•  13
    The bottleneck may be the solution, not the problem
    with Arnon Lotem, Oren Kolodny, Luca Onnis, and Shimon Edelman
    Behavioral and Brain Sciences 39. 2016.
    As a highly consequential biological trait, a memory “bottleneck” cannot escape selection pressures. It must therefore co-evolve with other cognitive mechanisms rather than act as an independent constraint. Recent theory and an implemented model of language acquisition suggest that a limit on working memory may evolve to help learning. Furthermore, it need not hamper the use of language for communication.
  •  59
    Reasoning about Knowledge: A Response by the Authors (review)
    with Ronald Fagin, Yoram Moses, and Moshe Y. Vardi
    Minds and Machines 7 (1): 113-113. 1997.
  •  46
    On the unusual effectiveness of logic in computer science
    with Robert Harper, Neil Immerman, Phokion G. Kolaitis, Moshe Y. Vardi, and Victor Vianu
    Bulletin 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
  •  32
    Evidence with uncertain likelihoods
    with Riccardo Pucella
    Synthese 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
  •  290
    Asymptotic conditional probabilities: The non-unary case
    with Adam J. Grove and Daphne Koller
    Journal 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
  •  90
    Great Expectations. Part I: On the Customizability of Generalized Expected Utility (review)
    with Francis C. Chu
    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
  •  100
    The Role of the Protocol in Anthropic Reasoning
    Ergo: 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.
  •  418
    Minimizing regret in dynamic decision problems
    with Samantha Leung
    Theory 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.
  •  130
    Defining knowledge in terms of belief: The modal logic perspective
    with Dov Samet and Ella Segev
    Review 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
  •  289
    What is an inference rule?
    with Ronald Fagin and Moshe Y. Vardi
    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
  •  128
    Should 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
  •  67
    From causal models to counterfactual structures
    Review 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
  •  437
    Causes and explanations: A structural-model approach. Part I: Causes
    with Judea Pearl
    British 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.