-
Probability logicIn Markus Knauff & Wolfgang Spohn (eds.), The Handbook of Rationality, Mit Press. 2021.This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability logic is characterized as a generalization of bivalent truth-functional propositional logic (short “logic”), as being connexive, and as being nonmonotonic. The chapter discusses selected argument forms and associated uncertainty propagation rules. Throughout t…Read more
-
35Probabilities of conditionals and previsions of iterated conditionalsInternational Journal of Approximate Reasoning 121. 2020.We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability to be the conditional probability. In our approach, however, we avoid triviality because the import-export principle is invalid. We then analyze an example of reasoning under partial knowledge where, given a conditional if A then Cas information, the probabil…Read more
-
28Probability propagation in selected Aristotelian syllogismsIn G. Kern-Isberner & Zoran Ognjanović (eds.), ECSQARU 2019: Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Springer. pp. 419-431. 2019.This paper continues our work on a coherence-based probability semantics for Aristotelian syllogisms (Gilio, Pfeifer, and Sanfilippo, 2016; Pfeifer and Sanfilippo, 2018) by studying Figure III under coherence. We interpret the syllogistic sentence types by suitable conditional probability assessments. Since the probabilistic inference of P|S from the premise set {
-
91Rezension: Was wir Karl R. Popper und seiner PhilosophieverdankenKriterion - Journal of Philosophy 17 (1): 23-27. 2003.
-
81Formal Epistemology and the New Paradigm Psychology of ReasoningReview of Philosophy and Psychology 5 (2): 199-221. 2014.This position paper advocates combining formal epistemology and the new paradigm psychology of reasoning in the studies of conditionals and reasoning with uncertainty. The new paradigm psychology of reasoning is characterized by the use of probability theory as a rationality framework instead of classical logic, used by more traditional approaches to the psychology of reasoning. This paper presents a new interdisciplinary research program which involves both formal and experimental work. To illu…Read more
-
601Reasoning About Uncertain ConditionalsStudia Logica 102 (4): 849-866. 2014.There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of …Read more
-
53A process model of the understanding of uncertain conditionalsThinking and Reasoning 24 (3): 386-422. 2018.ABSTRACTTo build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: the conditional event interpretation in the coherencebased probability logic, the discourse processingtheory of Hans Kamp, and the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-…Read more
-
55Conditionals, Counterfactuals, and Rational Reasoning: An Experimental Study on Basic PrinciplesMinds and Machines 27 (1): 119-165. 2017.We present a unified approach for investigating rational reasoning about basic argument forms involving indicative conditionals, counterfactuals, and basic quantified statements within coherence-based probability logic. After introducing the rationality framework, we present an interactive view on the relation between normative and empirical work. Then, we report a new experiment which shows that people interpret indicative conditionals and counterfactuals by coherent conditional probability ass…Read more
-
83Transitivity in coherence-based probability logicJournal of Applied Logic 14 46-64. 2016.We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by pro…Read more
-
27Rational argumentation under uncertaintyIn G. Kreuzbauer, N. Gratzl & E. Hiebl (eds.), Persuasion Und Wissenschaft: Aktuelle Fragestellungen von Rhetorik Und Argumentationstheorie, Lit. pp. 181--191. 2007.Common sense arguments are practically always about incomplete and uncertain information. We distinguish two aspects or kinds of uncertainty. The one is defined as a persons’ uncertainty about the truth of a sentence. The other uncertainty is defined as a persons’ uncertainty of his assessment of the truth of a sentence. In everyday life argumentation we are often faced with both kinds of uncertainty which should be distinguished to avoid misunderstandings among discussants. The paper presents a…Read more
-
41Human reasoning with imprecise probabilities: Modus ponens and Denying the antecedentIn Niki Pfeifer & G. D. Kleiter (eds.), Proceedings of the 5 T H International Symposium on Imprecise Probability: Theories and Applications, . pp. 347--356. 2007.The modus ponens (A -> B, A :. B) is, along with modus tollens and the two logically not valid counterparts denying the antecedent (A -> B, ¬A :. ¬B) and affirming the consequent, the argument form that was most often investigated in the psychology of human reasoning. The present contribution reports the results of three experiments on the probabilistic versions of modus ponens and denying the antecedent. In probability logic these arguments lead to conclusions with imprecise probabilities. In t…Read more
-
80Coherence and Nonmonotonicity in Human ReasoningSynthese 146 (1-2): 93-109. 2005.Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. We report four experiments which investigate three rules of SYSTEMP, namely the AND, the LEFT LOGICAL EQUIVALENCE, and the OR rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of SYSTEM P. We found a relatively good agreement …Read more
-
42Systematic rationality norms provide research roadmaps and clarityBehavioral and Brain Sciences 34 (5): 263-264. 2011.Normative theories like probability logic provide roadmaps for psychological investigations. They make theorizing precise. Therefore, normative considerations should not be subtracted from psychological research. I explain why conditional elimination inferences involve at least two norm paradigms; why reporting agreement with rationality norms is informative; why alleged asymmetric relations between formal and psychological theories are symmetric; and I discuss the arbitration problem.
-
89Towards a probability logic based on statistical reasoningIn Niki Pfeifer & G. D. Kleiter (eds.), Towards a probability logic based on statistical reasoning, . pp. 2308--2315. 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 (P´olya-Eggenberger distributions) are parallel to the corresponding lower and upper probabilities in conditional probability logic
-
42Nonmonotonicity and human probabilistic reasoningIn Niki Pfeifer & G. D. Kleiter (eds.), Proceedings of the 6 T H Workshop on Uncertainty Processing, . pp. 221--234. 2003.Nonmonotonic logics allow—contrary to classical (monotone) logics— for withdrawing conclusions in the light of new evidence. Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, have investigated this claim empirically. system p is a central, broadly accepted nonmonotonic reasoning system that proposes basic rationality postulates. We previously investigated empirically a probabilistic interpretation of three selected rules of system p. We fo…Read more
-
37Experiments on nonmonotonic reasoning. The coherence of human probability judgmentsIn H. Leitgeb & G. Schurz (eds.), Pre-Proceedings of the 1 s T Salzburg Workshop on Paradigms of Cognition, . 2002.Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, investigated this claim empirically. In the present paper four psychological experiments are reported, that investigate three rules of system p, namely the and, the left logical equivalence, and the or rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of system p. We …Read more
-
125How 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
-
43A system of intermediate quantifiers (“Most S are P”, “m/n S are P”) is proposed for evaluating the rationality of human syllogistic reasoning. Some relations between intermediate quantifiers and probabilistic interpretations are discussed. The paper concludes by the generalization of the atmosphere, matching and conversion hypothesis to syllogisms with intermediate quantifiers. Since our experiments are currently still running, most of the paper is theoretical and intended to stimulate psycholog…Read more
-
41Is human reasoning about nonmonotonic conditionals probabilistically coherent?In Niki Pfeifer & G. D. Kleiter (eds.), Proceedings of the 7 T H Workshop on Uncertainty Processing, . pp. 138--150. 2006.Nonmonotonic conditionals (A |∼ B) are formalizations of common sense expressions of the form “if A, normally B”. The nonmonotonic conditional is interpreted by a “high” coherent conditional probability, P(B|A) > .5. Two important properties are closely related to the nonmonotonic conditional: First, A |∼ B allows for exceptions. Second, the rules of the nonmonotonic system p guiding A |∼ B allow for withdrawing conclusions in the light of new premises. This study reports a series of three exper…Read more
-
34Contemporary syllogistics: Comparative and quantitative syllogismsIn Günther Kreuzbauer & Georg Dorn (eds.), Argumentation in Theorie Und Praxis: Philosophie Und Didaktik des Argumentierens, Lit. pp. 57--71. 2006.Traditionally, syllogisms are arguments with two premises and one conclusion which are constructed by propositions of the form “All… are…” and “At least one… is…” and their respective negated versions. Unfortunately, the practical use of traditional syllogisms is quite restricted. On the one hand, the “All…” propositions are too strict, since a single counterexample suffices for falsification. On the other hand, the “At least one …” propositions are too weak, since a single example suffices for …Read more
-
132The new psychology of reasoning: A mental probability logical perspectiveThinking and Reasoning 19 (3-4): 329-345. 2013.No abstract
-
31The conditional in mental probability logicIn Mike Oaksford & Nick Chater (eds.), Cognition and Conditionals: Probability and Logic in Human Thought, Oxford University Press. pp. 153--173. 2010.The present chapter describes a probabilistic framework of human reasoning. It is based on probability logic. While there are several approaches to probability logic, we adopt the coherence based approach.
-
19Nonmonotonic conditionals (A |∼ B) are formalizations of common sense expressions of the form “if A, normally B”. The nonmonotonic conditional is interpreted by a “high” coherent conditional probability, P(B|A) > .5. Two important properties are closely related to the nonmonotonic conditional: First, A |∼ B allows for exceptions. Second, the rules of the nonmonotonic system p guiding A |∼ B allow for withdrawing conclusions in the light of new premises. This study reports a series of three exper…Read more
-
116Framing human inference by coherence based probability logicJournal of Applied Logic 7 (2): 206--217. 2009.We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.
-
34A probability logical interpretation of fallaciesIn G. Kreuzbauer, N. Gratzl & E. Hiebl (eds.), Rhetorische Wissenschaft: Rede Und Argumentation in Theorie Und Praxis, Lit. pp. 225--244. 2008.This chapter presents a probability logical approach to fallacies. A special interpretation of (subjective) probability is used, which is based on coherence. Coherence provides not only a foundation of probability theory, but also a normative standard of reference for distinguishing fallacious from non-fallacious arguments. The violation of coherence is sufficient for an argument to be fallacious. The inherent uncertainty of everyday life argumentation is captured by attaching degrees of belief …Read more
-
41Probabilistic theories of reasoning need pragmatics too: Modulating relevance in uncertain conditionalsJournal of Pragmatics 43. 2011.According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance aects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of t…Read more
-
28Severe storm reports of the 17th century: Examples from the UK and FranceIn Niki Pfeifer & Katrin Pfeifer (eds.), Proceedings of the 6th European Conference on Severe Storms (ECSS2013), 3 - 7 June 2013, Helsinki, Finland, . 2013.In this work we survey reports on selected severe storms of the 17th century. Specifically, we investigate a severe storm which was accompanied by a ball lightning phenomenon in Cornwall (UK) in 1640. The “fiery Ball”, which reportedly made a “ter[r]ible sound”, entered the church, broke stones and smashed windows. It made holes in stone walls and injured about 14 people. Furthermore, we report on a 1672 storm in Bedford (UK) that tore down houses, blew down stone walls and uprooted trees. We al…Read more
-
47Inference in conditional probability logicKybernetika 42 (2): 391--404. 2006.An important field of probability logic is the investigation of inference rules that propagate point probabilities or, more generally, interval probabilities from premises to conclusions. Conditional probability logic (CPL) interprets the common sense expressions of the form “if . . . , then . . . ” by conditional probabilities and not by the probability of the material implication. An inference rule is probabilistically informative if the coherent probability interval of its conclusion is not n…Read more