Modal logic enjoys topological semantics that may be traced back to McKinsey and Tarski, and the classification of topological spaces via modal axioms is a lively area of research. In the past two decades, there has been interest in extending topological modal logic to the language of the mu-calculus, but previously no class of topological spaces was known to be mu-calculus definable that was not already modally definable. In this paper, we show that the full mu-calculus is indeed more expressive than standard modal logic, in the sense that there are classes of topological spaces (and weakly transitive Kripke frames), which are mu-definable but not modally definable. The classes we exhibit satisfy a modally definable property outside of their perfect core, and thus we dub them imperfect spaces. We show that the mu-calculus is sound and complete for these classes. Our examples are minimal in the sense that they use a single instance of a greatest fixed point, and we show that least fixed points alone do not suffice to define any class of spaces that is not already modally definable.

This paper examines the role of prosody in a little-studied type of non-canonical questions: syntactically and lexically canonical interrogative sentences that have been uttered by the speaker in order to express surprise. The study compares Estonian surprise questions with string-identical information-seeking questions elicited by means of context descriptions. The materials comprise 1,008 utterances by 21 speakers.

It is concluded that the prosody of the examined utterances has three roles that are relevant to the expression of surprise by ordinary interrogative sentences. First, the enhanced prosodic realisation of the utterances as manifested in a longer duration, a wider pitch range, and a more frequent occurrence of upstepped pitch accents conveys emotional expressivity. Second, lower pitch along with the creaky voice quality signals that the utterances are not canonical questions, while the main prosodic correlate of information-seeking questions is high pitch. Phonological pitch accents and boundary tones, however, are not used to distinguish between surprise questions and information-seeking questions. Third, the nuclear accent placement signals an information structure that is associated with the expression of incongruity or counterexpectation: the focal accent can evoke an alternative (set) that arises from the speaker’s expectations.

Emerson and Halpern (1986, Journal of the Association for Computing Machinery33, 151–178) prove that the Computation Tree Logic (CTL) cannot express the existence of a path on which a proposition holds infinitely often (fairness for short).

The scope is widened from CTL to a general branching-time logic. A path quantifier is followed by a language with temporal descriptions. In this extended setting, the said inexpressiveness is strengthened in two aspects. First, universal path quantifiers are unrestricted. In this way, they are relieved of any temporal quantifiers such as of those in $\mathtt{AU}$ and $\mathtt{AR}$ from CTL. Second, existential path quantifiers are allowed with any countable language. Instances are the temporal quantifiers in $\mathtt{EU}$ and $\mathtt{ER}$ from CTL. By contrast, the fairness statement is an existential path quantifier with an uncountable language. Both aspects indicate that this inexpressiveness is optimal with respect to the polarity of path quantifiers and to the cardinality of their languages.

It has been hypothesized that even ‘perfect’ polygenic scores (PGSs) composed of only causal variants may not be fully portable between different social groups owing to gene-by-environment interactions modifying the expression of relevant variants. The impacts of such interactions involving two forms of social adversity (low socioeconomic status [SES] and discrimination) are examined in relation to the expressivity of a PGS for educational attainment composed of putatively causal variants in a large, representatively sampled and genotyped cohort of US children. A relatively small-magnitude Scarr–Rowe effect is present (SES × PGSEDU predicting General Cognitive Ability [GCA]; sR = .02, 95% CI [.00, .04]), as is a distinct discrimination × PGSEDU interaction predicting GCA (sR = −.02, 95% CI [−.05, 00]). Both are independent of the confounding main effects of 10 ancestral principal components, PGSEDU, SES, discrimination and interactions among these factors. No sex differences were found. These interactions were examined in relation to phenotypic and genotypic data on height, a prospectively more socially neutral trait. They were absent in both cases. The discrimination × PGSEDU interaction is a co-moderator of the differences posited in modern versions of Spearman’s hypothesis (along with shared environmentality), lending support to certain environmental explanations of those differences. Behavior-genetic analysis of self-reported discrimination indicates that it is nonsignificantly heritable (h2 = .027, 95% CI [−.05, .10]), meaning that it is not merely proxying some underlying source of heritable phenotypic variability. This suggests that experiences of discrimination might stem instead from the action of purely social forces.

In topological modal logic, it is well known that the Cantor derivative is more expressive than the topological closure, and the ‘elsewhere’, or ‘difference’, operator is more expressive than the ‘somewhere’ operator. In 2014, Kudinov and Shehtman asked whether the combination of closure and elsewhere becomes strictly more expressive when adding the Cantor derivative. In this paper we give an affirmative answer: in fact, the Cantor derivative alone can define properties of topological spaces not expressible with closure and elsewhere. To prove this, we develop a novel theory of morphisms which preserve formulas with the elsewhere operator.

We study the decidability of termination for two CHR dialects which, similarly to the Datalog like languages, are defined by using a signature which does not allow function symbols (of arity > 0). Both languages allow the use of the = built-in in the body of rules, thus are built on a host language that supports unification. However each imposes one further restriction. The first CHR dialect allows only range-restricted rules, that is, it does not allow the use of variables in the body or in the guard of a rule if they do not appear in the head. We show that the existence of an infinite computation is decidable for this dialect. The second dialect instead limits the number of atoms in the head of rules to one. We prove that in this case, the existence of a terminating computation is decidable. These results show that both dialects are strictly less expressive1 than Turing Machines. It is worth noting that the language (without function symbols) without these restrictions is as expressive as Turing Machines.

The problem of hypoxia adaptation in high altitudes is an unsolved brainteaser in the field of the life sciences. As one of the best chicken breeds with adaptability to highland environment, the Tibet chicken, is genetically different from lowland chicken breeds. It is well known that hypoxia has significant impact on growth by inducing the expression of the alpha subunit of the heterodimeric transcription factor, hypoxia-inducible factor 1 (HIF1α). In the present study, HIF1α expression in brain, heart and liver tissues of the Tibet and Dwarf Recessive White chicken embryos were investigated at the different development stages of days 10, 17 and 20 by real-time PCR, and the expression pattern of HIF1α in chicken embryos of the two chicken breeds incubated under conditions of hypoxia (13% O2) and normoxia (21% O2) was studied. The incubation mortality of the Tibet chicken was lower than the Dwarf Recessive White chicken during the whole incubation in hypoxia, and the mRNA expression of HIF1α had presented the differences in three tissues. The results implied that the hypoxia adaptability of the Tibet chicken embryo was higher than the Dwarf Recessive White chicken, especially in the early stage (day 10) and at a later time (day 20) during the incubation period, but the mechanism of the oxygen transfer of embryos of mountain species is not completely understood, and hypoxia adaptability of the Tibetan chicken remains to be studied further.