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ON EXISTENTIAL DECLARATIONS OF INDEPENDENCE IN IF LOGIC

Published online by Cambridge University Press:  26 March 2013

FAUSTO BARBERO
FAUSTO BARBERO*
Affiliation:
Università di Torino
*
*DIPARTIMENTO DI MATEMATICA, UNIVERSITÀ DI TORINO, TORINO 10123, ITALIA, E-mail:[email protected]
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Abstract

We analyze the behaviour of declarations of independence between existential quantifiers in quantifier prefixes of Independence-Friendly (IF) sentences; we give a syntactical criterion to decide whether a sentence beginning with such prefix exists, such that its truth values may be affected by removal of the declaration of independence. We extend the result also to equilibrium semantics values for undetermined IF sentences.

The main theorem defines a schema of sound and recursive inference rules; we show more explicitly what happens for some simple special classes of sentences.

In the last section, we extend the main result beyond the scope of prenex sentences, in order to give a proof of the fact that the fragment of IF sentences with knowledge memory has only first-order expressive power.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 6 , Issue 2 , June 2013 , pp. 254 - 280
Copyright
Copyright © Association for Symbolic Logic 2013 

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References

BIBLIOGRAPHY

Caicedo, X., Dechesne, F., & Janssen, T. M. V. (2009). Equivalence and quantifier rules for logic with imperfect information. Logic Journal of the IGPL, 17, 91–129.Google Scholar
Galliani, P. (2008a). Game values and equilibria for undetermined sentences of Dependence Logic. M.Sc. Thesis, Published in ILLC MoL Series, MoL-2008-08.Google Scholar
Galliani, P. (2008b). Probabilistic Dependence Logic. http://www.illc.uva.nl/Research/Reports/PP-2008-55.text.pdf.Google Scholar
Hintikka, J. (1996). The Principles of Mathematics Revisited. Cambridge, UK: Cambridge University Press.Google Scholar
Hintikka, J., & Sandu, G. (1989). Informational independence as a semantical phenomenon. In Fenstad, J. E., et al. ., editors. Logic, Methodology and Philosophy of Science VIII, Amsterdam, The Netherlands: Elsevier Science Publishers B.V., pp. 571–589.Google Scholar
Hodges, W. (1997a). Compositional semantics for a language of imperfect information. Logic Journal of the IGPL, 5(4), 539–563.CrossRefGoogle Scholar
Hodges, W. (1997b). Some strange quantifiers. In Mycielski, J., Rozenberg, G., and Salomaa, A., editors. Structures in Logic and Computer Science. Lecture Notes in Computer Science, 1261, 51–65.Google Scholar
Hyttinen, T., & Tulenheimo, T. (2005). Decidability of IF modal logic of perfect recall. In Schmidt, R., et al. ., editors.) Advances in Modal Logic, London, UK: Kings College London Publications, 5, 111–131.Google Scholar
Janssen, T. M. V. (2002). Independent choices and the interpretation of IF logic. Journal of Logic, Language and Information, 11(3), 367–387.CrossRefGoogle Scholar
Janssen, T. M. V. (2005). Independence friendly logic as a strategic game. Proceedings Fifteenth Amsterdam Colloquium, pp. 125–130.Google Scholar
Mann, A. L., Sandu, G., & Sevenster, M. (2011). Independence-friendly logic: A game-theoretic approach. Cambridge, UK: Cambridge University Press.Google Scholar
Sandu, G. (1993). On the logic of informational independence and its applications. Journal of Philosophical Logic Volume, 22(1), 29–60.Google Scholar
Nurmi, V. (2009). Dependence logic: Investigations into higher-order semantics defined on teams. PhD thesis, Helsinki: University of Helsinki, Department of Mathematics and Statistics.Google Scholar
Sevenster, M. (2006). Branches of imperfect information: Games, logic, and computation. PhD thesis, ILLC, Universiteit van Amsterdam.Google Scholar
Sevenster, M. (2007). A strategic perspective on IF games. http://www.illc.uva.nl/Research/Reports/PP-2007-29.text.pdf.Google Scholar
Sevenster, M., & Sandu, G. (2010). Nash equilibrium semantics. Annals of Pure and Applied Logic, 161(5), 618–631.Google Scholar
Tulenheimo, T. (2004). Independence-Friendly Modal Logic. Studies in its Expressive Power and Theoretical Relevance, Philosophical Studies from the University of Helsinki 4 (Doctoral dissertation).Google Scholar
Väänänen, J. (2007). Dependence Logic: A New Approach to Independence Friendly Logic. London Mathematical Society Student Texts (No. 70), Cambridge, UK: Cambridge University Press.Google Scholar