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52Presburger arithmetic with unary predicates is Π11 completeJournal of Symbolic Logic 56 (2). 1991.We give a simple proof characterizing the complexity of Presburger arithmetic augmented with additional predicates. We show that Presburger arithmetic with additional predicates is Π 1 1 complete. Adding one unary predicate is enough to get Π 1 1 hardness, while adding more predicates (of any arity) does not make the complexity any worse
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45Intransitivity and vagueness - corrigendumReview of Symbolic Logic 2 (3): 591-591. 2009.doi: 10.1017/S1755020308090084, Published by Cambridge University Press 31 March 2009 in Volume 1, Number 4 of The Review of Symbolic Logic . On page 541, in the 4 th paragraph, in line 7, an error occurred. The sentence should correctly read: “For all worlds w , if there is more than one grain of sand in the pile in w , then there is still more than one grain of sand after removing one grain of sand.”
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Characterizing and reasoning about probabilistic and non-probabilistic expectationJ. Acm 54 (3): 15. 2007.
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58Reasoning about Knowledge: A Response by the Authors (review)Minds and Machines 7 (1): 113-113. 1997.
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3Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous SystemsIn Tamar Szabo Gendler & John Hawthorne (eds.), Proceedings of the Twentieth Conference on Uncertainty in Ai, Oxford University Press. pp. 111-142. 2004.
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45On 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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283Asymptotic 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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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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99The 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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Presburger arithmetic with uninterpreted function symbols is 1 1-completeJournal of Symbolic Logic 56 637-642. 1991.
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407Minimizing 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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283What 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
Ithaca, New York, United States of America
Areas of Specialization
Epistemology |
Areas of Interest
Epistemology |
Logic and Philosophy of Logic |