Niki Pfeifer

Angelo Gilio, David E. Over, Niki Pfeifer et al.

In this paper we recall some results for conditional events, compound conditionals, conditional random quantities, p-consistency, and p-entailment. Then, we show the equivalence between bets on conditionals and conditional bets, by reviewing de Finetti's trivalent analysis of conditionals. But our approach goes beyond de Finetti's early trivalent logical analysis and is based on his later ideas, aiming to take his proposals to a higher level. We examine two recent articles that explore trivalent logics for conditionals and their definitions of logical validity and compare them with our approach to compound conditionals. We prove a Probabilistic Deduction Theorem for conditional events. After that, we study some probabilistic deduction theorems, by presenting several examples. We focus on iterated conditionals and the invalidity of the Import-Export principle in the light of our Probabilistic Deduction Theorem. We use the inference from a disjunction, "$A$ or $B$", to the conditional,"if not-$A$ then $B$", as an example to show the invalidity of the Import-Export principle. We also introduce a General Import-Export principle and we illustrate it by examining some p-valid inference rules of System P. Finally, we briefly discuss some related work relevant to AI.

Niki Pfeifer

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 the chapter, the descriptive validity of probability logic is compared to logic, which was used as the gold standard of reference for assessing the rationality of human reasoning in the 20th century.

Niki Pfeifer, Hiroshi Yama

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.

Niki Pfeifer, Leena Tulkki

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.

Niki Pfeifer, Hanna Pankka

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.

Angelo Gilio, Niki Pfeifer, Giuseppe Sanfilippo

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