Qualitative probabilities for default reasoning, belief revision, and causal modeling
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Artificial Intelligence 84:57-112 (1996)
This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change.
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Niels Skovgaard‐Olsen (2016). Ranking Theory and Conditional Reasoning. Cognitive Science 40 (4):848-880.
Franz Huber (forthcoming). Why Follow the Royal Rule? Synthese:1-26.
Emiliano Lorini (2013). On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective Attitudes. [REVIEW] Journal of Philosophical Logic 42 (6):863-904.
Paul D. Thorn & Gerhard Schurz (2014). A Utility Based Evaluation of Logico-Probabilistic Systems. Studia Logica 102 (4):867-890.
Horacio Arló-Costa & Richmond H. Thomason (2001). Iterative Probability Kinematics. Journal of Philosophical Logic 30 (5):479-524.
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