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89How people interpret an uncertain IfIn T. Kroupa & J. Vejnarova (eds.), Proceedings of the 8th Workshop on Uncertainty Processing, . pp. 80-91. 2009.Conditionals are central to inference. Before people can draw inferences about a natural language conditional, they must interpret its meaning. We investigated interpretation of uncertain conditionals using a probabilistic truth table task, focussing on (i) conditional event, (ii) material conditional, and (iii) conjunction interpretations. The order of object (shape) and feature (color) in each conditional's antecedent and consequent was varied between participants. The conditional event was th…Read more
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32Towards a probability logic based on statistical reasoningIn Niki Pfeifer & G. D. Kleiter (eds.), Proceedings of the 11th IPMU Conference (Information Processing and Management of Uncertainty in Knowledge-Based Systems, . pp. 9. 2006.Logical argument forms are investigated by second order probability density functions. When the premises are expressed by beta distributions, the conclusions usually are mixtures of beta distributions. If the shape parameters of the distributions are assumed to be additive (natural sampling), then the lower and upper bounds of the mixing distributions (Polya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic.
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59Reasoning and argumentation under uncertainty (Habilitation thesis)Dissertation, Department of Philosophy, University of Regensburg. 2023.Die kumulative Habilitation besteht aus einer philosophiegeschichtlichen Arbeit (G), drei vorwiegend theoretischen Arbeiten (T1–T3) und vier anwendungsorientierten Arbeiten (A1–A4).
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21Probability propagation rules for Aristotelian syllogismsAnnals of Pure and Applied Logic 175 (9): 103340. 2024.
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33Connexive Logic, Probabilistic Default Reasoning, and Compound ConditionalsStudia Logica 112 (1): 167-206. 2023.We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, thenA, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event $${A| \overline{A}}$$ A | A ¯ is $${p(A| \over…Read more
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62Towards a Conceptual Framework for Conspiracy Theory TheoriesSocial Epistemology 37 (4): 510-521. 2023.I present a conceptual framework for classifying generalist and particularist approaches to conspiracy theories (CTs). Specifically, I exploit a probabilistic version of the hexagon of opposition which allows for systematically visualising the logical relations among basic philosophical positions concerning CTs. The probabilistic interpretation can also account for positions, which make weaker claims about CTs: e.g. instead of claiming ‘every CT is suspicious’ some theorists might prefer to clai…Read more
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30Probabilistic interpretations of argumentative attacks: Logical and experimental resultsArgument and Computation 14 (1): 75-107. 2023.We present an interdisciplinary approach to argumentation combining logical, probabilistic, and psychological perspectives. We investigate logical attack principles which relate attacks among claims with logical form. For example, we consider the principle that an argument that attacks another argument claiming A triggers the existence of an attack on an argument featuring the stronger claim A ∧ B. We formulate a number of such principles pertaining to conjunctive, disjunctive, negated, and impl…Read more
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266While Classical Logic (CL) used to be the gold standard for evaluating the rationality of human reasoning, certain non-theorems of CL—like Aristotle’s and Boethius’ theses—appear intuitively rational and plausible. Connexive logics have been developed to capture the underlying intuition that conditionals whose antecedents contradict their consequents, should be false. We present results of two experiments (total n = 72), the first to investigate connexive principles and related formulae systemat…Read more
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9Rezension: Was wir Karl R. Popper und seiner PhilosophieverdankenKriterion - Journal of Philosophy 1 (17): 23-27. 2003.
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Naturalized formal epistemology of uncertain reasoningDissertation, The Tilburg Center for Logic and Philosophy of Science, Tilburg University. 2012.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 ne…Read more
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41On Mental Probability LogicDissertation, Department of Psychology, University of Salzburg. 2006.Mental probability logic is a psychological competence theory about how humans interpret and reason about common-sense conditionals. Probability logic is proposed as an appropriate standard of reference for evaluating the rationality of human inferences. Common-sense conditionals are interpreted as “high” conditional probabilities, P(B|A) > .5. Probability logical accounts of nonmonotonic reasoning and inference rules like the modus ponens are explored. Categorical syllogisms with comparative an…Read more
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30On argument strengthIn Frank Zenker (ed.), Bayesian Argumentation – The Practical Side of Probability, Springer. pp. 185-193. 2012.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 secon…Read more
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35Square of opposition under coherenceIn 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. 2017.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 s…Read more
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40Centering and compound conditionals under coherenceIn 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. 2017.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 illustra…Read more
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38Generalized probabilistic modus ponensIn 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. 2017.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 previ…Read more
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35Counterfactuals, indicative conditionals, and negation under uncertainty: Are there cross-cultural differences?In G. Gunzelmann, A. Howes, T. Tenbrink & E. Davelaar (eds.), Proceedings of the 39th Cognitive Science Society Meeting. pp. 2882-2887. 2017.In this paper we study selected argument forms involving counterfactuals and indicative conditionals under uncertainty. We selected argument forms to explore whether people with an Eastern cultural background reason differently about conditionals compared to Westerners, because of the differences in the location of negations. In a 2x2 between-participants design, 63 Japanese university students were allocated to four groups, crossing indicative conditionals and counterfactuals, and each presente…Read more
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23Modeling the Ellsberg paradox by argument strengthIn G. Gunzelmann, A. Howes, T. Tenbrink & E. Davelaar (eds.), Proceedings of the 39th Cognitive Science Society Meeting, . pp. 925-930. 2017.We present a formal measure of argument strength, which combines the ideas that conclusions of strong arguments are (i) highly probable and (ii) their uncertainty is relatively precise. Likewise, arguments are weak when their conclusion probability is low or when it is highly imprecise. We show how the proposed measure provides a new model of the Ellsberg paradox. Moreover, we further substantiate the psychological plausibility of our approach by an experiment (N = 60). The data show that the pr…Read more
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36Abductive, causal, and counterfactual conditionals under incomplete probabilistic knowledgeIn G. Gunzelmann, A. Howes, T. Tenbrink & E. Davelaar (eds.), Proceedings of the 39th Cognitive Science Society Meeting. pp. 2888-2893. 2017.We study abductive, causal, and non-causal conditionals in indicative and counterfactual formulations using probabilistic truth table tasks under incomplete probabilistic knowledge (N = 80). We frame the task as a probability-logical inference problem. The most frequently observed response type across all conditions was a class of conditional event interpretations of conditionals; it was followed by conjunction interpretations. An interesting minority of participants neglected some of the releva…Read more
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36Probabilistic semantics for categorical syllogisms of Figure IIIn D. Ciucci, G. Pasi & B. Vantaggi (eds.), Scalable Uncertainty Management. pp. 196-211. 2018.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 {????|????, …Read more
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173Probabilistic interpretations of argumentative attacks: logical and experimental foundationsIn V. Kratochvíl & J. Vejnarová (eds.), 11th Workshop on Uncertainty Processing (WUPES'18). pp. 141-152. 2018.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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31What society can and cannot learn from coherence: theoretical and practical considerationsIn Hiroshi Yama & Véronique Salvano-Pardieu (eds.), Adapting Human Thinking and Moral Reasoning in Contemporary Society, Igi Global, Information Science Reference. pp. 176-198. 2019.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 psychol…Read more
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29Probabilistic entailment and iterated conditionalsIn 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. 2020.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 of F, whe…Read more
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28Probabilistic squares and hexagons of opposition under coherenceInternational Journal of Approximate Reasoning 88 282-294. 2017.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 oppos…Read more
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42Probabilistic inferences from conjoined to iterated conditionalsInternational Journal of Approximate Reasoning 93 103-118. 2018.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…Read more
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84We present a coherence-based probability semantics for (categorical) Aristotelian syllogisms. For framing the Aristotelian syllogisms as probabilistic inferences, we interpret basic syllogistic sentence types A, E, I, O by suitable precise and imprecise conditional probability assessments. Then, we define validity of probabilistic inferences and probabilistic notions of the existential import which is required, for the validity of the syllogisms. Based on a generalization of de Finetti's fundame…Read more
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31Interpreting connexive principles in coherence-based probability logic.In J. Vejnarová & J. Wilson (eds.), Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2021, LNAI 12897). pp. 672-687. 2021.We present probabilistic approaches to check the validity of selected connexive principles within the setting of coherence. Connexive logics emerged from the intuition that conditionals of the form If ∼A, then A, should not hold, since the conditional’s antecedent ∼A contradicts its consequent A. Our approach covers this intuition by observing that for an event A the only coherent probability assessment on the conditional event A|~A is p(A|~A)=0 . Moreover, connexive logics aim to capt…Read more