Classical BI: Its Semantics and Proof Theory

We present Classical BI (CBI), a new addition to the family of bunched logics which originates in O'Hearn and Pym's logic of bunched implications BI. CBI differs from existing bunched logics in that its multiplicative connectives behave classically rather than intuitionistically (including in particular a multiplicative version of classical negation). At the semantic level, CBI-formulas have the normal bunched logic reading as declarative statements about resources, but its resource models necessarily feature more structure than those for other bunched logics; principally, they satisfy the requirement that every resource has a unique dual. At the proof-theoretic level, a very natural formalism for CBI is provided by a display calculus \`a la Belnap, which can be seen as a generalisation of the bunched sequent calculus for BI. In this paper we formulate the aforementioned model theory and proof theory for CBI, and prove some fundamental results about the logic, most notably completeness of the proof theory with respect to the semantics.Comment: 42 pages, 8 figure

The effects of AMPA receptor blockade on resting magnetoencephalography recordings

The ionotropic N-methyl-D-aspartate and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptors of the glutamatergic neurotransmitter system are of fundamental importance to healthy brain function. Neuroimaging studies in humans have previously been conducted using various drugs that interact with N-methyl-D-aspartate glutamate receptors, but no such studies have investigated AMPA receptor signalling. The recent approval of perampanel (Fycompa) for use in humans provides a means to specifically study the role of AMPA receptors in the pharmacological basis of neuroimaging signals. Twenty male subjects participated in this placebo-controlled crossover study that consisted of two study days separated by a minimum two-week washout period. On one occasion participants ingested a 6 mg dose of perampanel, and on the other a placebo. Ten minutes of wakeful rest was recorded before and after each dose using magnetoencephalography. Subjective ratings of intoxication were significantly higher following drug than placebo. Cluster-based randomisation testing of sensor-level magnetoencephalography data showed significant drug-induced increases in low frequency power (1–4 Hz, 4–8 Hz, 8–13 Hz, 13–30 Hz), along with a significant decrease in the high gamma range (50–90 Hz). We also observed selective increases in functional connectivity in the alpha and beta bands. The findings are consistent with preclinical work and are similar to the spectral profile of other anti-epileptic drugs

Bridging the Two Plans in the Semantics for Relevant Logic

Part of the Synthese Library book series (SYLI, volume 418)This paper considers how the two plans in the semantics for relevant logic are related to each other. The so-called American plan, classical-style four-valued semantics, is intuitive, but weak. The so-called Australian plan, two-valued frame semantics, is very powerful, but the semantic devices employed need some explanation. Examining R. Routley’s 1984 paper ‘American plan completed, ’ this paper argues that the American plan provides an explanatory and ontological basis for the Australian plan, and that the latter is just a developed form of the former

Energy landscape of resting magnetoencephalography reveals frontoparietal network impairments in epilepsy

Juvenile myoclonic epilepsy (JME) is a form of idiopathic generalized epilepsy. It is yet unclear to what extent JME leads to abnormal network activation patterns. Here, we characterised statistical regularities in MEG resting-state networks and their differences between JME patients and controls, by combining a pairwise maximum entropy model (pMEM) and novel energy landscape analyses for MEG. First, we fitted the pMEM to the MEG oscillatory power in the frontoparietal network (FPN) and other resting-state networks, which provided a good estimation of the occurrence probability of network states. Then, we used energy values derived from the pMEM to depict an energy landscape, with a higher energy state corresponding to a lower occurrence probability. JME patients showed fewer local energy minima than controls and had elevated energy values for the FPN within the theta, beta and gamma-bands. Furthermore, simulations of the fitted pMEM showed that the proportion of time the FPN was occupied within the basins of energy minima was shortened in JME patients. These network alterations were highlighted by significant classification of individual participants employing energy values as multivariate features. Our findings suggested that JME patients had altered multi-stability in selective functional networks and frequency bands in the frontoparietal cortices

The bearable lightness of being

How are philosophical questions about what kinds of things there are to be understood and how are they to be answered? This paper defends broadly Fregean answers to these questions. Ontological categories-such as object, property, and relation-are explained in terms of a prior logical categorization of expressions, as singular terms, predicates of varying degree and level, etc. Questions about what kinds of object, property, etc., there are are, on this approach, reduce to questions about truth and logical form: for example, the question whether there are numbers is the question whether there are true atomic statements in which expressions function as singular terms which, if they have reference at all, stand for numbers, and the question whether there are properties of a given type is a question about whether there are meaningful predicates of an appropriate degree and level. This approach is defended against the objection that it must be wrong because makes what there depend on us or our language. Some problems confronting the Fregean approach-including Frege's notorious paradox of the concept horse-are addressed. It is argued that the approach results in a modest and sober deflationary understanding of ontological commitments

Avoiding deontic explosion by contextually restricting aggregation

In this paper, we present an adaptive logic for deontic conflicts, called P2.1(r), that is based on Goble's logic SDLaPe-a bimodal extension of Goble's logic P that invalidates aggregation for all prima facie obligations. The logic P2.1(r) has several advantages with respect to SDLaPe. For consistent sets of obligations it yields the same results as Standard Deontic Logic and for inconsistent sets of obligations, it validates aggregation "as much as possible". It thus leads to a richer consequence set than SDLaPe. The logic P2.1(r) avoids Goble's criticisms against other non-adjunctive systems of deontic logic. Moreover, it can handle all the 'toy examples' from the literature as well as more complex ones

Multiplexity of human brain oscillations as a personal brain signature

Human individuality is likely underpinned by the constitution of functional brain networks that ensure consistency of each person's cognitive and behavioral profile. These functional networks should, in principle, be detectable by noninvasive neurophysiology. We use a method that enables the detection of dominant frequencies of the interaction between every pair of brain areas at every temporal segment of the recording period, the dominant coupling modes (DoCM). We apply this method to brain oscillations, measured with magnetoencephalography (MEG) at rest in two independent datasets, and show that the spatiotemporal evolution of DoCMs constitutes an individualized brain fingerprint. Based on this successful fingerprinting we suggest that DoCMs are important targets for the investigation of neural correlates of individual psychological parameters and can provide mechanistic insight into the underlying neurophysiological processes, as well as their disturbance in brain diseases

Predicting MEG resting-state functional connectivity using microstructural information

Understanding how human brain microstructure influences functional connectivity is an important endeavor. In this work, magnetic resonance imaging data from ninety healthy participants were used to calculate structural connectivity matrices using the streamline count, fractional anisotropy, radial diffusivity and a myelin measure (derived from multi-component relaxometry) to assign connection strength. Unweighted binarized structural connectivity matrices were also constructed. Magnetoencephalography resting-state data from those participants were used to calculate functional connectivity matrices, via correlations of the Hilbert envelopes of beamformer timeseries in the delta, theta, alpha and beta frequency bands. Non-negative matrix factorization was performed to identify the components of the functional connectivity. Shortest-path-length and search-information analyses of the structural connectomes were used to predict functional connectivity patterns for each participant. The microstructure-informed algorithms predicted the components of the functional connectivity more accurately than they predicted the total functional connectivity. This provides a methodology to understand functional mechanisms better. The shortest-path-length algorithm exhibited the highest prediction accuracy. Of the weights of the structural connectivity matrices, the streamline count and the myelin measure gave the most accurate predictions, while the fractional anisotropy performed poorly. Overall, different structural metrics paint very different pictures of the structural connectome and its relationship to functional connectivity

Electrophysiological network alterations in adults with copy number variants associated with high neurodevelopmental risk

Rare copy number variants associated with increased risk for neurodevelopmental and psychiatric disorders (referred to as ND-CNVs) are characterized by heterogeneous phenotypes thought to share a considerable degree of overlap. Altered neural integration has often been linked to psychopathology and is a candidate marker for potential convergent mechanisms through which ND-CNVs modify risk; however, the rarity of ND-CNVs means that few studies have assessed their neural correlates. Here, we used magnetoencephalography (MEG) to investigate resting-state oscillatory connectivity in a cohort of 42 adults with ND-CNVs, including deletions or duplications at 22q11.2, 15q11.2, 15q13.3, 16p11.2, 17q12, 1q21.1, 3q29, and 2p16.3, and 42 controls. We observed decreased connectivity between occipital, temporal and parietal areas in participants with ND-CNVs. This pattern was common across genotypes and not exclusively characteristic of 22q11.2 deletions, which were present in a third of our cohort. Furthermore, a data-driven graph theory framework enabled us to successfully distinguish participants with ND-CNVs from unaffected controls using differences in node centrality and network segregation. Together, our results point to alterations in electrophysiological connectivity as a putative common mechanism through which genetic factors confer increased risk for neurodevelopmental and psychiatric disorders