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Propositional Dependence Logic
May 19, 2015 @ 1:30 pm - 3:30 pm
Dependence logic is a new logical formalism that characterizes the notion of “dependence” and “independence" in social and natural sciences. First-order dependence logic was introduced by Väänänen (2007) as a development of Henkin quantifier (Henkin, 1961) and independence-friendly logic (Hintikka and Sandu, 1989). Recently, propositional dependence logic was studied and axiomatized in (Yang and Väänänen, 2015). It turned out that a natural variant of propositional dependence logic, called propositional intuitionistic dependence logic, is essentially equivalent to inquisitive logic, introduced by Ciardelli and Roelofsen (2011) with a different motivation.
In the first part of the talk, we will give a brief introduction to this multidisciplinary new field. Then, we will prove that propositional dependence logic and some of its variants (including inquisitive logic) are structurally complete with respect to a class of substitutions under which the logics are closed, that is, all admissible rules of these logics are derivable in their deductive systems. (This part of the talk is based on a joint work with Rosalie Iemhoff.) Finally, we will point out some interesting directions for future research.
[Ciardelli and Roelofsen, 2011] I. Ciardelli and F. Roelofsen, Inquisitive Logic, Journal of Philosophical Logic, vol. 40, no. 1, pp. 55-94, 2011.
[Henkin, 1961] L. Henkin, Some remarks on infinitely long formulas, Infinitistic Methods, Proceedings Symposium Foundations of Mathematics, pp 167-183, 1961
[Hintikka and Sandu 1989] J. Hintikka and G. Sandu, Informational Independence as a Semantical Phenomenon, Logic, Methodology and Philosophy of Science, Amsterdam: Elsevier, pp. 571-589, 1989
[Väänänen 2007] J. Väänänen, Dependence Logic: A New Approach to Independence Friendly Logic, Cambridge: Cambridge University Press, 2007
[Yang and Väänänen, 2015] F. Yang and J. Väänänen, Propositional Logics of Dependence and Independence, Part I, submitted, preprint available at: http://arxiv.org/abs/1412.7998.