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22A note on the existence of ratifiable actsReview of Symbolic Logic 13 (3): 503-508. 2020.Sufficient conditions are given under which ratifiable acts exist.
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416Graded Causation and DefaultsBritish Journal for the Philosophy of Science 66 (2): 413-457. 2015.Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also suggested that an appeal to such factors can help deal with problems facing existing accounts of actual causation. This article develops a flexible formal framework for incorporating defaults, typicality, and normality into an account of actual causation. The resu…Read more
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78Updating Probability: Tracking Statistics as CriterionBritish Journal for the Philosophy of Science. 2016.ABSTRACT 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 …Read more
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99Reasoning about knowledgeMIT Press. 2003.Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed ...
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1Actual causation and the art of modelingIn Halpern Joseph & Hitchcock Christopher (eds.), Causality, Probability, and Heuristics: A Tribute to Judea Pearl, College Publications. pp. 383-406. 2010.
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87Compact Representations of Extended Causal ModelsCognitive Science 37 (6): 986-1010. 2013.Judea Pearl (2000) was the first to propose a definition of actual causation using causal models. A number of authors have suggested that an adequate account of actual causation must appeal not only to causal structure but also to considerations of normality. In Halpern and Hitchcock (2011), we offer a definition of actual causation using extended causal models, which include information about both causal structure and normality. Extended causal models are potentially very complex. In this study…Read more
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55Appropriate causal models and the stability of causationReview of Symbolic Logic 9 (1): 76-102. 2016.
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30Sufficient conditions for causality to be transitivePhilosophy of Science 83 (2): 213-226. 2016.Natural conditions are provided that are sufficient to ensure that causality as defined by approaches that use counterfactual dependence and structural equations will be transitive.
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21Actual CausalityMIT Press. 2016.A new approach for defining causality and such related notions as degree of responsibility, degrees of blame, and causal explanation. Causality plays a central role in the way people structure the world; we constantly seek causal explanations for our observations. But what does it even mean that an event C "actually caused" event E? The problem of defining actual causation goes beyond mere philosophical speculation. For example, in many legal arguments, it is precisely what needs to be establish…Read more
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46On the unusual effectiveness of logic in computer scienceBulletin of Symbolic Logic 7 (2): 213-236. 2001.In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed th…Read more
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57Evidence with uncertain likelihoodsSynthese 171 (1): 111-133. 2009.An agent often has a number of hypotheses, and must choose among them based on observations, or outcomes of experiments. Each of these observations can be viewed as providing evidence for or against various hypotheses. All the attempts to formalize this intuition up to now have assumed that associated with each hypothesis h there is a likelihood function μ h , which is a probability measure that intuitively describes how likely each observation is, conditional on h being the correct hypothesis.…Read more
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289Asymptotic conditional probabilities: The non-unary caseJournal of Symbolic Logic 61 (1): 250-276. 1996.Motivated by problems that arise in computing degrees of belief, we consider the problem of computing asymptotic conditional probabilities for first-order sentences. Given first-order sentences φ and θ, we consider the structures with domain {1,..., N} that satisfy θ, and compute the fraction of them in which φ is true. We then consider what happens to this fraction as N gets large. This extends the work on 0-1 laws that considers the limiting probability of first-order sentences, by considering…Read more
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100The Role of the Protocol in Anthropic ReasoningErgo: An Open Access Journal of Philosophy 2 195-206. 2015.I show how thinking in terms of the protocol used can help clarify problems related to anthropic reasoning and self-location, such as the Doomsday Argument and the Sleeping Beauty Problem.
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90Great Expectations. Part I: On the Customizability of Generalized Expected Utility (review)Theory and Decision 64 (1): 1-36. 2008.We propose a generalization of expected utility that we call generalized EU (GEU), where a decision maker’s beliefs are represented by plausibility measures and the decision maker’s tastes are represented by general (i.e., not necessarily real-valued) utility functions. We show that every agent, “rational” or not, can be modeled as a GEU maximizer. We then show that we can customize GEU by selectively imposing just the constraints we want. In particular, we show how each of Savage’s postulates c…Read more
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Presburger arithmetic with uninterpreted function symbols is 1 1-completeJournal of Symbolic Logic 56 637-642. 1991.
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417Minimizing regret in dynamic decision problemsTheory and Decision 81 (1): 123-151. 2016.The menu-dependent nature of regret-minimization creates subtleties when it is applied to dynamic decision problems. It is not clear whether forgone opportunities should be included in the menu. We explain commonly observed behavioral patterns as minimizing regret when forgone opportunities are present. If forgone opportunities are included, we can characterize when a form of dynamic consistency is guaranteed.
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130Defining knowledge in terms of belief: The modal logic perspectiveReview 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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289What is an inference rule?Journal of Symbolic Logic 57 (3): 1018-1045. 1992.What is an inference rule? This question does not have a unique answer. One usually finds two distinct standard answers in the literature; validity inference $(\sigma \vdash_\mathrm{v} \varphi$ if for every substitution $\tau$, the validity of $\tau \lbrack\sigma\rbrack$ entails the validity of $\tau\lbrack\varphi\rbrack)$, and truth inference $(\sigma \vdash_\mathrm{t} \varphi$ if for every substitution $\tau$, the truth of $\tau\lbrack\sigma\rbrack$ entails the truth of $\tau\lbrack\varphi\rbr…Read more
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128Should knowledge entail belief?Journal of Philosophical Logic 25 (5). 1996.The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have …Read more
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51Probability and conditionals: Belief revision and rational decisionPhilosophical Review 109 (2): 277-281. 2000.
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67From causal models to counterfactual structuresReview of Symbolic Logic 6 (2): 305-322. 2013.Galles & Pearl (l998) claimed that s [possible-worlds] framework.s framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pea…Read more
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436Causes and explanations: A structural-model approach. Part I: CausesBritish Journal for the Philosophy of Science 56 (4): 843-887. 2005.We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account.
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32Weighted sets of probabilities and minimax weighted expected regret: a new approach for representing uncertainty and making decisionsTheory and Decision 79 (3): 415-450. 2015.We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation …Read more
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77Maxmin weighted expected utility: a simpler characterizationTheory and Decision 80 (4): 581-610. 2016.Chateauneuf and Faro axiomatize a weighted version of maxmin expected utility over acts with nonnegative utilities, where weights are represented by a confidence function. We argue that their representation is only one of many possible, and we axiomatize a more natural form of maxmin weighted expected utility. We also provide stronger uniqueness results.
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64Decision Theory with Resource‐Bounded AgentsTopics in Cognitive Science 6 (2): 245-257. 2014.There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein (), charges an agent for doing costly computation; the second, initiated by Neyman (), does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in a d…Read more
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97Belief revision: A critique (review)Journal of Logic, Language and Information 8 (4): 401-420. 1999.We examine carefully the rationale underlying the approaches to belief change taken in the literature, and highlight what we view as methodological problems. We argue that to study belief change carefully, we must be quite explicit about the ontology or scenario underlying the belief change process. This is something that has been missing in previous work, with its focus on postulates. Our analysis shows that we must pay particular attention to two issues that have often been taken for granted: …Read more
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Areas of Specialization
Epistemology |
Areas of Interest
Epistemology |
Logic and Philosophy of Logic |