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Probabilistic Reasoning

Assistant editor: Joshua Luczak (University of Western Ontario)
About this topic
Summary What principles govern uncertain reasoning?  And how do they apply to other philosophical problems; like whether a decision is rational, or whether one thing is a cause of another? Most philosophers think uncertain reasoning should at least obey the axioms of the mathematical theory of probability; though some prefer other axioms, like those of Dempster-Shafer theory or ranking theory.  Many also endorse principles governing beliefs about physical probabilities (chance-credence principles), and principles for responding to new evidence (updating principles).  Some also endorse principles for reasoning in the absence of relevant information (indifference principles).  A perennial question is how many principles we should accept: how "objective" is probabilistic reasoning? Probabilistic principles have traditionally been applied to the study of scientific reasoning (confirmation theory) and practical rationality (decision theory).  But they also apply to more traditional epistemological issues, like foundationalism vs. coherentism, and to metaphysical questions, e.g. about the nature of causality and our access to it.
Key works Key works defending the probability axioms as normative principles are Ramsey 2010, De 1989, Savage 1954, and Joyce 1998.  Locus classici for additional probabilistic principles are Lewis 2010 (chance-credence), van Fraassen 1984 (reflection), Carnap 1950, Jaynes 1973 (indifference), and Lewis 2010 (updating). Alternative axiomatic frameworks originate with Shafer 1976 (Dempster-Shafer theory) and Spohn 1988 (ranking theory). Some classic applications of probabilistic principles to epistemological and other problems are Good 1960 (the raven paradox), Pearl 2000 (causal inference), and Elga 2000 (sleeping beauty and self-location). 
Introductions Skyrms 1975 is an excellent and gentle introduction for non-initiates.  A next step up is Jeffrey 1965.  More advanced introductions are Urbach & Howson 1993 and Earman 1992.  More recently, Halpern 2003 provides an excellent overview of the mathematical options.  A recent overview of the more philosophical issues can be found in Weisberg 2011.
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  1. Elementary probabilistic operations: a framework for probabilistic reasoning.Siegfried Macho & Thomas Ledermann - 2024 - Thinking and Reasoning 30 (2):259-300.
    The framework of elementary probabilistic operations (EPO) explains the structure of elementary probabilistic reasoning tasks as well as people’s performance on these tasks. The framework comprises three components: (a) Three types of probabilities: joint, marginal, and conditional probabilities; (b) three elementary probabilistic operations: combination, marginalization, and conditioning, and (c) quantitative inference schemas implementing the EPO. The formal part of the EPO framework is a computational level theory that provides a problem space representation and a classification of elementary probabilistic problems based (...)
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  2. Is Causal Reasoning Harder Than Probabilistic Reasoning?Milan Mossé, Duligur Ibeling & Thomas Icard - 2024 - Review of Symbolic Logic 17 (1):106-131.
    Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. (...)
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  3. Deference Principles for Imprecise Credences.Giacomo Molinari - manuscript
    This essay gives an account of epistemic deference for agents with imprecise credences. I look at the two main imprecise deference principles in the literature, known as Identity Reflection and Pointwise Reflection (Moss, 2021). I show that Pointwise Reflection is strictly weaker than Identity Reflection, and argue that, if you are certain you will update by conditionalisation, you should defer to your future self according to Identity Reflection. Then I give a more general justification for Pointwise and Identity Reflection from (...)
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  4. The Conditional in Three-Valued Logic.Jan Sprenger (ed.) - forthcoming - Cambridge, Massachusetts: The MIT Press.
    By and large, the conditional connective in three-valued logic has two different functions. First, by means of a deduction theorem, it can express a specific relation of logical consequence in the logical language itself. Second, it can represent natural language structures such as "if/then'" or "implies''. This chapter surveys both approaches, shows why none of them will typically end up with a three-valued material conditional, and elaborates on connections to probabilistic reasoning.
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  5. Belief about Probability.Ray Buchanan & Sinan Dogramaci - forthcoming - Journal of Philosophy.
    Credences are beliefs about evidential probabilities. We give the view an assessment-sensitive formulation, show how it evades the standard objections, and give several arguments in support.
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  6. Suspending belief in credal accounts.Andrew del Rio - 2024 - Noûs 58 (1):3-25.
    Traditionally epistemologists have taken doxastic states to come in three varieties—belief, disbelief, and suspension. Recently many epistemologists have taken our doxastic condition to be usefully represented by credences—quantified degrees of belief. Moreover, some have thought that this new credal picture is sufficient to account for everything we want to explain with the old traditional picture. Therefore, belief, disbelief, and suspension must map onto the new picture somehow. In this paper I challenge that possibility. Approaching the question from the angle of (...)
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  7. Ashes to ashes, digit to digit: the nonhuman temporality of Facebook’s Feed.Talha Issevenler - 2023 - Subjectivity 30 (4):373–393.
    This article examines how Facebook’s Feed, its dynamic user interface, incorporates and refashions the capacity to temporalize cultural material and experience that has classically been attributed to subjectivity. I problematize the ambiguous historicity of digital culture across the experience of the ordinary that it produces by arranging the subjective time and ‘ruined’ bits of cultural material into algorithmic timelines. Drawing on recent media theory, I underscore the irreducible alienness of algorithmic temporalizations, which undermine habitual normalization. I show subjectivity moves beyond (...)
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  8. Nhóm nhà khoa học Việt phát triển Cổng thông tin hỗ trợ đào tạo nghiên cứu.T. Công - 2024 - Tạp Chí Khoa Học Và Công Nghệ (Feb. 5, 2024).
    Trước những khó khăn và thách thức của các nhà khoa học trẻ và các nhà khoa học ở những nước đang phát triển do thiếu tài nguyên và cơ hội được tiếp cận với các kiến thức và phương pháp nghiên cứu bài bản…, các nhà khoa học Việt Nam đã phát triển nền tảng Cổng thông tin SM3D hỗ trợ đào tạo phương pháp nghiên cứu khoa học xã hội cho các nhà khoa học. Sau gần 2 năm (...)
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  9. Slurring Individuals.Víctor Carranza-Pinedo - manuscript
  10. Probabilistic Learning and Psychological Similarity.Nina Poth - 2023 - Entropy 25 (10).
    The notions of psychological similarity and probabilistic learning are key posits in cognitive, computational, and developmental psychology and in machine learning. However, their explanatory relationship is rarely made explicit within and across these research fields. This opinionated review critically evaluates how these notions can mutually inform each other within computational cognitive science. Using probabilistic models of concept learning as a case study, I argue that two notions of psychological similarity offer important normative constraints to guide modelers’ interpretations of representational primitives. (...)
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  11. Probability, normalcy and the right against risk imposition.Martin Smith - forthcoming - Journal of Ethics and Social Philosophy.
    Many philosophers accept that, as well as having a right that others not harm us, we also have a right that others not subject us to a risk of harm. And yet, when we attempt to spell out precisely what this ‘right against risk imposition’ involves, we encounter a series of notorious puzzles. Existing attempts to deal with these puzzles have tended to focus on the nature of rights – but I propose an approach that focusses instead on the nature (...)
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  12. Conjunctive Explanations: A Coherentist Appraisal.Stephan Hartmann & Borut Trpin - 2023 - In Conjunctive Explanations. The Nature, Epistemology, and Psychology of Explanatory Multiplicity. J. Schupbach and D. Glass (eds.), New York: Routledge. pp. 111-134.
    A conjunction of two hypotheses may provide a better explanation than either one of them individually, even if each already provides a good explanation on its own. An appropriate measure of explanatory power should reflect this, but none of the measures discussed in the literature do so because they only consider how much an explanatory hypothesis reduces our surprise at the evidence – which is problematic. This chapter introduces and defends a class of coherentist measures of explanatory power, and shows (...)
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  13. Being Rational and Being Wrong.Kevin Dorst - 2023 - Philosophers' Imprint 23 (1).
    Do people tend to be overconfident? Many think so. They’ve run studies on whether people are calibrated: whether their average confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically ‘over-calibrated’—for example, of the opinions they’re 80% confident in, only 60% are true. From this empirical over-calibration, it’s inferred that people are irrationally overconfident. My question: When and why is this inference warranted? Answering it requires articulating a general connection between being (...)
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  14. Probing the quantitative–qualitative divide in probabilistic reasoning.Duligur Ibeling, Thomas Icard, Krzysztof Mierzewski & Milan Mossé - forthcoming - Annals of Pure and Applied Logic.
  15. Logical perspectives on the foundations of probability.Jürgen Landes & Hykel Hosni - 2023 - Open Mathematics 21 (1).
    We illustrate how a variety of logical methods and techniques provide useful, though currently underappreciated, tools in the foundations and applications of reasoning under uncertainty. The field is vast spanning logic, artificial intelligence, statistics, and decision theory. Rather than (hopelessly) attempting a comprehensive survey, we focus on a handful of telling examples. While most of our attention will be devoted to frameworks in which uncertainty is quantified probabilistically, we will also touch upon generalisations of probability measures of uncertainty, which have (...)
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  16. Unspecific Evidence and Normative Theories of Decision.Rhys Borchert - forthcoming - Episteme:1-23.
    The nature of evidence is a problem for epistemology, but I argue that this problem intersects with normative decision theory in a way that I think is underappreciated. Among some decision theorists, there is a presumption that one can always ignore the nature of evidence while theorizing about principles of rational choice. In slogan form: decision theory only cares about the credences agents actually have, not the credences they should have. I argue against this presumption. In particular, I argue that (...)
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  17. Accuracy and Probabilism in Infinite Domains.Michael Nielsen - 2023 - Mind 132 (526):402-427.
    The best accuracy arguments for probabilism apply only to credence functions with finite domains, that is, credence functions that assign credence to at most finitely many propositions. This is a significant limitation. It reveals that the support for the accuracy-first program in epistemology is a lot weaker than it seems at first glance, and it means that accuracy arguments cannot yet accomplish everything that their competitors, the pragmatic (Dutch book) arguments, can. In this paper, I investigate the extent to which (...)
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  18. Probability and Inductive Logic.Antony Eagle - manuscript
    Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...)
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  19. Conditionals, Support and Connexivity.Hans Rott - manuscript
    In natural language, conditionals are frequently used for giving explanations. Thus the antecedent of a conditional is typically understood as being connected to, being relevant for, or providing evidential support for the conditional's consequent. This aspect has not been adequately mirrored by the logics that are usually offered for the reasoning with conditionals: neither in the logic of the material conditional or the strict conditional, nor in the plethora of logics for suppositional conditionals that have been produced over the past (...)
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  20. A Causal Safety Criterion for Knowledge.Jonathan Vandenburgh - forthcoming - Erkenntnis:1-21.
    Safety purports to explain why cases of accidentally true belief are not knowledge, addressing Gettier cases and cases of belief based on statistical evidence. However, problems arise for using safety as a condition on knowledge: safety is not necessary for knowledge and cannot always explain the Gettier cases and cases of statistical evidence it is meant to address. In this paper, I argue for a new modal condition designed to capture the non-accidental relationship between facts and evidence required for knowledge: (...)
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  21. Reasoning Studies. From Single Norms to Individual Differences.Niels Skovgaard-Olsen - 2022 - Dissertation, University of Freiburg
    Habilitation thesis in psychology. The book consists of a collection of reasoning studies. The experimental investigations will take us from people’s reasoning about probabilities, entailments, pragmatic factors, argumentation, and causality to morality. An overarching theme of the book is norm pluralism and individual differences in rationality research.
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  22. Schum, David A.: Evidential Foundations of Probabilistic Reasoning, John Wiley & Sons, New York, 1994, 545 págs.Carlos Ortiz de Landázuri - 1997 - Anuario Filosófico 30 (3):749-750.
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  23. Una revisión de la condicionalización bayesiana.Rodrigo Iván Barrera Guajardo - 2021 - Culturas Cientificas 2 (1):24-54.
    La epistemología bayesiana tiene como concepto capital la condicionalización simple. Para comprender de buena forma cómo opera esta regla, se debe dar cuenta de la concepción subjetiva de la probabilidad. Sobre la base de lo anterior es posible esclarecer alcances y límites de la condicionalización simple. En general, cuando esta regla enfrenta una dificultad se hacen esfuerzos por resolver dicha particular cuestión, pero no es usual encontrar propuestas unificadas con la intención de resolver varias de las complicaciones subyacentes al bayesianismo (...)
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  24. The mindsponge and BMF analytics for innovative thinking in social sciences and humanities.Quan-Hoang Vuong, Minh-Hoang Nguyen & Viet-Phuong La (eds.) - 2022 - Berlin, Germany: De Gruyter.
    Academia is a competitive environment. Early Career Researchers (ECRs) are limited in experience and resources and especially need achievements to secure and expand their careers. To help with these issues, this book offers a new approach for conducting research using the combination of mindsponge innovative thinking and Bayesian analytics. This is not just another analytics book. 1. A new perspective on psychological processes: Mindsponge is a novel approach for examining the human mind’s information processing mechanism. This conceptual framework is used (...)
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  25. Probabilistic semantics for epistemic modals: Normality assumptions, conditional epistemic spaces and the strength of must and might.Guillermo Del Pinal - 2021 - Linguistics and Philosophy 45 (4):985-1026.
    The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...)
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  26. Erratum to: Is global consequentialism more expressive than act consequentialism?Elliott Thornley - 2022 - Analysis 82 (2):299-299.
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  27. Cosmic Skepticism and the Beginning of Physical Reality (Doctoral Dissertation).Linford Dan - 2022 - Dissertation, Purdue University
    This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause (...)
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  28. Look at the time!David Builes - 2022 - Analysis 82 (1):15-23.
    I argue that we can get evidence for the temporal ontology of the universe simply by looking at the time. The argument is an extension of the ‘epistemic objection’ towards Growing Block theories.
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  29. Speed-Optimal Induction and Dynamic Coherence.Michael Nielsen & Eric Wofsey - 2022 - British Journal for the Philosophy of Science 73 (2):439-455.
    A standard way to challenge convergence-based accounts of inductive success is to claim that they are too weak to constrain inductive inferences in the short run. We respond to such a challenge by answering some questions raised by Juhl (1994). When it comes to predicting limiting relative frequencies in the framework of Reichenbach, we show that speed-optimal convergence—a long-run success condition—induces dynamic coherence in the short run.
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  30. Knowledge from multiple experiences.Simon Goldstein & John Hawthorne - 2021 - Philosophical Studies 179 (4):1341-1372.
    This paper models knowledge in cases where an agent has multiple experiences over time. Using this model, we introduce a series of observations that undermine the pretheoretic idea that the evidential significance of experience depends on the extent to which that experience matches the world. On the basis of these observations, we model knowledge in terms of what is likely given the agent’s experience. An agent knows p when p is implied by her epistemic possibilities. A world is epistemically possible (...)
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  31. Reconsidering the Rule of Consideration: Probabilistic Knowledge and Legal Proof.Tim Smartt - 2022 - Episteme 19 (2):303-318.
    In this paper, I provide an argument for rejecting Sarah Moss's recent account of legal proof. Moss's account is attractive in a number of ways. It provides a new version of a knowledge-based theory of legal proof that elegantly resolves a number of puzzles about mere statistical evidence in the law. Moreover, the account promises to have attractive implications for social and moral philosophy, in particular about the impermissibility of racial profiling and other harmful kinds of statistical generalisation. In this (...)
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  32. Statistik und Einheit der Wissenschaften von Quetelets Physique Sociale zu Neuraths Soziologie im Physikalismus.Donata Romizi - 2016 - In C. Bonnet & E. Nemeth (eds.), .): Wissenschaft und Praxis. Zur Wissenschaftsphilosophie in Österreich und Frankreich in der ersten Hälfte des 20. Jahrhunderts. Wien; New York:
    The present paper focuses on the work of Adolphe Quetelet (1796-1874), the Belgian author of the Social Physics who worked in the tradition of the French mathématique sociale, and of Otto Neurath (1882-1945), the Vienna Circle’s member who supported a “sociology within physicalism”. They shared some important philosophical and methodological positions: an empiricist approach to the social sciences, a unitary conception of the natural and the social sciences, and the appreciation of statistics as a tool for investigating and also reforming (...)
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  33. New Wave Consequentialism: An Introduction.Christian Seidel - 2019 - In Consequentialism: New Directions, New Problems. Oxford, New York 13830, USA: pp. 1-28.
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  34. The Ineffability of Induction.David Builes - 2020 - Philosophy and Phenomenological Research 104 (1):129-149.
    My first goal is to motivate a distinctively metaphysical approach to the problem of induction. I argue that there is a precise sense in which the only way that orthodox Humean and non-Humean views can justify induction is by appealing to extremely strong and unmotivated probabilistic biases. My second goal is to sketch what such a metaphysical approach could possibly look like. After sketching such an approach, I consider a toy case that illustrates the way in which such a metaphysics (...)
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  35. Paraconsistent Logics for Knowledge Representation and Reasoning: advances and perspectives.Walter A. Carnielli & Rafael Testa - 2020 - 18th International Workshop on Nonmonotonic Reasoning.
    This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the importance of (...)
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  36. Dynamic Formal Epistemology.Patrick Girard, Olivier Roy & Mathieu Marion (eds.) - 2010 - Berlin, Germany: Springer.
    This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and (...)
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  37. Naturalized formal epistemology of uncertain reasoning.Niki Pfeifer - 2012 - Dissertation, The Tilburg Center for Logic and Philosophy of Science, Tilburg University
    This thesis consists of a collection of five papers on naturalized formal epistemology of uncertain reasoning. In all papers I apply coherence based probability logic to make fundamental epistemological questions precise and propose new solutions to old problems. I investigate the rational evaluation of uncertain arguments, develop a new measure of argument strength, and explore the semantics of uncertain indicative conditionals. Specifically, I study formally and empirically the semantics of negated apparently selfcontradictory conditionals (Aristotle’s theses), resolve a number of paradoxes (...)
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  38. On argument strength.Niki Pfeifer - 2013 - In Frank Zenker (ed.), Bayesian argumentation. The practical side of probability. Dordrecht, Netherlands: pp. 185-193.
    Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...)
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  39. Square of opposition under coherence.Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, P. Grzegorzewski, O. Hryniewicz & María Ángeles Gil (eds.), Soft Methods for Data Science. pp. 407-414.
    Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...)
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  40. Centering and compound conditionals under coherence.A. Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2017 - In M. B. Ferraro, P. Giordani, B. Vantaggi, M. Gagolewski, P. Grzegorzewski, O. Hryniewicz & María Ángeles Gil (eds.), Soft Methods for Data Science. pp. 253-260.
    There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti’s conditional event, B | A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, (...)
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  41. Generalized probabilistic modus ponens.Giuseppe Sanfilippo, Niki Pfeifer & Angelo Gilio - 2017 - In A. Antonucci, L. Cholvy & O. Papini (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (Lecture Notes in Artificial Intelligence, vol. 10369). pp. 480-490.
    Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the (...)
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  42. Probabilistic semantics for categorical syllogisms of Figure II.Niki Pfeifer & Giuseppe Sanfilippo - 2018 - In D. Ciucci, G. Pasi & B. Vantaggi (eds.), Scalable Uncertainty Management. pp. 196-211.
    A coherence-based probability semantics for categorical syllogisms of Figure I, which have transitive structures, has been proposed recently (Gilio, Pfeifer, & Sanfilippo [15]). We extend this work by studying Figure II under coherence. Camestres is an example of a Figure II syllogism: from Every P is M and No S is M infer No S is P. We interpret these sentences by suitable conditional probability assessments. Since the probabilistic inference of ~????|???? from the premise set {????|????, ~????|????} is not informative, (...)
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  43. Probabilistic interpretations of argumentative attacks: logical and experimental foundations.Niki Pfeifer & C. G. Fermüller - 2018 - In V. Kratochvíl & J. Vejnarová (eds.), 11th Workshop on Uncertainty Processing (WUPES'18). Prague, Czechia: pp. 141-152.
    We present an interdisciplinary approach to study systematic relations between logical form and attacks between claims in an argumentative framework. We propose to generalize qualitative attack principles by quantitative ones. Specifically, we use coherent conditional probabilities to evaluate the rationality of principles which govern the strength of argumentative attacks. Finally, we present an experiment which explores the psychological plausibility of selected attack principles.
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  44. What society can and cannot learn from coherence: theoretical and practical considerations.Niki Pfeifer & Andrea Capotorti - 2019 - In Hiroshi Yama & Véronique Salvano-Pardieu (eds.), Adapting Human Thinking and Moral Reasoning in Contemporary Society. Hershey, PA: IGI Global, Information Science Reference. pp. 176-198.
    Society is facing uncertainty on a multitude of domains and levels: usually, reasoning and decisions about political, economic, or health issues must be made under uncertainty. Among various approaches to probability, this chapter presents the coherence approach to probability as a method for uncertainty management. The authors explain the role of uncertainty in the context of important societal issues like legal reasoning and vaccination hesitancy. Finally, the chapter presents selected psychological factors which impact probabilistic representation and reasoning and discusses what (...)
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  45. Probabilistic entailment and iterated conditionals.A. Gilio, Niki Pfeifer & Giuseppe Sanfilippo - 2020 - In S. Elqayam, Igor Douven, J. St B. T. Evans & N. Cruz (eds.), Logic and uncertainty in the human mind: a tribute to David E. Over. Routledge. pp. 71-101.
    In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval [0,1]. We examine the iterated conditional (B|K)|(A|H), by showing that A|H p-entails B|K if and only if (B|K)|(A|H) = 1. Then, we show that a p-consistent family F={E1|H1, E2|H2} p-entails a conditional event E3|H3 if and only if E3|H3= 1, or (E3|H3)|QC(S) = 1 for some nonempty subset S (...)
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  46. Probabilistic squares and hexagons of opposition under coherence.Niki Pfeifer & Giuseppe Sanfilippo - 2017 - International Journal of Approximate Reasoning 88:282-294.
    Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square and of the hexagon in terms of acceptability. Then, we show how to construct probabilistic versions of the square and of the hexagon of opposition by forming suitable tripartitions of the (...)
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  47. Probabilistic inferences from conjoined to iterated conditionals.Giuseppe Sanfilippo, Niki Pfeifer, D. E. Over & A. Gilio - 2018 - International Journal of Approximate Reasoning 93:103-118.
    There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, P(if A then B), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that P(if A then B)=P(B|A) with de Finetti's conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate (...)
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  48. A Multinational Data Set of Game Players' Behaviors in a Virtual World and Environmental Perceptions.Vuong Quan-Hoang, Manh-Toan Ho, Viet-Phuong La, Tam-Tri Le, Thanh Huyen T. Nguyen & Minh-Hoang Nguyen - 2021 - Data Intelligence 3 (4):606-630.
    Video gaming has been rising rapidly to become one of the primary entertainment media, especially during the COVID-19 pandemic. Playing video games has been reported to associate with many psychological and behavioral traits. However, little is known about the connections between game players' behaviors in the virtual environment and environmental perceptions. Thus, the current data set offers valuable resources regarding environmental worldviews and behaviors in the virtual world of 640 Animal Crossing: New Horizons (ACNH) game players from 29 countries around (...)
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  49. Counterexamples to Some Characterizations of Dilation.Michael Nielsen & Rush T. Stewart - 2021 - Erkenntnis 86 (5):1107-1118.
    We provide counterexamples to some purported characterizations of dilation due to Pedersen and Wheeler :1305–1342, 2014, ISIPTA ’15: Proceedings of the 9th international symposium on imprecise probability: theories and applications, 2015).
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  50. Independent Natural Extension for Choice Functions.Jason Konek, Arthur Van Camp & Kevin Blackwell - 2021 - PMLR 147:320-330.
    We investigate epistemic independence for choice functions in a multivariate setting. This work is a continuation of earlier work of one of the authors [23], and our results build on the characterization of choice functions in terms of sets of binary preferences recently established by De Bock and De Cooman [7]. We obtain the independent natural extension in this framework. Given the generality of choice functions, our expression for the independent natural extension is the most general one we are aware (...)
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