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Thomas F. Icard [10]Thomas Icard [9]
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Thomas Icard
Stanford University
  1. Why Be Random?Thomas Icard - forthcoming - Mind:fzz065.
    When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both precise (...)
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  2. Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy.Thomas Icard - forthcoming - Journal of Mathematical Psychology 95.
  3. Subjective Probability as Sampling Propensity.Thomas Icard - 2016 - Review of Philosophy and Psychology 7 (4):863-903.
    Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work in neuroscience and (...)
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  4. Normality and Actual Causal Strength.Thomas F. Icard, Jonathan F. Kominsky & Joshua Knobe - 2017 - Cognition 161:80-93.
    Existing research suggests that people's judgments of actual causation can be influenced by the degree to which they regard certain events as normal. We develop an explanation for this phenomenon that draws on standard tools from the literature on graphical causal models and, in particular, on the idea of probabilistic sampling. Using these tools, we propose a new measure of actual causal strength. This measure accurately captures three effects of normality on causal judgment that have been observed in existing studies. (...)
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  5.  97
    Moorean Phenomena in Epistemic Logic.Wesley H. Holliday & Thomas F. Icard - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic 8. College Publications. pp. 178-199.
    A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...)
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  6. On the Instrumental Value of Hypothetical and Counterfactual Thought.Thomas Icard, Fiery Cushman & Joshua Knobe - 2018 - Proceedings of the 40th Annual Conference of the Cognitive Science Society.
  7. Measure Semantics and Qualitative Semantics for Epistemic Modals.Wesley H. Holliday & Thomas F. Icard - 2013 - Proceedings of SALT 23:514-534.
    In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown to result from Kratzer’s (1991) semantics by Yalcin (2006, 2009, 2010). In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011), based on finitely additive probability measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991). All of these (...)
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  8. A Note on Cancellation Axioms for Comparative Probability.Matthew Harrison-Trainor, Wesley H. Holliday & Thomas F. Icard - 2016 - Theory and Decision 80 (1):159-166.
    We prove that the generalized cancellation axiom for incomplete comparative probability relations introduced by Rios Insua and Alon and Lehrer is stronger than the standard cancellation axiom for complete comparative probability relations introduced by Scott, relative to their other axioms for comparative probability in both the finite and infinite cases. This result has been suggested but not proved in the previous literature.
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  9.  81
    A Uniform Logic of Information Dynamics.Wesley H. Holliday, Tomohiro Hoshi & Thomas F. Icard - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic 9. College Publications. pp. 348-367.
    Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a non-uniform dynamic epistemic logic is Public Announcement Logic (PAL), and a well-known open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely (...)
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  10.  49
    Bayes, Bounds, and Rational Analysis.Thomas F. Icard - 2018 - Philosophy of Science 85 (1):79-101.
    While Bayesian models have been applied to an impressive range of cognitive phenomena, methodological challenges have been leveled concerning their role in the program of rational analysis. The focus of the current article is on computational impediments to probabilistic inference and related puzzles about empirical confirmation of these models. The proposal is to rethink the role of Bayesian methods in rational analysis, to adopt an independently motivated notion of rationality appropriate for computationally bounded agents, and to explore broad conditions under (...)
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  11.  25
    Pragmatic Considerations on Comparative Probability.Thomas F. Icard - 2016 - Philosophy of Science 83 (3):348-370.
    While pragmatic arguments for numerical probability axioms have received much attention, justifications for axioms of qualitative probability have been less discussed. We offer an argument for the requirement that an agent’s qualitative judgments be probabilistically representable, inspired by, but importantly different from, the Money Pump argument for transitivity of preference and Dutch book arguments for quantitative coherence. The argument is supported by a theorem, to the effect that a subject is systematically susceptible to dominance given her preferred acts, if and (...)
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  12.  27
    Indicative Conditionals and Dynamic Epistemic Logic.Wesley H. Holliday & Thomas Icard - 2017 - Proceedings of the Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017.
    Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...)
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  13.  4
    Iterating Semantic Automata.Shane Steinert-Threlkeld & Thomas F. Icard - 2013 - Linguistics and Philosophy 36 (2):151-173.
    The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic results on semantic automata in a modern style, we present the first application of semantic automata to polyadic quantification, exhibiting automata for iterated quantifiers. We also discuss the role of semantic automata in (...)
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  14.  58
    Inclusion and Exclusion in Natural Language.Thomas F. Icard - 2012 - Studia Logica 100 (4):705-725.
    We present a formal system for reasoning about inclusion and exclusion in natural language, following work by MacCartney and Manning. In particular, we show that an extension of the Monotonicity Calculus, augmented by six new type markings, is sufficient to derive novel inferences beyond monotonicity reasoning, and moreover gives rise to an interesting logic of its own. We prove soundness of the resulting calculus and discuss further logical and linguistic issues, including a new connection to the classes of weak, strong, (...)
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  15.  45
    Inferring Probability Comparisons.Matthew Harrison-Trainor, Wesley H. Holliday & Thomas Icard - forthcoming - Mathematical Social Sciences.
    The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≥ on events that does not preclude a probabilistic interpretation, in the sense that ≥ has extensions that are probabilistically representable, we characterize the extension ≥+ of ≥ that is exactly the intersection of all probabilistically representable extensions of (...)
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  16.  28
    Axiomatization in the Meaning Sciences.Wesley H. Holliday & Thomas Icard - 2018 - In Derek Ball & Brian Rabern (eds.), The Science of Meaning: Essays on the Metatheory of Natural Language Semantics. Oxford, UK: Oxford University Press. pp. 73-97.
    While much of semantic theorizing is based on intuitions about logical phenomena associated with linguistic constructions—phenomena such as consistency and entailment—it is rare to see axiomatic treatments of linguistic fragments. Given a fragment interpreted in some class of formally specified models, it is often possible to ask for a characterization of the reasoning patterns validated by the class of models. Axiomatizations provide such a characterization, often in a perspicuous and efficient manner. In this paper, we highlight some of the benefits (...)
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  17.  33
    Provability and Interpretability Logics with Restricted Realizations.Thomas F. Icard & Joost J. Joosten - 2012 - Notre Dame Journal of Formal Logic 53 (2):133-154.
    The provability logic of a theory $T$ is the set of modal formulas, which under any arithmetical realization are provable in $T$. We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$. We make an analogous modification for interpretability logics. We first study provability logics with restricted realizations and show that for various natural candidates of $T$ and restriction set $\Gamma$, the result is the logic of linear frames. However, for the theory Primitive (...)
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  18.  6
    Expectations Affect Physical Causation Judgments.Tobias Gerstenberg & Thomas Icard - forthcoming - Journal of Experimental Psychology: General.
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  19. Exclusion and Containment in Natural Language.Thomas Icard - forthcoming - Studia Logica.