Frankfurt School Of Finance And Management
  •  25
    Traditionally, logic has been the dominant formal method within philosophy. Are logical methods still dominant today, or have the types of formal methods used in philosophy changed in recent times? To address this question, we coded a sample of philosophy papers from the late 2000s and from the late 2010s for the formal methods they used. The results indicate that (a) the proportion of papers using logical methods remained more or less constant over that time period but (b) the proportion of pap…Read more
  •  34
    Moving Beyond Sets of Probabilities
    Statistical Science 36 (2): 201--204. 2021.
    The theory of lower previsions is designed around the principles of coherence and sure-loss avoidance, thus steers clear of all the updating anomalies highlighted in Gong and Meng's "Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradox" except dilation. In fact, the traditional problem with the theory of imprecise probability is that coherent inference is too complicated rather than unsettling. Progress has been made simplifying coherent inference by demotin…Read more
  •  10
    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
  •  172
    A sound and complete axiomatization of two tabloid blogs is presented, Leiter Logic (KB) and Deontic Leiter Logic (KDB), the latter of which can be extended to Shame Game Logic for multiple agents. The (B) schema describes the mechanism behind this class of tabloids, and illustrates the perils of interpreting a provability operator as an epistemic modal. To mark this difference, and to avoid sullying Brouwer's good name, the (B) schema for epistemic modals should be called the Blog Schema.
  •  32
    In this paper, we present a new semantic challenge to the moral error theory. Its first component calls upon moral error theorists to deliver a deontic semantics that is consistent with the error-theoretic denial of moral truths by returning the truth-value false to all moral deontic sentences. We call this the ‘consistency challenge’ to the moral error theory. Its second component demands that error theorists explain in which way moral deontic assertions can be seen to differ in meaning despite…Read more
  •  106
    Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.
  •  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
  •  167
    In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other
  •  101
    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.
  •  21
    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.
  •  664
    Coherence and Confirmation through Causation
    with Richard Scheines
    Mind 122 (485): 135-170. 2013.
    Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be …Read more
  •  98
    Error statistics and Duhem's problem
    Philosophy of Science 67 (3): 410-420. 2000.
    No one has a well developed solution to Duhem's problem, the problem of how experimental evidence warrants revision of our theories. Deborah Mayo proposes a solution to Duhem's problem in route to her more ambitious program of providing a philosophical account of inductive inference and experimental knowledge. This paper is a response to Mayo's Error Statistics (ES) program, paying particular attention to her response to Duhem's problem. It turns out that Mayo's purported solution to Duhem's pro…Read more
  •  64
    Dilation and Asymmetric Relevance
    Proceedings in Machine Learning Research, Vol. 103. 2019.
    A characterization result of dilation in terms of positive and negative association admits an extremal counterexample, which we present together with a minor repair of the result. Dilation may be asymmetric whereas covariation itself is symmetric. Dilation is still characterized in terms of positive and negative covariation, however, once the event to be dilated has been specified.
  •  9
    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
  •  80
    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
  •  481
    Is there a logic of information?
    Journal of Theoretical and Applied Artificial Intelligence 27 (1): 95-98. 2015.
    Information-based epistemology maintains that ‘being informed’ is an independent cognitive state that cannot be reduced to knowledge or to belief, and the modal logic KTB has been proposed as a model. But what distinguishes the KTB analysis of ‘being informed’, the Brouwersche schema (B), is precisely its downfall, for no logic of information should include (B) and, more generally, no epistemic logic should include (B), either.
  •  82
    Probabilistic Logics and Probabilistic Networks
    with Rolf Haenni, Jan-Willem Romeijn, and Jon Williamson
    Synthese Library. 2010.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
  •  63
    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
  •  24
    Announcement
    Minds and Machines 24 (4): 477-477. 2014.
  •  130
    Why the Hardest Logic Puzzle Ever Cannot Be Solved in Less than Three Questions
    with Pedro Barahona
    Journal of Philosophical Logic 41 (2): 493-503. 2012.
    Rabern and Rabern (Analysis 68:105–112 2 ) and Uzquiano (Analysis 70:39–44 4 ) have each presented increasingly harder versions of ‘the hardest logic puzzle ever’ (Boolos The Harvard Review of Philosophy 6:62–65 1 ), and each has provided a two-question solution to his predecessor’s puzzle. But Uzquiano’s puzzle is different from the original and different from Rabern and Rabern’s in at least one important respect: it cannot be solved in less than three questions. In this paper we solve Uzquiano…Read more
  •  144
    Focused Correlation, Confirmation, and the Jigsaw Puzzle of Variable Evidence
    with Maximilian Schlosshauer
    Philosophy of Science 78 (3): 376-92. 2011.
    Focused correlation compares the degree of association within an evidence set to the degree of association in that evidence set given that some hypothesis is true. A difference between the confirmation lent to a hypothesis by one evidence set and the confirmation lent to that hypothesis by another evidence set is robustly tracked by a difference in focused correlations of those evidence sets on that hypothesis, provided that all the individual pieces of evidence are equally, positively relevant …Read more
  •  48
    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.
  •  47
    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
  •  17
    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