The Dynamification of Modal Dependence Logic
- 208 Downloads
We examine the transitions between sets of possible worlds described by the compositional semantics of Modal Dependence Logic, and we use them as the basis for a dynamic version of this logic. We give a game theoretic semantics, a (compositional) transition semantics and a power game semantics for this new variant of modal Dependence Logic, and we prove their equivalence; and furthermore, we examine a few of the properties of this formalism and show that Modal Dependence Logic can be recovered from it by reasoning in terms of reachability. Then we show how we can generalize this approach to a very general formalism for reasoning about transformations between pointed Kripke models.
KeywordsModal Logic Dependence Logic Dynamic semantics Game Theoretic Semantics
This work has been supported by the EUROCORES, LogICCC LINT programme, by the Väisälä Foundation and by grant 264917 of the Academy of Finland. The author thanks a referee for a number of very useful suggestions and comments.
- Abramsky, S. (2007). A compositional game semantics for multi-agent logics of partial information. In J. van Bentham, D. Gabbay, & B. Lowe (Eds.), Interactive logic, volume 1 of texts in logic and games (pp. 11–48). Amsterdam: Amsterdam University Press.Google Scholar
- Baltag, A., Moss, L. S., & Solecki, S. (1998). The logic of public announcements, common knowledge, and private suspicions. Proceedings of the 7th conference on theoretical aspects of rationality and knowledge, TARK ’98 (pp. 43–56). San Francisco, CA, USA: Morgan Kaufmann Publishers Inc.Google Scholar
- Bradfield, J. (2000). Independence: Logics and concurrency. In P. Clote & H. Schwichtenberg (Eds.), Computer science logic volume 1862 of Lecture Notes in Computer Science (pp. 247–261). Berlin/Heidelberg: Springer.Google Scholar
- Dekker, P. (2008). A guide to dynamic semantics. ILLC Prepublication Series, (PP-2008-42).Google Scholar
- Durand, A., & Kontinen, J. (2011). Hierarchies in dependence logic. CoRR, abs/1105.3324.Google Scholar
- Ebbing, J., & Lohmann, P. (2012). Complexity of model checking for modal dependence logic. In M. Bielikov, G. Friedrich, G. Gottlob, S. Katzenbeisser, & G. Turn (Eds.), SOFSEM 2012: theory and practice of Computer Science volume 7147 of Lecture Notes in Computer Science (pp. 226–237). Berlin/Heidelberg: Springer.Google Scholar
- Galliani, P. (2012b, September). The dynamics of imperfect information. PhD thesis, University of Amsterdam.Google Scholar
- Grädel, E., & Väänänen, J. (2013). Dependence and Independence. Studia Logica, 101(2), 399–410. doi: 10.1007/s11225-013-9479-2.
- Henkin, L. (1961). Some remarks on infinitely long formulas. In Infinitistic Methods. Proceedings of symposium on foundations of mathematics (pp. 167–183). Pergamon Press.Google Scholar
- Hintikka, J., & Sandu, G. (1989). Informational independence as a semantic phenomenon. In J. E. Fenstad, I. T. Frolov, & R. Hilpinen, (Eds.), Logic, methodology and philosophy of science (pp. 571–589). Amsterdam: Elsevier.Google Scholar
- Hodges, W. (1997). Compositional semantics for a language of imperfect information. Journal of the Interest Group in Pure and Applied Logics, 5(4), 539–563.Google Scholar
- Lohmann, P., & Vollmer, H. (2010). Complexity results for modal dependence logic. In A. Dawar, & H. Veith (Eds.), Computer science logic, volume 6247 of Lecture Notes in Computer Science (pp. 411–425). Berlin/Heidelberg: Springer.Google Scholar
- Tulenheimo, T. (2004). Independence-friendly Modal Logic. PhD thesis, University of Helsinki.Google Scholar
- Väänänen, J. (2008). Modal Dependence Logic. In K. R. Apt & R. van Rooij (Eds.), New perspectives on games and interaction. Amsterdam: Amsterdam University Press.Google Scholar
- van Benthem, J. (1997). Exploring logical dynamics. Stanford, CA, USA: Center for the Study of Language and Information.Google Scholar
- van Benthem, J. (2006). The epistemic logic of IF games. In R. E. Auxier, & L. E. Hahn (Eds.), The Philosophy of Jaakko Hintikka, volume 30 of Library of living philosophers, chapter 13 (pp. 481–513). Open Court Publishers. Google Scholar
- van Eijck, J., & Visser, A. (2012). Dynamic semantics. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. (Winter ed.). http://plato.stanford.edu/archives/win2012/entries/dynamic.