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    Arló-Costa, Horacio and Bicchieri, Cristina 2007. Knowing and Supposing in Games of Perfect Information. Studia Logica, Vol. 86, Issue. 3, p. 353.

    Bonanno, Giacomo 2007. Axiomatic characterization of the AGM theory of belief revision in a temporal logic. Artificial Intelligence, Vol. 171, Issue. 2-3, p. 144.

    Bonanno, Giacomo 2005. A Simple Modal Logic for Belief Revision. Synthese, Vol. 147, Issue. 2, p. 193.

    Ryan, Matthew J. 2002. Violations of Belief Persistence in Dempster–Shafer Equilibrium. Games and Economic Behavior, Vol. 39, Issue. 1, p. 167.

    Battigalli, Pierpaolo and Bonanno, Giacomo 1999. Recent results on belief, knowledge and the epistemic foundations of game theory. Research in Economics, Vol. 53, Issue. 2, p. 149.

    Samet, Dov 1999. Bayesianism without learning. Research in Economics, Vol. 53, Issue. 2, p. 227.

    Friedman, Nir and Halpern, Joseph Y. 1997. Modeling belief in dynamic systems, part I: Foundations. Artificial Intelligence, Vol. 95, Issue. 2, p. 257.


The Logic of Belief Persistence

  • Pierpaolo Battigalli (a1) and Giacomo Bonanno (a2)
  • DOI:
  • Published online: 01 December 2008

The principle of belief persistence, or conservativity principle, states that ‘When changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible’ (Harman, 1986, p. 46). In particular, this means that if an individual gets new information, she has to accommodate it in her new belief set (the set of propositions she believes), and, if the new information is not inconsistent with the old belief set, then (1) the individual has to maintain all the beliefs she previously had and (2) the change should be minimal in the sense that every proposition in the new belief set must be deducible from the union of the old belief set and the new information (see, e.g., Gärdenfors, 1988; Stalnaker, 1984). We focus on this minimal notion of belief persistence and characterize it both semantically and syntactically.

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P. M. Brown 1976. ‘Conditionalization and expected utility’. Philosophy of Science, 43:415–19

Joseph Halpern . 1991. ‘The relationship between knowledge, belief and certainty’. Annals of Mathematics and Artificial Intelligence, 4:301–22

Wiebe van der Hoek . 1993. ‘Systems for knowledge and belief’, Journal of Logic and Computation, 3:173–95

Sarit Kraus and Danile Lehmann . 1988. ‘Knowledge, belief and time’. Theoretical Computer Science, 58:155–74

P. Teller 1973. ‘Conditionalization and observation’. Synthese, 26:218–58

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