Niki Pfeifer

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 of human reasoning and principles of nonmonotonic reasoning. Contrary to the results reported in the ‘heuristics and biases’ tradition, the subjects committed relatively few upper bound violations (conjunction fallacies).

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 found a relatively good agreement of human reasoning and principles of nonmonotonic reasoning according to the coherence interpretation of system p. This study reports an experiment on the cautious monotonicity Rule and its “incautious” counterpart that is not contained in system p, namely the monotonicity Rule. In accordance with our previous results, the data suggest that people reason nonmonotonically: the subjects in the cautious monotonicity condition infer significantly tighter intervals close to the coherence interpretation of system p compared with the subjects in the incautious monotonicity condition where rather wide (and hence non-informative) intervals are inferred.

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 found a relatively good agreement of human reasoning and principles of nonmonotonic reasoning according to the coherence interpretation of system p. Contrary to the results reported in the “heuristics and biases” tradition, the subjects committed relatively few upper bound violations (conjunction fallacies). More lower than upper bound violations were observed. When the premises were presented in terms of intervals higher mean lower bounds were observed as when the premises were presented in terms of point percentages.

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 the dominant interpretation, followed by conjunction, and took longer to process than conjunction (mean dierence 500 ms). Material conditional responses were rare. The proportion of conditional event responses increased from around 40% at the beginning of the task to nearly 80% at the end, with 55% of participants showing a qualitative shift of interpretation. Shifts to the conditional event occurred later in the feature-object order than in the object-feature order. We discuss the results in terms of insight and suggest implications for theories of interpretation.

A 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 psychological studies.

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

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 verification. The present contribution studies algebraic interpretations of syllogisms with comparative quantifiers (e.g., “Most… are…”) and quantitative quantifiers (e.g., “n/m… are…”, “all, except n… are…”). This modern version of syllogistics is intended to be a more adequate framework for argumentation theory than traditional syllogistics.