Apostoli and Brown have shown that the class of formulae valid with respect to the class of -ary relational frames is completely axiomatized by Kn: an n-place aggregative system which adjoins [RM], [RN], and a complete axiomatization of propositional logic, with [Kn]:□α1 ∧...∧□αn+1 → □2/ is the disjunction of all pairwise conjunctions αi∧αj )).Their proof exploits the chromatic indices of n-uncolourable hypergraphs, or n-traces. Here, we use the notion of the χ-product of a family of sets to formulate an alternative (...) definition of an n-trace, which in turn enables a new and simpler completeness proof. (shrink)

Quattrocki and Friston (2014) argued that abnormalities in interoception—the process of representing one’s internal physiological states—could lie at the heart of autism, because of the critical role interoception plays in the ontogeny of social-affective processes. This proposal drew criticism from proponents of the alexithymia hypothesis, who argue that social-affective and underlying interoceptive impairments are not a feature of autism per se, but of alexithymia (a condition characterized by difficulties describing and identifying one’s own emotions), which commonly co-occurs with autism. Despite (...) the importance of this debate for our understanding of autism spectrum disorder (ASD), and of the role of interoceptive impairments in psychopathology, more generally, direct empirical evidence is scarce and inconsistent. Experiment 1 examined in a sample of 137 neurotypical (NT) individuals the association among autistic traits, alexithymia, and interoceptive accuracy (IA) on a standard heartbeat-tracking measure of IA. In Experiment 2, IA was assessed in 46 adults with ASD (27 of whom had clinically significant alexithymia) and 48 NT adults. Experiment 1 confirmed strong associations between autistic traits and alexithymia, but yielded no evidence to suggest that either was associated with interoceptive difficulties. Similarly, Experiment 2 provided no evidence for interoceptive impairments in autistic adults, irrespective of any co-occurring alexithymia. Bayesian analyses consistently supported the null hypothesis. The observations pose a significant challenge to notions that interoceptive impairments constitute a core feature of either ASD or alexithymia, at least as far as the direct perception of interoceptive signals is concerned. (shrink)