University Press.
5. Chalmers, David J. 2011. „Actuality and knowability“. Analysis. 71
(3) :411‑419.
6. van Ditmarsch, H.P., B.P. Kooi and W. van der Hoek. 2006. Dynamic
Epistemic Logic. Springer Publishing Company.
7. van Ditmarsch, H.P., W. van der Hoek, P. Iliev. 2012. „Everything is
Knowable – How to Get to Know Whether a Proposition is True“. Theoria,
78(2) :93 ‑ 114, 2012.
8. Edgington, D., 1985. „The Paradox of Knowability“. Mind. 94 : 557–568.
9. Fagin, R., J.Y. Halpern, Y. Moses, M. Vardi. 1995. Reasoning about Knowledge.
Cambridge, Massachusetts : The MIT Press 1995.
10. Groeneveld, W. and J. Gerbrandy. 1997. „Reasoning about Information
Change“. Journal of Logic, Language and Information, 6(2) :147‑169.
11. Hintikka, J. 1962. Knowledge and Belief. Ithaca, N.Y., Cornell University
Press.
12. Holliday, W.H. Forthcoming. „Epistemic logic and epistemology“. In
Sven Ove Hansson, Vincent F. Hendricks, eds., Handbook of Formal
Philosophy. Springer.
13. Hoshi, T. 2009. Epistemic dynamics and protocol information. PhD Thesis,
Stanford University, ILLC DISSERTATION SERIES DS‑200X‑NN, http ://www.illc.uva.nl/Research/Publications/Dissertations/DS‑2009‑08.text.pdf
14. Kooi, B.P. 2007. „Expressivity and completeness for public update
logics via reduction axioms“. Journal of Applied Non‑Classical Logics,
17(2) :231‑253.
15. Plaza, J. 1989. „Logics of public communcations“. In M. L. Emrich, M. Z.
Pfeifer, M. Hadzikadic, Z. W. Ras (eds.), Proc. 4th Inernational Symposium
on Methodologies for Intelligent Systems, pages 201–216. Oak Ridge National
Laboratory, ORNL/DSRD‑24.
16. Solecki, S., A. Baltag, and L.S. Moss. 1999. „The logic of public announce‑
ments, common knowledge and private suspicions“. Technical report,
Centrum voor Wiskunde en Informatica, Amsterdam. CWI Report
SEN‑R9922.
17. Wang, Y. 2010. Epistemic Modelling and Protocol Dynamics. Dissertation,
University of Amsterdam.
18. Wang, Y. 2011. „Reasoning about protocol change and knowledge“. In
ICLA’11 Proceedings of the 4th Indian conference on Logic and its ap‑
plications, pages. 189‑203, Springer‑Verlag Berlin, Heidelberg.
19. Williamson, T. 1987. „On the paradox of knowability“. Mind 96 :256‑61.