Representation of finitely additive semiordered qualitative probability structures

Given a finite Boolean algebra together with a binary relation, necessary and sufficient conditions are given for the existence of a probability measure on the algebra and a real number (the so-called jnd) such that for any two Boolean elements the relation holds if and only if the corresponding probability values of the elements satisfy the threshold inequality (the difference of the probabilities is greater than the jnd).     

Unconscious structural knowledge of tonal symmetry: Tang poetry redefines limits of implicit learning

The study aims to help characterize the sort of structures about which people can acquire unconscious knowledge. It is already well established that people can implicitly learn n-grams (chunks) and also repetition patterns. We explore the acquisition of unconscious structural knowledge of symmetry. Chinese Tang poetry uses a specific sort of mirror symmetry, an inversion rule with respect to the tones of characters in successive lines of verse. We show, using artificial poetry to control both n-gram structure and repetition patterns, that people can implicitly learn to discriminate inversions from non-inversions, presenting a challenge to existing models of implicit learning.     

A Puzzle About Free Speech, Legitimacy, and Countermajoritarian Constraints

This paper argues that there is a tension between two central features of Dworkin’s partnership conception of democracy. The conception holds, on the one hand, that it is a necessary condition of the legitimacy of the decisions of a political majority that every member of the political community has a very robust right to publicly criticize those decisions. A plausible interpretation of this argument is that free political speech constitutes a normatively privileged vehicle for political minorities to become majorities, and therefore in the absence of freedom of speech minorities could not be rightfully compelled to comply with majority decisions. On the other hand, the partnership conception holds that properly exercised constraints on majority rule do not incur any moral costs. The no-moral-costs thesis is argued for on the basis that nothing of significance is lost when individuals’ influence on political decisions is diminished. However, the legitimacy argument for free speech assumes the significance of individual political influence, which the no-moral-costs thesis denies. Hence the tension.     

Prior familiarity with components enhances unconscious learning of relations

The influence of prior familiarity with components on the implicit learning of relations was examined using artificial grammar learning. Prior to training on grammar strings, participants were familiarised with either the novel symbols used to construct the strings or with irrelevant geometric shapes. Participants familiarised with the relevant symbols showed greater accuracy when judging the correctness of new grammar strings. Familiarity with elemental components did not increase conscious awareness of the basis for discriminations (structural knowledge) but increased accuracy even in its absence. The subjective familiarity of test strings predicted grammaticality judgments. However, prior exposure to relevant symbols did not increase overall test string familiarity or reliance on familiarity when making grammaticality judgments. Familiarity with the symbols increased the learning of relations between them (bigrams and trigrams) thus resulting in greater familiarity for grammatical versus ungrammatical strings. The results have important implications for models of implicit learning.     

Implicit learning of mappings between forms and metaphorical meanings

Previous research has shown that people can implicitly acquire mappings between word forms and literal meanings (Williams, 2004, Williams, 2005). We argue, from the metaphor-representation and embodiment perspectives, that people can unconsciously establish mappings between word forms and not only literal but also metaphorical meanings. Using Williams’ (2005) paradigm, we found that transfer of form-meaning connections from a concrete domain (space) to an abstract domain (power) was achieved in a metaphor-consistent way without awareness. Our results support the view that unconscious knowledge can be flexibly deployed in an abstract way not previously explored in the implicit learning literature.     

Explicit feedback maintains implicit knowledge

The role of feedback was investigated with respect to conscious and unconscious knowledge acquired during artificial grammar learning (AGL). After incidental learning of training sequences, participants classified further sequences in terms of grammaticality and reported their decision strategy with or without explicit veridical feedback. Sequences that disobeyed the learning structure conformed to an alternative structure. Feedback led to an increase in the amount of reported conscious knowledge of structure (derived rules and recollections) but did not increase its accuracy. Conversely, feedback maintained the accuracy of unconscious knowledge of structure (intuition or familiarity-based responses) which otherwise degraded. Results support a dual-process account of AGL. They suggest that implicit learning of the to-be-rejected structure at test contaminates familiarity-based classifications whereas feedback allows competing familiarity signals to be contextualised, which is incompatible with theories that consider familiarity context-insensitive.     

Connectionist and Memory-Array Models of Artificial Grammar Learning

Subjects exposed to strings of letters generated by a finite state grammar can later classify grammatical and nongrammatical test strings, even though they cannot adequately say what the rules of the grammar are (e.g., Reber, 1989). The MINERVA 2 (Hintzman, 1986) and Medin and Schaffer (1978) memory-array models and a number of connectionist outoassociator models are tested against experimental data by deriving mainly parameter-free predictions from the models of the rank order of classification difficulty of test strings. The importance of different assumptions regarding the coding of features (How should the absence of a feature be coded? Should single letters or digrams be coded?), the learning rule used (Hebb rule vs. delta rule), and the connectivity (Should features be predicted only by previous features in the string, or by all features simultaneously?) is investigated by determining the performance of the models with and without each assumption. Only one class of connectionist model (the simultaneous delta rule) passes all the tests. It is shown that this class of model can be regarded by abstracting a set of representative but incomplete rules of the grammar.