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14Defining knowledge in terms of belief: The modal logic perspective: Defining knowledge in terms of beliefReview of Symbolic Logic 2 (3): 469-487. 2009.The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, the…Read more
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10On definability in multimodal logic: On definability in multimodal logicReview of Symbolic Logic 2 (3): 451-468. 2009.Three notions of definability in multimodal logic are considered. Two are analogous to the notions of explicit definability and implicit definability introduced by Beth in the context of first-order logic. However, while by Beth’s theorem the two types of definability are equivalent for first-order logic, such an equivalence does not hold for multimodal logics. A third notion of definability, reducibility, is introduced; it is shown that in multimodal logics, explicit definability is equivalent …Read more
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20Probabilistic and Causal Inference: the Works of Judea Pearl (edited book)ACM Books. 2022.Professor Judea Pearl won the 2011 Turing Award "for fundamental contributions to artificial intelligence through the development of a calculus for probabilistic and causal reasoning." This book contains the original articles that led to the award, as well as other seminal works, divided into four parts: heuristic search, probabilistic reasoning, causality, first period (1988-2001), and causality, recent period (2002-2020). Each of these parts starts with an introduction written by Judea Pearl. …Read more
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18A Causal Analysis of HarmAdvances in Neural Information Processing Systems 35. 2022.As autonomous systems rapidly become ubiquitous, there is a growing need for a legal and regulatory framework to address when and how such a system harms someone. There have been several attempts within the philosophy literature to define harm, but none of them has proven capable of dealing with with the many examples that have been presented, leading some to suggest that the notion of harm should be abandoned and "replaced by more well-behaved notions". As harm is generally something that is ca…Read more
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16Approximate Causal AbstractionProceedings of the 35Th Conference on Uncertainty in Artificial Intelligence. 2019.Scientific models describe natural phenomena at different levels of abstraction. Abstract descriptions can provide the basis for interventions on the system and explanation of observed phenomena at a level of granularity that is coarser than the most fundamental account of the system. Beckers and Halpern (2019), building on work of Rubenstein et al. (2017), developed an account of abstraction for causal models that is exact. Here we extend this account to the more realistic case where an abstrac…Read more
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24Causal Models with ConstraintsProceedings of the 2Nd Conference on Causal Learning and Reasoning. 2023.Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables LDL, HDL, and TOT that represent the level of low-density lipoprotein cholesterol, the level of lipoprotein high-density lipoprotein cholesterol, and total cholesterol level, with the relation LDL+HDL=TOT. This cannot be done in standard causal models, becaus…Read more
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10Abstracting Causal ModelsProceedings of the 33Rd Aaai Conference on Artificial Intelligence. 2019.We consider a sequence of successively more restrictive definitions of abstraction for causal models, starting with a notion introduced by Rubenstein et al. (2017) called exact transformation that applies to probabilistic causal models, moving to a notion of uniform transformation that applies to deterministic causal models and does not allow differences to be hidden by the "right" choice of distribution, and then to abstraction, where the interventions of interest are determined by the map from…Read more
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21Zero-one laws for modal logic (vol 69, pg 157, 1994)Annals of Pure and Applied Logic 69 (2-3): 281-283. 1994.We show that a 0–1 law holds for propositional modal logic, both for structure validity and frame validity. In the case of structure validity, the result follows easily from the well-known 0–1 law for first-order logic. However, our proof gives considerably more information. It leads to an elegant axiomatization for almost-sure structure validity and to sharper complexity bounds. Since frame validity can be reduced to a Π11 formula, the 0–1 law for frame validity helps delineate when 0–1 laws ex…Read more
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Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous SystemsIn Tamar Szabo Gendler & John Hawthorne (eds.), Oxford Studies in Epistemology Volume 1, Oxford University Press Uk. 2005.
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21Dealing with logical omniscience: Expressiveness and pragmaticsArtificial Intelligence 175 (1): 220-235. 2011.
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13From statistical knowledge bases to degrees of beliefArtificial Intelligence 87 (1-2): 75-143. 1996.
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6Levesque's axiomatization of only knowing is incompleteArtificial Intelligence 74 (2): 381-387. 1995.
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13A nonstandard approach to the logical omniscience problemArtificial Intelligence 79 (2): 203-240. 1995.
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3Erratum to ‘A logic for reasoning about ambiguity’ [Artificial Intelligence 209 (2014) 1–10]Artificial Intelligence 212 (C): 158. 2014.
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9Great expectations. Part II: generalized expected utility as a universal decision ruleArtificial Intelligence 159 (1-2): 207-229. 2004.
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14Two views of belief: belief as generalized probability and belief as evidenceArtificial Intelligence 54 (3): 275-317. 1992.
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44A guide to completeness and complexity for modal logics of knowledge and beliefArtificial Intelligence 54 (3): 319-379. 1992.
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9Modeling belief in dynamic systems, part I: FoundationsArtificial Intelligence 95 (2): 257-316. 1997.
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6The effect of bounding the number of primitive propositions and the depth of nesting on the complexity of modal logicArtificial Intelligence 75 (2): 361-372. 1995.
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19Reasoning about noisy sensors and effectors in the situation calculusArtificial Intelligence 111 (1-2): 171-208. 1999.
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10Updating Probability: Tracking Statistics as CriterionBritish Journal for the Philosophy of Science 68 (3): 725-743. 2017.For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex co…Read more
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Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous SystemsOxford Studies in Epistemology 1. 2006.
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Why Bother with Syntax?In Ramaswamy Ramanujam, Lawrence Moss & Can Başkent (eds.), Rohit Parikh on Logic, Language and Society, Springer Verlag. 2017.
Ithaca, New York, United States of America
Areas of Specialization
Epistemology |
Areas of Interest
Epistemology |
Logic and Philosophy of Logic |