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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
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132The new psychology of reasoning: A mental probability logical perspectiveThinking and Reasoning 19 (3-4): 329-345. 2013.No abstract
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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.
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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
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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.
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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
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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
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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
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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