Performance in perceptual tasks often improves with practice. This effect is known as ‘perceptual learning,’ and it has been the source of a great deal of interest and debate over the course of the last century. Here, we consider the effects of perceptual learning within the context of signal detection theory. According to signal detection theory, the improvements that take place with perceptual learning can be due to increases in internal signal strength or decreases in internal noise. We used a (...) combination of psychophysical techniques (external noise masking and double‐pass response consistency) that involve corrupting stimuli with externally added noise to discriminate between the effects of changes in signal and noise as observers learned to identify sets of unfamiliar visual patterns. Although practice reduced thresholds by as much as a factor of 14, internal noise remained virtually fixed throughout training, indicating learning served to predominantly increase the strength of the internal signal. We further examined the specific nature of the changes that took place in signal strength by correlating the externally added noise with observer's decisions across trials (response classification). This technique allowed us to visualize some of the changes that took place in the linear templates used by the observers as learning occurred, as well as test the predictions of a linear template‐matching model. Taken together, the results of our experiments offer important new theoretical constraints on models of perceptual learning. (shrink)

In this work, we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vector formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in complex matrices preprocessing an implication matrix with one of the square roots of NOT, a complex matrix. This mathematical approach puts in evidence the virtual character of the counterfactuals. This happens because this representation produces a valuation of a counterfactual that is the superposition of the two opposite truth (...) values weighted, respectively, by two complex conjugated coefficients. This result shows that this procedure gives an uncertain evaluation projected on the complex domain. After this basic representation, the judgement of the plausibility of a given counterfactual allows us to shift the decision towards an acceptance or a refusal. This shift is the result of applying for a second time one of the two square roots of NOT. (shrink)