Which is the best introduction to Kripke-models for modal logics? I am a M.Sc in mathematics and know predicatlogic.
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3$\begingroup$ The textbook on modal logic by Chagrov and Zakharyaschev, and the one by Blackburn, De Rijke, and Venema, contain a lot of introductory material on Kripke models, but neither is specifically focused on Kripke models. $\endgroup$– Emil JeřábekCommented Sep 28, 2016 at 9:08
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$\begingroup$ You can see also an introductory exposition for Modal Logic into : James Garson, Modal Logic for Philosophers (2nd ed, 2013). $\endgroup$– Mauro ALLEGRANZACommented Sep 29, 2016 at 9:26
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$\begingroup$ Reagrding Intuitionistic Logic, you can see ; Anne Troelstra & Dirk van Dalen, Constructivism in mathematics : An Introduction. Volume 1 (1988). $\endgroup$– Mauro ALLEGRANZACommented Sep 29, 2016 at 9:30
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$\begingroup$ May also be useful : John Burgess, Philosophical logic (2009). $\endgroup$– Mauro ALLEGRANZACommented Sep 29, 2016 at 9:36
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$\begingroup$ Maybe also Appendix A: Models of John Burgess, Kripke (2012). $\endgroup$– Mauro ALLEGRANZACommented Sep 29, 2016 at 9:41
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2 Answers
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Brian F. Chellas: Modal Logic: An Introduction, 1980.
Starts very basic but covers in detail the beautiful completeness theorem proofs for the basic systems like $S5$, $S4$, $K$.
answered Nov 28, 2016 at 19:09
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I can't say that this is the 'best' introduction to Kripke models (as 'best' is always a relative term), but John P. Burgess's survey article "Kripke Models" presumes only knowledge of propositional and predicate logic. It can be found in Alan Berger (ed.), Saul Kripke, Cambridge University Press (2011), or on the Web at www.gauss.ececs.uc.edu/Courses/c626/reports.Kripke1.pdf . It covers most basic applications of Kripke models to modal logic adequately except for the application of Kripke models to forcing. A nice introduction to that topic might be the references in the comments and answer to the mathoverflow question, "Forcing is Intuitionistic". Also the Wikipedia entry, "Kripke Semantics".
answered Sep 29, 2016 at 7:02
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$\begingroup$ Thank you for this reference, (the link worked fine) which seems to be to the point for me. $\endgroup$ Commented Sep 29, 2016 at 8:34
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$\begingroup$ @AndersGöransson: Glad you found this reference helpful. The complete article is at www.gauss.ececs.uc.edu/.... , as referenced above. $\endgroup$ Commented Sep 29, 2016 at 11:39
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$\begingroup$ I got the article downloaded straight away from the link you provided. It seems to cover all that I hoped for. $\endgroup$ Commented Sep 30, 2016 at 8:14