Simplicial Models for the Epistemic Logic of Faulty Agents

In recent years, several authors have been investigating simplicial models, a model of epistemic logic based on higher-dimensional structures called simplicial complexes. In the original formulation, simplicial models were always assumed to be pure, meaning that all worlds have the same dimension. This is equivalent to the standard S5n semantics of epistemic logic, based on Kripke models. By removing the assumption that models must be pure, we can go beyond the usual Kripke semantics and study epistemic logics where the number of agents participating in a world can vary. This approach has been developed in a number of papers, with applications in fault-tolerant distributed computing where processes may crash during the execution of a system. A difficulty that arises is that subtle design choices in the definition of impure simplicial models can result in different axioms of the resulting logic. In this paper, we classify those design choices systematically, and axiomatize the corresponding logics. We illustrate them via distributed computing examples of synchronous systems where processes may crash

Two-agent approximate agreement from an epistemic logic perspective

We investigate the two agents approximate agreement problem in a dynamic network in which topology may change unpredictably,and where consensus is not solvable. It is known that the number of rounds necessary and sufficient to guarantee that the two agents output values 1/k^3 away from each other is k. We distil ideas from previous papers to provide a self-contained, elementary introduction, that explains this result from the epistemic logic perspective

Two-agent approximate agreement from an epistemic logic perspective

We investigate the two agents approximate agreement problem in a dynamic network in which topology may change unpredictably, and where consensus is not solvable. It is known that the number of rounds necessary and sufficient to guarantee that the two agents output values 1/k3 away from each other is k. We distil ideas from previous papers to provide a self-contained, elementary introduction, that explains this result from the epistemic logic perspective

Control of inhibition by the direct action of cannabinoids on GABA_A receptors

Cannabinoids are known to regulate inhibitory synaptic transmission via activation of presynaptic G protein-coupled cannabinoid CB1 receptors (CB1Rs). Additionally, recent studies suggest that cannabinoids can also directly interact with recombinant GABAA receptors (GABAARs), potentiating currents activated by micromolar concentrations of γ-aminobutyric acid (GABA). However, the impact of this direct interaction on GABAergic inhibition in central nervous system is unknown. Here we report that currents mediated by recombinant GABAARs activated by high (synaptic) concentrations of GABA as well as GABAergic inhibitory postsynaptic currents (IPSCs) at neocortical fast spiking (FS) interneuron to pyramidal neuron synapses are suppressed by exogenous and endogenous cannabinoids in a CB1R-independent manner. This IPSC suppression may account for disruption of inhibitory control of pyramidal neurons by FS interneurons. At FS interneuron to pyramidal neuron synapses, endocannabinoids induce synaptic low-pass filtering of GABAAR-mediated currents evoked by high-frequency stimulation. The CB1R-independent suppression of inhibition is synapse specific. It does not occur in CB1R containing hippocampal cholecystokinin-positive interneuron to pyramidal neuron synapses. Furthermore, in contrast to synaptic receptors, the activity of extrasynaptic GABAARs in neocortical pyramidal neurons is enhanced by cannabinoids in a CB1R-independent manner. Thus, cannabinoids directly interact differentially with synaptic and extrasynaptic GABAARs, providing a potent novel context-dependent mechanism for regulation of inhibition.SCOPUS: ar.jinfo:eu-repo/semantics/publishe