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Applied Logics Based on Plausibility for Reasoning about Uncertainty

Equipe et encadrants
Département / Equipe: 
Site Web Equipe: 
Directeur de thèse
Olivier Ridoux
Co-directeur(s), co-encadrant(s)
Guillaume Aucher
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Guillaume Aucher
+33 (0) 2 99 84 22 60
Sujet de thèse

Context :

Numerous formalisms have been introduced in Artificial Intelligence to represent the uncertainty that an agent or a group of agents have about a given situation: probability measures, possibility measures, ranking functions, preferential structures, just to name a few. Friedman and Halpern (2001) showed that all these formalisms are in fact instances of a more general formalism: plausibility measures. The way the agents update their uncertainty about the situation after the occurrence of events or after incoming information is formalized by means of some sort of conditional plausibility measures.

Independently from this research line, numerous logics for reasoning about uncertainty have been developped in a research area known as Dynamic Epistemic Logic (DEL). Many of these logics are extensions of epistemic logic or modal logic and they include sometimes some refined representation of uncertainty based on probability or ranking functions for example. Moreover, they often deal with situations that involve multiple agents, which are more difficult to handle and to reason about in general.

Objectives :

  1. The first objective is to reformulate the extensions of DEL with probability, ranking functions, etc. within the framework of Friedman and Halpern (2001) based on conditional plausibility measures. In particular, this implies a reformulation of the various update mechanisms that have been proposed in DEL as some sorts of conditional updates, such as public announcements to all agents, private announcements to some agents, semi-private announcements, deceptions, lies, etc. This will give rise to a family of logics which are all extensions of the same generic logic whose semantics is based on conditional plausibility measures.
  2. The second objective is to develop a correspondence theory that would relate the properties of these update mechanisms expressed in first-order logic with axioms or inference rules of the generic logical framework based on conditional plausibility measures developed in the first part of the PhD. This correspondence theory would allow to characterize the different update mechanisms in terms of axioms or inference rules and it would provide means in order to define actual update mechanisms.
  3. The third objective is to specify, design, develop and test a software tool that would be based on the generic logic developed in the first part of the PhD and the correspondence theory developed in the second part of the PhD. This software tool would allow a user to answer and solve some decision problems (such as theorem proving or model checking) related to a specific logic defined by the user and based on the various properties elicited and identified in the second part of the PhD and that extends the generic logic elicited in the first part of the PhD.

The modularity and versatility of the software tool, which is not related to a single logic but to a family of logics, should ease the transfer and usability of the important amount of work that has been pursued in logic for reasoning about uncertainty in the last 30 years. 

  • Friedman, N. and Halpern, J. Y. (2001). Plausibility measures and default​ reasoning. Journal of the ACM, 48(4):648–685.
  • Friedman, N., and J. Y. Halpern (1997). "Modeling Belief in Dynamic Systems, Part I: Foundations." Artificial Intelligence 95: 257 – 316.
  • Aucher, G. (2003). A Combined System for Update Logic and Belief Revision.​ Master’s Thesis. ILLC University of Amsterdam.
  • Aucher, G. (2007). "Interpreting an Action from What We Perceive and What We​ Expect." Journal of Applied Non-Classical Logics 17: 9 – 38.
  • Baltag, A., and S. Smets (2008). "A Qualitative Theory of Dynamic Interactive​ Belief Revision." Logic and the Foundations of Game and Decision Theory (LOFT7). Eds. G. Bonanno, W. van der Hoek, and M. Wooldridge. Amsterdam:​ Amsterdam University Press. 11 – 58. Vol. 3 of Texts in Logic and Games.
  • Van Benthem, J. (2007). "Dynamic Logic for Belief Revision." Journal of Applied​ Non-Classical Logics 17.2: 129 – 155.
Début des travaux: 
September 2017
Mots clés: 
Applied Logic, Reasoning about Uncertainty, Dynamic Epistemic Logic, Plausibility Measures
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