# Bayesian Logic and Trial-by-Trial Learning

- Momme von Sydow,
*University of Heidelberg, Dept. of Psychology*
- Klaus Fiedler,
*University of Heidelberg, Dept. of Psychology*

## Abstract

Standard logic and probability theory are both beset with
fundamental problems if used as adequacy criteria for relating logical
propositions to learning data. We discuss the problems of exception, of sample
size, and of inclusion. Bayesian pattern logic (‘Bayesian logic’ or
BL for short) has been proposed as a possible rational resolution of these
problems. BL can also be taken as psychological theory suggesting frequency-based
conjunction fallacies (CFs) and a generalization of CFs to other logical
inclusion fallacies. In this paper, this generalization is elaborated using
trial-by-trial learning scenarios without memory load. In each trial participants
have to provide a probability judgment. Apart from investigating logical
probability judgments in this trial-by-trial context, it is explored whether
under no memory load the propositional assessment of previous evidence has an
influence on further probability judgments. The results generally support BL and
cannot easily be explained by other theories of CFs.

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