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Logic Aggregation

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Logic, Rationality, and Interaction (LORI 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8196))

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Abstract

We study the possibility and impossibility of aggregating logics, which may come from different sources (individuals, agents, groups, societies, cultures). A logic is treated as a binary relation between sets of formulas and formulas (or a set of accepted arguments). Logic aggregation is treated as argument-wise. We prove that certain logical properties can be preserved by some desired aggregation functions, while some other logical properties cannot be preserved together under non-degenerate aggregation functions, as long as some natural conditions for the aggregation function are satisfied. We compare our framework of logic aggregation with other aggregation frameworks, including preference aggregation and judgment aggregation.

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References

  1. Benamara, F., Kaci, S., Pigozzi, G.: Individual Opinions-Based Judgment Aggregation Procedures. In: Torra, V., Narukawa, Y., Daumas, M. (eds.) MDAI 2010. LNCS (LNAI), vol. 6408, pp. 55–66. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Dietrich, F.: A generalised model of judgment aggregation. Social Choice and Welfare 28(4), 529–565 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dietrich, F., List, C.: Arrow’s theorem in judgment aggregation. Social Choice and Welfare 29(1), 19–33 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dietrich, F., Mongin, P.: The premiss-based approach to judgment aggregation. Journal of Economic Theory 145(2), 562–582 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  5. Endriss, U., Grandi, U.: Graph Aggregation. In: Proceedings of the 4th International Workshop on Computational Social Choice (COMSOC 2012) (2012)

    Google Scholar 

  6. Endriss, U., Grandi, U., Porello, D.: Complexity of Judgment Aggregation: Safety of the Agenda. In: Proceedings of AAMAS 2010, pp. 359–366 (2010)

    Google Scholar 

  7. Fishburn, P.C.: Arrow’s impossibility theorem: Concise proof and infinite voters. Journal of Economic Theory 2(1), 103–106 (1970)

    Article  MathSciNet  Google Scholar 

  8. Gabbay, D.M. (ed.): What is a Logical System? Oxford University Press (1995)

    Google Scholar 

  9. Gärdenfors, P.: A Representation Theorem for Voting with Logical Consequences. Economics and Philosophy 22(2), 181 (2006)

    Article  Google Scholar 

  10. Grandi, U., Endriss, U.: Lifting Rationality Assumptions in Binary Aggregation. In: Proceedings of AAAI 2010, pp. 780–785 (2010)

    Google Scholar 

  11. Grossi, D., Pigozzi, G.: Introduction to Judgment Aggregation. In: Bezhanishvili, N., Goranko, V. (eds.) ESSLLI 2010/2011. LNCS, vol. 7388, pp. 160–209. Springer, Heidelberg (2012)

    Google Scholar 

  12. Jansana, R.: Propositional Consequence Relations and Algebraic Logic. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy. Spring 2011 edn. (2011), http://plato.stanford.edu/archives/spr2011/entries/consequence-algebraic/

  13. Klamler, C., Eckert, D.: A simple ultrafilter proof for an impossibility theorem in judgment aggregation. Economics Bulletin 29(1), 319–327 (2009)

    Google Scholar 

  14. List, C.: The theory of judgment aggregation: an introductory review. Synthese 187(1), 179–207 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. List, C., Pettit, P.: Aggregating Sets of Judgments: An Impossibility Result. Economics and Philosophy 18(1), 89–110 (2002)

    Google Scholar 

  16. Miller, M.K.: Judgment Aggregation and Subjective Decision-Making. Economics and Philosophy 24(2) (2008)

    Google Scholar 

  17. Mongin, P.: Factoring out the impossibility of logical aggregation. Journal of Economic Theory 141(1), 100–113 (2008), http://linkinghub.elsevier.com/retrieve/pii/S0022053107001457

    Article  MathSciNet  MATH  Google Scholar 

  18. Pigozzi, G.: Belief merging and the discursive dilemma: an argument-based account to paradoxes of judgment aggregation. Synthese 152(2), 285–298 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pini, M.S., Rossi, F., Venable, K.B., Walsh, T.: Aggregating Partially Ordered Preferences. Journal of Logic and Computation 19(3), 475–502 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  20. Porello, D., Endriss, U.: Ontology Merging as Social Choice. In: Leite, J., Torroni, P., Ågotnes, T., Boella, G., van der Torre, L. (eds.) CLIMA XII 2011. LNCS, vol. 6814, pp. 157–170. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Logic and Cognition & Department of Philosophy, Sun Yat-sen University, Guangzhou, 510275, China

    Xuefeng Wen & Hu Liu

Authors
  1. Xuefeng Wen
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  2. Hu Liu
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Liverpool, Ashton Building, Ashton Street, L69 3BX, Liverpool, UK

    Davide Grossi

  2. Fakultät für Philosophie, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539, München, Germany

    Olivier Roy

  3. Center for the Study of Language and Cognition, Zhejiang University, Xixi Campus, Tianmushan Road 148, 310028,, Hangzhou, China

    Huaxin Huang

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Wen, X., Liu, H. (2013). Logic Aggregation. In: Grossi, D., Roy, O., Huang, H. (eds) Logic, Rationality, and Interaction. LORI 2013. Lecture Notes in Computer Science, vol 8196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40948-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-40948-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40947-9

  • Online ISBN: 978-3-642-40948-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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