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Propositional term modal logic is interpreted over Kripke structures with unboundedly many accessibility relations and hence the syntax admits variables indexing modalities and quantification over them. This logic is undecidable, and we consider a variable-free propositional bi-modal logic with implicit quantification. Thus [∀]α asserts necessity over all accessibility relations and [∃]α is classical necessity over some accessibility relation. The logic is associated with a natural bisimulation relation over models and we show that the logic is exactly the bisimulation invariant fragment of a two sorted first order logic. The logic is easily seen to be decidable and admits a complete axiomatization of valid formulas. Moreover the decision procedure extends naturally to the 'bundled fragment' of full term modal logic.

Objectives Evidence from several lines of research suggests the critical role of neuropeptide oxytocin in social cognition and social behavior. Though a few studies have examined the effect of oxytocin on clinical symptoms of schizophrenia, the underlying neurobiological changes are underexamined. Hence, in this study, we examined the effect of oxytocin on the brain’s effective connectivity in schizophrenia. Methods 31 male patients with schizophrenia (SCZ) and 21 healthy male volunteers (HV) underwent resting functional magnetic resonance imaging scans with intra-nasal oxytocin (24 IU) and placebo administered in counterbalanced order. We conducted a whole-brain effective connectivity analysis using a multivariate vector autoregressive granger causality model. We performed a conjunction analysis to control for spurious changes and canonical correlation analysis between changes in connectivity and clinical and demographic variables. Results Three connections, sourced from the left caudate survived the FDR correction threshold with the conjunction analysis; connections to the left supplementary motor area, left precentral gyrus, and left frontal inferior triangular gyrus. At baseline, SCZ patients had significantly weaker connectivity from caudate to these three regions. Oxytocin, but not placebo, significantly increased the strength of connectivity in these connections. Better cognitive insight and lower negative symptoms were associated with a greater increase in connectivity with oxytocin. Conclusions These findings provide a preliminary mechanistic understanding of the effect of oxytocin on brain connectivity in schizophrenia. The study findings provide the rationale to examine the potential utility of oxytocin for social cognitive deficits in schizophrenia.