Niki Pfeifer

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 to the premises. Probability logic analyzes the structure of the argument and deduces the uncertainty of the conclusion from the premises. The approach is illustrated by prominent examples of fallacies, like the argumentum ad ignorantiam, affirming the consequent and the conjunction fallacy

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. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.

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 probability of A should intuitively increase. We explain this intuition by making some implicit background information explicit. We consider several iterated conditionals, which allow us to formalize different kinds of latent information. We verify that for these iterated conditionals the prevision is greater than or equal to the probability of A. We also investigate the lower and upper bounds of the Affirmation of the Consequent inference. We conclude our study with some remarks on the supposed "independence" of two conditionals, and we interpret this property as uncorrelation between two random quantities. 2020 Elsevier Inc. All rights reserved.

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 also examine two severe thunderstorms that tore off roofs and uprooted trees in Oxfordshire (UK) and Blois (F) in 1680. In Oxfordshire, hailstone killed farm animals, and later lightning caused a fire, which damaged houses and burned down barns. In Blois, houses were torn down by the wind, eight parishes were ruined by hail (hailstone were the size of a “man’s fist”). Furthermore, houses were damaged and glass windows were shattered. Based on various primary sources, we discuss the impact of these severe storms on society. Moreover, we briefly discuss how people perceived atmospheric phenomena like storms, tornadoes, and hail. Finally, we discuss selected key issues of investigating historical severe storms.

We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with system p, and conditional syllogisms (modus ponens, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the “most . . . ” quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we summarize our empirical studies on human nonmonotonic reasoning.

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 probabilistic account of both kinds of uncertainty in the framework of coherence. Furthermore, intuitions about the evaluation of the strength of arguments are explored. Both reasoning about uncertainty and the development of a theory of argument strength are central for a realistic theory of rational argumentation

Modern cognitive and clinical psychology offer insight into how people deal with natural disasters. In my methodological paper, I make a strong case for incorporating experimental findings and theoretical concepts of modern psychology into environmental historical disaster research. I show how psychological factors may influence the production and interpretation of historical sources with respect to perceptions of and responses to disasters. While previous psychological approaches to history mostly involve psychoanalysis, I focus on empirical psychology. Specifically, I review a number of well documented heuristics, biases, and memory modulations as described by cognitive psychology. Moreover, I argue that including investigations on disaster related mental disorders would complement the environmental historical research of natural disasters. My approach highlights a strong potential for interdisciplinary collaborations among environmental historians and psychologists

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 how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities which, given some logical dependencies, may reduce to conditional events. We show how the inference to B|A from A and B can be extended to compounds and iterations of both conditional events and biconditional events. Moreover, we determine the respective uncertainty propagation rules. Finally, we make some comments on extending our analysis to counterfactuals.

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 conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic modus ponens coincide with the respective bounds on the conclusion for the (non-nested) probabilistic modus ponens.

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, we add ????(????|(????∨????))>0 as a probabilistic constraint (i.e., an “existential import assumption”) to obtain probabilistic informativeness. We show how to propagate the assigned (precise or interval-valued) probabilities to the sequence of conditional events (????|????,~????|????,????|(????∨????)) to the conclusion ~????|???? . Thereby, we give a probabilistic meaning to the other syllogisms of Figure II. Moreover, our semantics also allows for generalizing the traditional syllogisms to new ones involving generalized quantifiers (like Most S are P) and syllogisms in terms of defaults and negated defaults.

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 relevant imprecision involved in the premises when inferring lower or upper probability bounds on the target conditional/counterfactual ("halfway responses"). We discuss the results in the light of coherence-based probability logic and the new paradigm psychology of reasoning.

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 how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds and iterations as conditional random quantities, which sometimes reduce to conditional events, given logical dependencies. We also show, for the first time, how to extend the inference of centering for conditional events, inferring B|A from the conjunction A ^ B, to compounds and iterations of both conditional events and biconditional events, B || A, and generalize it to n-conditional events.

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 $${p(A| \overline{A})=0}$$ p ( A | A ¯ ) = 0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles: Aristotle’s theses, Aristotle’s Second Thesis, Abelard’s First Principle, and Boethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (like non-symmetry). Both approaches satisfy minimal requirements for a connexive logic. Finally, we compare both approaches conceptually.

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 of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers.

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 capture the intuition that conditionals should express some “connection” between the antecedent and the consequent or, in terms of inferences, validity should require some connection between the premise set and the conclusion. This intuition is covered by a number of principles, a selection of which we analyze in our contribution. We present two approaches to connexivity within coherence-based probability logic. Specifically, we analyze connections between antecedents and consequents firstly, in terms of probabilistic constraints on conditional events (in the sense of defaults, or negated defaults) and secondly, in terms of constraints on compounds of conditionals and iterated conditionals. After developing different notions of negations and notions of validity, we analyze the following connexive principles within both approaches: Aristotle’s Theses, Aristotle’s Second Thesis, Abelard’s First Principle and selected versions of Boethius’ Theses. We conclude by remarking that coherence-based probability logic offers a rich language to investigate the validity of various connexive principles.

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 experiments on reasoning with inference rules about nonmonotonic conditionals in the framework of coherence. We investigated the cut, and the right weakening rule of system p. As a critical condition, we investigated basic monotonic properties of classical (monotone) logic, namely monotonicity, transitivity, and contraposition. The results suggest that people reason nonmonotonically rather than monotonically. We propose nonmonotonic reasoning as a competence model of human reasoning.

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 presented in two random task orders. The data show close agreement between the responses of Easterners and Westerners. The modal responses provide strong support for the hypothesis that conditional probability is the best predictor for counterfactuals and indicative conditionals. Finally, the grand majority of the responses are probabilistically coherent, which endorses the psychological plausibility of choosing coherence-based probability logic as a rationality framework for psychological reasoning research.

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 problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set.

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 society can and cannot learn from the coherence approach from theoretical and practical perspectives.

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, where QC(S) is the quasi conjunction of the conditional events in S. Then, we examine the inference rules And, Cut, Cautious Monotonicity, and Or of System P and other well known inference rules (Modus Ponens, Modus Tollens, Bayes). We also show that QC(F)|C(F) = 1, where C(F) is the conjunction of the conditional events in F. We characterize p-entailment by showing that F p-entails E3|H3 if and only if (E3|H3)|C(F) = 1. Finally, we examine Denial of the antecedent and Affirmation of the consequent, where the p-entailment of (E3|H3) from F does not hold, by showing that (E3|H3)|C(F) is not equal to 1.

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 proposed measure predicts human inferences in the original Ellsberg task and in corresponding argument strength tasks. Finally, we report qualitative data taken from structured interviews on folk psychological conceptions on what argument strength means.

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 implicational claims. Some of these attack principles seem to be prima facie more plausible than others. To support this intuition, we suggest an interpretation of these principles in terms of coherent conditional probabilities. This interpretation is naturally generalized from qualitative to quantitative principles. Specifically, we use our probabilistic semantics to evaluate the rationality of principles which govern the strength of argumentative attacks. In order to complement our theoretical analysis with an empirical perspective, we present an experiment with students of the TU Vienna ( n = 139) which explores the psychological plausibility of selected attack principles. We also discuss how our qualitative attack principles relate to well-known types of logical argumentation frameworks. Finally, we briefly discuss how our approach relates to the computational argumentation literature.

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 set of all coherent assessments. Finally, as an application, we present new versions of the square and of the hexagon involving generalized quantifiers.