Abstract
AGM’s belief revision is one of the main paradigms in the study of belief change operations. Recently, several logics for belief and information change have been proposed in the literature, which were used to encode belief change operations in a rich and expressive framework. While the connection of AGM-like operations and their encoding in dynamic doxastic logics have been studied before, by the exceptional work of Segerberg, most work on the area of Dynamic Epistemic Logics (DEL) have not attempted to characterize belief change operators by means of their logical properties. This work investigates how Dynamic Preference Logic, a logic in the DEL family, can be used to characterise properties of dynamic belief change operators, focusing on well-known postulates of iterated belief change.
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
Notes
- 1.
Similarly, works such as that of Baltag and Smets’ [4] concern themselves with how to encode some types of belief change using the framework of Dynamic Epistemic Logic, not clearly delineating, however, how the properties of a given operator are reflected in the resulting logic.
- 2.
Some classical examples were proposed by Darwich and Pearl [7].
- 3.
In this work we will not investigate lexicographic contraction due to space constraints.
- 4.
- 5.
Notice that we are interpreting possible worlds in our model as epistemically possible worlds. As such, the universal modality, in our encoding, encodes epistemic necessity. Notice that we could introduce the modality \(\sim \) as epistemic indistinguishably instead of epistemic necessity, as done by Baltag and Smets [4], obtaining the same results presented here.
- 6.
Notice that, as commented before, Proposition 6 can be replicated for any postulate investigated in this work. As such, given a class of models \(\mathcal {M}\) satisfying the characterizing formula restriction, the class \(\mathcal {C}\) in Theorem 16 can be characterized as the intersection of all classes \(C_i\), where \(C_i\) is the class of all dynamic operators satisfying each axiom \(P_i\).
References
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: partial meet contraction and revision functions. J. Symb. Logic 50(2), 510–530 (1985)
Aucher, G.: Characterizing updates in dynamic epistemic logic. In: Twelfth International Conference on the Principles of Knowledge Representation and Reasoning (2010)
Baltag, A., Fiutek, V., Smets, S.: DDL as an “internalization” of dynamic belief revision. In: Trypuz, R. (ed.) Krister Segerberg on Logic of Actions. Outstanding Contributions to Logic, vol. 1, pp. 253–280. Springer, Dordrecht (2014). https://doi.org/10.1007/978-94-007-7046-1_12
Baltag, A., Smets, S.: A qualitative theory of dynamic interactive belief revision. In: Texts in Logic and Games, vol. 3, pp. 9–58 (2008)
Blackburn, P., van Benthem, J.F., Wolter, F.: Handbook of Modal Logic, vol. 3. Elsevier, Amsterdam (2006)
Cantwell, J.: Some logics of iterated belief change. Stud. Logica. 63(1), 49–84 (1999)
Darwiche, A., Pearl, J.: On the logic of iterated belief revision. Artif. Intell. 89(1), 1–29 (1997)
Girard, P., Seligman, J., Liu, F.: General dynamic dynamic logic. In: Bolander, T., Brauner, T., Ghilardi, S., Moss, L. (eds.) Advances in Modal Logic, vol. 9, pp. 239–260. College Publications, London (2012)
Girard, P.: Modal logic for belief and preference change. Ph.D. thesis, Stanford University (2008)
Girard, P., Rott, H.: Belief revision and dynamic logic. In: Baltag, A., Smets, S. (eds.) Johan van Benthem on Logic and Information Dynamics. OCL, vol. 5, pp. 203–233. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-06025-5_8
Grove, A.: Two modelings for theory change. J. Philos. Logic 17(2), 157–170 (1988)
Jin, Y., Thielscher, M.: Iterated belief revision, revised. Artif. Intell. 171(1), 1–18 (2007)
Lindström, S., Rabinowicz, W.: DDL unlimited: dynamic doxastic logic for introspective agents. Erkenntnis 50(2), 353–385 (1999)
Liu, F.: Reasoning About Preference Dynamics, vol. 354. Springer, Dordrecht (2011). https://doi.org/10.1007/978-94-007-1344-4
Moss, L.S.: Finite models constructed from canonical formulas. J. Philos. Logic 36(6), 605–640 (2007)
Nayak, A., Goebel, R., Orgun, M., Pham, T.: Taking Levi Identity seriously: a plea for iterated belief contraction. In: Lang, J., Lin, F., Wang, J. (eds.) KSEM 2006. LNCS (LNAI), vol. 4092, pp. 305–317. Springer, Heidelberg (2006). https://doi.org/10.1007/11811220_26
Nayak, A.C., Pagnucco, M., Peppas, P.: Dynamic belief revision operators. Artif. Intell. 146(2), 193–228 (2003)
Ramachandran, R., Nayak, A.C., Orgun, M.A.: Three approaches to iterated belief contraction. J. Philos. Logic 41(1), 115–142 (2012)
Rott, H.: Two dogmas of belief revision. J. Philos. 97(9), 503–522 (2000)
Rott, H.: Shifting priorities: simple representations for twenty-seven iterated theory change operators. In: Makinson, D., Malinowski, J., Wansing, H. (eds.) Towards Mathematical Philosophy. Trends in Logic, vol. 28, pp. 269–296. Springer, Dordrecht (2009). https://doi.org/10.1007/978-1-4020-9084-4_14
Segerberg, K.: Two traditions in the logic of belief: bringing them together. In: Ohlbach, H.J., Reyle, U. (eds.) Logic, Language and Reasoning. Trends in Logic (Studia Logica Library), vol. 5, pp. 135–147. Springer, Dordrecht (1999). https://doi.org/10.1007/978-94-011-4574-9_8
Souza, M.: Choices that make you change your mind: a dynamic epistemic logic approach to the semantics of BDI agent programming languages. Ph.D. thesis, Universidade Federal do Rio Grande do Sul (2016)
Souza, M., Moreira, A., Vieira, R., Meyer, J.J.C.: Preference and priorities: a study based on contraction. In: KR 2016, pp. 155–164. AAAI Press (2016)
Van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Classical Logics 17(2), 129–155 (2007)
Van Benthem, J.: Two logical faces of belief revision. In: Trypuz, R. (ed.) Krister Segerberg on Logic of Actions. Outstanding Contributions to Logic, vol. 1, pp. 281–300. Springer, Dordrecht (2014). https://doi.org/10.1007/978-94-007-7046-1_13
Van Benthem, J., Girard, P., Roy, O.: Everything else being equal: a modal logic for ceteris paribus preferences. J. Philos. Logic 38(1), 83–125 (2009)
Van Benthem, J., Grossi, D., Liu, F.: Priority structures in deontic logic. Theoria 80(2), 116–152 (2014)
Van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. J. Appl. Non-Classical Logics 17(2), 157–182 (2007)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Souza, M., Moreira, Á., Vieira, R. (2018). Dynamic Preference Logic as a Logic of Belief Change. In: Madeira, A., Benevides, M. (eds) Dynamic Logic. New Trends and Applications. DALI 2017. Lecture Notes in Computer Science(), vol 10669. Springer, Cham. https://doi.org/10.1007/978-3-319-73579-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-73579-5_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73578-8
Online ISBN: 978-3-319-73579-5
eBook Packages: Computer ScienceComputer Science (R0)