Gregory Wheeler

Frankfurt School Of Finance And Management
  •  105
    Summary. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
  •  105
    A Gentle Approach to Imprecise Probabilities
    In Thomas Augustin, Fabio Gagliardi Cozman & Gregory Wheeler (eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld, Springer. pp. 37-67. 2022.
    The field of of imprecise probability has matured, in no small part because of Teddy Seidenfeld’s decades of original scholarship and essential contributions to building and sustaining the ISIPTA community. Although the basic idea behind imprecise probability is (at least) 150 years old, a mature mathematical theory has only taken full form in the last 30 years. Interest in imprecise probability during this period has also grown, but many of the ideas that the mature theory serves can be diffic…Read more
  •  105
    Causation, Association, and Confirmation
    with Richard Scheines
    In Stephan Hartmann, Marcel Weber, Wenceslao Gonzalez, Dennis Dieks & Thomas Uebe (eds.), Explanation, Prediction, and Confirmation: New Trends and Old Ones Reconsidered, Springer. pp. 37--51. 2010.
    Many philosophers of science have argued that a set of evidence that is "coherent" confirms a hypothesis which explains such coherence. In this paper, we examine the relationships between probabilistic models of all three of these concepts: coherence, confirmation, and explanation. For coherence, we consider Shogenji's measure of association (deviation from independence). For confirmation, we consider several measures in the literature, and for explanation, we turn to Causal Bayes Nets and resor…Read more
  •  90
    Modeling of Phenomena and Dynamic Logic of Phenomena
    with Boris Kovalerchuk and Leonid Perlovsky
    Journal of Applied Non-Classical Logic 22 (1): 1-82. 2011.
    Modeling a complex phenomena such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, a problem or some theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. Th…Read more
  •  83
    NO Revision and NO Contraction
    with Marco Alberti
    Minds and Machines 21 (3): 411-430. 2011.
    One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an an…Read more
  •  82
    Explaining the limits of Olsson's impossibility result
    Southern Journal of Philosophy 50 (1): 136-150. 2012.
    In his groundbreaking book, Against Coherence (2005), Erik Olsson presents an ingenious impossibility theorem that appears to show that there is no informative relationship between probabilistic measures of coherence and higher likelihood of truth. Although Olsson's result provides an important insight into probabilistic models of epistemological coherence, the scope of his negative result is more limited than generally appreciated. The key issue is the role conditional independence conditions p…Read more
  •  73
    The structural view of rational acceptance is a commitment to developing a logical calculus to express rationally accepted propositions sufficient to represent valid argument forms constructed from rationally accepted formulas. This essay argues for this project by observing that a satisfactory solution to the lottery paradox and the paradox of the preface calls for a theory that both (i) offers the facilities to represent accepting less than certain propositions within an interpreted artificial…Read more
  •  70
    Humanists and Scientists
    The Reasoner 1 (1). 2007.
    C.P. Snow observed that universities are largely made up of two broad types of people, literary intellectuals and scientists, yet a typical individual of each type is barely able, if able at all, to communicate with his counterpart. Snow's observation, popularized in his 1959 lecture Two Cultures and the Scientific Revolution (reissued by Cambridge 1993), goes some way to explaining the two distinct cultures one hears referred to as "the humanities" and "the sciences." Snow's lecture is a study …Read more
  •  67
    Applied Logic without Psychologism
    Studia Logica 88 (1): 137-156. 2008.
    Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invarianti…Read more
  •  62
    “Visualizing High-Dimensional Loss Landscapes with Hessian Directions”
    with Lucas Böttcher
    Journal of Statistical Mechanics: Theory and Experiment. forthcoming.
    Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the …Read more
  •  61
    A Resource-bounded Default Logic
    In J. Delgrande & T. Schaub (eds.), Proceedings of NMR 2004, Aaai. 2004.
    This paper presents statistical default logic, an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, including hypothesis testing and the estimation of a populations mean, variance and proportions. The logic replaces classical defaults with ordered pairs consisting of a Reiter default in the first coordinate and a real number within the unit interval in the second coordinate. This real number represents a…Read more
  •  61
    AGM Belief Revision in Monotone Modal Logics
    LPAR 2010 Short Paper Proceedings. 2010.
    Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. This paper defines AGM revision operators on several first-order monotonic modal correspondents, where each first-order correspondence language is defined by Marc Pauly’s version of the van Benthem characterization theorem for monotone modal logic. A revision problem expressed in a monotone modal system is translated into first-orde…Read more
  •  60
    New Challenges to Philosophy of Science (edited book)
    with Hanne Andersen, Dennis Dieks, Wenceslao J. Gonzalez, and Thomas Uebel
    Springer Verlag. 2013.
    This fourth volume of the Programme “The Philosophy of Science in a European Perspective” deals with new challenges in this field. In this regard, it seeks to broaden the scope of the philosophy of science in two directions. On the one hand, ...
  •  54
    An implementation of statistical default logic
    with Carlos Damasio
    In Jose Alferes & Joao Leite (eds.), Logics in Artificial Intelligence (JELIA 2004), Springer. 2004.
    Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population‘s mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniqu…Read more
  •  51
    Rational acceptance and conjunctive/disjunctive absorption
    Journal of Logic, Language and Information 15 (1-2): 49-63. 2006.
    A bounded formula is a pair consisting of a propositional formula φ in the first coordinate and a real number within the unit interval in the second coordinate, interpreted to express the lower-bound probability of φ. Converting conjunctive/disjunctive combinations of bounded formulas to a single bounded formula consisting of the conjunction/disjunction of the propositions occurring in the collection along with a newly calculated lower probability is called absorption. This paper introduces two …Read more
  •  48
    Erratum to: Introduction
    Synthese 187 (2): 815-815. 2012.
  •  30
    Epistemology and artificial intelligence
    Journal of Applied Logic 2 (4): 469-493. 2004.
  •  29
    Conditionals and Testimony
    with Stephan Hartmann, Peter J. Collins, Karolina Krzyżanowska, and Ulrike Hahn
    Cognitive Psychology 122. 2020.
    Conditionals and conditional reasoning have been a long-standing focus of research across a number of disciplines, ranging from psychology through linguistics to philosophy. But almost no work has concerned itself with the question of how hearing or reading a conditional changes our beliefs. Given that we acquire much—perhaps most—of what we believe through the testimony of others, the simple matter of acquiring conditionals via others’ assertion of a conditional seems integral to any full under…Read more
  •  29
    Logical relations in a statistical problem
    with Jon Williamson, Jan-Willem Romeijn, and Rolf Haenni
    In Benedikt Lowe, Jan-Willem Romeijn & Eric Pacuit (eds.), Foundations of the Formal Sciences Vi: Probabilistic Reasoning and Reasoning With Probabilities. Studies in Logic, College Publications. 2008.
    This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The f…Read more
  •  25
    Combining Probability and Logic
    with Fabio Cozman, Rolf Haenni, Jan-Willem Romeijn, Federica Russo, and Jon Williamson
    Journal of Applied Logic 7 (2): 131-135. 2009.
  •  24
    Announcement
    Minds and Machines 24 (4): 477-477. 2014.
  •  21
    Modelling phenomena and dynamic logic of phenomena
    with Boris Kovalerchuk and Leonid Perlovsky
    Journal of Applied Non-Classical Logics 22 (1-2): 53-82. 2012.
    Modelling a complex phenomenon such as the mind presents tremendous computational complexity challenges. Modelling field theory addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logi…Read more
  •  18
    Recent advances in philosophy, artificial intelligence, mathematical psychology, and the decision sciences have brought a renewed focus to the role and interpretation of probability in theories of uncertain reasoning. Henry E. Kyburg, Jr. has long resisted the now dominate Bayesian approach to the role of probability in scientific inference and practical decision. The sharp contrasts between the Bayesian approach and Kyburg's program offer a uniquely powerful framework within which to study seve…Read more
  •  15
    A sound and complete axiomatization of two philosophy tabloids is given, Leiter Logic (KB) and Deontic Leiter Logic (KDB), in single agent format, the latter of which can be extended to Shame Game Logic for multiple players. The (B) schema captures the mechanism of tabloid inference, illustrating the perils of interpreting a provability operator as an epistemic modal. To mark this hazard, and to preserve Brouwer's good name, the (B) schema interpreted to govern epistemic modals should be called …Read more