Provably Total Functions of Arithmetic with Basic Terms

A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and existential introduction.Comment: In Proceedings DICE 2011, arXiv:1201.034

Formal Derivation of Concurrent Garbage Collectors

Concurrent garbage collectors are notoriously difficult to implement correctly. Previous approaches to the issue of producing correct collectors have mainly been based on posit-and-prove verification or on the application of domain-specific templates and transformations. We show how to derive the upper reaches of a family of concurrent garbage collectors by refinement from a formal specification, emphasizing the application of domain-independent design theories and transformations. A key contribution is an extension to the classical lattice-theoretic fixpoint theorems to account for the dynamics of concurrent mutation and collection.Comment: 38 pages, 21 figures. The short version of this paper appeared in the Proceedings of MPC 201

On Semantic Gamification

The purpose of this essay is to study the extent in which the semantics for different logical systems can be represented game theoretically. I will begin by considering different definitions of what it means to gamify a semantics, and show completeness and limitative results. In particular, I will argue that under a proper definition of gamification, all finitely algebraizable logics can be gamified, as well as some infinitely algebraizable ones (like Łukasiewicz) and some non-algebraizable (like intuitionistic and van Fraassen supervaluation logic)

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

27 p.A conditional is natural if it fulfils the three following conditions. (1) It coincides with the classical conditional when restricted to the classical values T and F; (2) it satisfies the Modus Ponens; and (3) it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements. (We understand the notion ‘natural conditional’ according to N. Tomova, ‘A lattice of implicative extensions of regular Kleene's logics’, Reports on Mathematical Logic, 47, 173–182, 2012.)S

A Selective PMCA Inhibitor Does Not Prolong the Electroolfactogram in Mouse

Within the cilia of vertebrate olfactory receptor neurons, Ca(2+) accumulates during odor transduction. Termination of the odor response requires removal of this Ca(2+), and prior evidence suggests that both Na(+)/Ca(2+) exchange and plasma membrane Ca(2+)-ATPase (PMCA) contribute to this removal.In intact mouse olfactory epithelium, we measured the time course of termination of the odor-induced field potential. Replacement of mucosal Na(+) with Li(+), which reduces the ability of Na(+)/Ca(2+) exchange to expel Ca(2+), prolonged the termination as expected. However, treating the epithelium with the specific PMCA inhibitor caloxin 1b1 caused no significant increase in the time course of response termination.Under these experimental conditions, PMCA does not contribute detectably to the termination of the odor response

Limits of Calcium Clearance by Plasma Membrane Calcium ATPase in Olfactory Cilia

BACKGROUND: In any fine sensory organelle, a small influx of Ca(2+) can quickly elevate cytoplasmic Ca(2+). Mechanisms must exist to clear the ciliary Ca(2+) before it reaches toxic levels. One such organelle has been well studied: the vertebrate olfactory cilium. Recent studies have suggested that clearance from the olfactory cilium is mediated in part by plasma membrane Ca(2+)-ATPase (PMCA). PRINCIPAL FINDINGS: In the present study, electrophysiological assays were devised to monitor cytoplasmic free Ca(2+) in single frog olfactory cilia. Ca(2+) was allowed to enter isolated cilia, either through the detached end or through membrane channels. Intraciliary Ca(2+) was monitored via the activity of ciliary Ca(2+)-gated Cl(-) channels, which are sensitive to free Ca(2+) from about 2 to 10 microM. No significant effect of MgATP on intraciliary free Ca(2+) could be found. Carboxyeosin, which has been used to inhibit PMCA, was found to substantially increase a ciliary transduction current activated by cyclic AMP. This increase was ATP-independent. CONCLUSIONS: Alternative explanations are suggested for two previous experiments taken to support a role for PMCA in ciliary Ca(2+) clearance. It is concluded that PMCA in the cilium plays a very limited role in clearing the micromolar levels of intraciliary Ca(2+) produced during the odor response

Towards balance and boundaries in public discourse : expressing and perceiving online hate speech (XPEROHS)

This study presents an overview and preliminary findings from the XPEROHS-project on hate speech in online contexts. The data is extracted from large-scale Facebook and Twitter corpora, while comparing linguistic instantiations of hate speech in the Danish and German languages. Findings are based on four sub-projects involving the semantics and pragmatics of denigration, the covert dynamics of hate speech, perceptions of spoken and written hate speech, and rhetorical hate speech strategies employed in online interaction. The results demonstrate both overt and covert hate speech towards minority groups, especially Muslims, that are symptomatic of larger societal othering processes and stigmatization