Abstract
We present a modular approach to the logic of aggregated group preferences based on hybrid modal logic. The modularity of the system is twofold: 1) lifting preference relations between states to complex relations between propositions and 2) lifting individual preferences to group preferences. The preferences may be doxastic or proairetic, generating a logic of aggregated belief or aggregated desire, respectively, using a specific aggregation policy known as ‘lexicographic re-ordering’. Each agent and each group of agents has an associated modal operator representing their preferences between states. The addition of the existential modality and nominals allows us to produce, first, a Hilbert-style axiomatization of the logic and then a more thorough analysis of inference using a Gentzen-style sequent calculus, in which the role of each operator is revealed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andréka, H., Ryan, M., Schobbens, P.-Y.: Operators and laws for combining preference relations. Journal of logic and computation 12(1), 13–53 (2002)
Areces, C., ten Cate, B.: Hybrid logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Elsevier, Amsterdam (2007)
Arrow, K.: Social choice and individual value. Wiley, Chichester (1951)
Boutilier, C.: Toward a logic for qualitative decision theory. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) Principles of Knowledge Representation and Reasoning, pp. 75–86 (1994)
Brandom, R.B.: Making it explicit. Harvard university press (1994)
Dummett, M.: The logical basis of metaphysics. Harvard university press (1991)
Gargov, G., Passy, S., Tinchev, T.: Modal environment for boolean speculations (preliminary report). In: Skordev, D. (ed.) Mathematical Logic and its Applications. Proceedings of the Summer School and Conference dedicated to the 80th Anniversary of Kurt Gödel, pp. 253–263. Plenum Press, Druzhba (1987)
Gentzen, G.: Untersuchungen über das logische schließen. Mathematische Zeitschrift (39), 405–431 (1934)
Girard, P.: Modal logic for lexicographic preference aggregation (to appear, 2008)
Lang, J., van der Torre, L., Weydert, E.: Hidden uncertainty in the logical representation of desires. In: Proceedings of Eighteenth International Joint Conference on Artificial Intelligence, IJCAI 2003 (2003)
Restall, G.: An introduction to substructural logics. Routledge (2000)
Segerberg, K.: The basic dynamic doxastic logic of AGM. In: Williams, M.-A., Rott, H. (eds.) Frontiers in belief revision, pp. 57–84. Kluwer, Dordrecht (2001)
Seligman, J.: Internalization: The case of hybrid logics. Journal of logic and computation 11(5), 671–689 (2001)
Smullyan, R.M.: First-order logic. Dover (1995)
ten Cate, B.: Model Theory for Extended Modal Languages. PhD thesis, University of Amsterdam, ILLC Dissertation Series DS-2005-01 (2005)
Troelstra, A.S., Schwichtenberg, H.: Basic proof theory, 2nd edn. Cambridge tracts in theoretical computer science, vol. 43. Cambridge University Press, Cambridge (2000)
van Benthem, J., Girard, P., Roy, O.: Everything else being equal: a modal logic for ceteris paribus preferences. Journal of philosophical logic (August 2008)
van Benthem, J., van Otterloo, S., Roy, O.: Preference logic, conditionals, and solution concepts in games. In: Lagerlund, H., Lindström, S., Sliwinski, R. (eds.) Modality Matters: Twenty-Five Essays in Honour of Krister Segerberg. Uppsala Philosophical Studies, Uppsala (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Girard, P., Seligman, J. (2008). An Analytic Logic of Aggregation. In: Ramanujam, R., Sarukkai, S. (eds) Logic and Its Applications. ICLA 2009. Lecture Notes in Computer Science(), vol 5378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92701-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-92701-3_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92700-6
Online ISBN: 978-3-540-92701-3
eBook Packages: Computer ScienceComputer Science (R0)