Many tasks in statistical and causal inference can be construed as problems of entailment in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for causal probabilistic languages than for pure probabilistic (or “associational”) languages. Despite several senses in which causal reasoning is indeed more complex—both expressively and inferentially—we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. (...) Along the way we answer several open problems concerning the complexity of well-known probability logics, in particular demonstrating the ${\exists \mathbb {R}}$ -completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability. (shrink)

Based on the analysis of the accumulated experimental data and on the informational concepts of the Informational Model of Consciousness (IMC), in this article is presented an informational modeling of the operability of the posterior cingulate cortex (PCC). Examination of the experimental results obtained with the modern non-destructive, high spatial resolution investigation tools to study the functional characteristics of the PCC and associate metabolic processes, shows mainly that this is involved in the large scale default mode network (DMN), composed primarily (...) by PCC, medial prefrontal cortex (MPFC), and the inferior parietal lobe (IPL), displaying an increased activity under passive task conditions (i.e. negative mode). This operability mode is in an opposing balance with attention and task performances mode, acting thus as a disruption process. One of the main conclusions is that the PCC cognitive orientation is primarily focused on the self person or on the “self” (I) projected from others, in “daydreaming” or “mind-wandering" wakeful rest, involved in present or future virtual projects. In spite of these advances, the particular role and specific functions of PCC are not yet fully understood, PCC remaining an enigmatic/contradictory structure of the brain, not included up to date in any brain model, so the PCC informational modeling presented here in terms of IMC covers this lack. IMC assigns to the brain the fundamental role of informational processor, composed by various operating structures according to specific objectives synthetically expressed by seven main cognitive centers of “self" (I) as: Iknow (memory), Iwant (decision), Ilove (emotions), Iam (self-status), Icreate (genetic transmission), Icreated (genetic inheritance), Ibelive (info-selection), assuring the info-connectivity with the body and external/internal world, the adaptability (learning process) and survival. It is deduced in this way that the specific behavior of PCC according to its intermediary architectural position between the vital central region of the brain, connecting the mind with the external/internal reality, is that of a moderator/integrator hub/informational YES/NO switcher from the external/awake captured focusing information to the internal accumulated experience of life, used as a valid reference. Therefore, the specific operability of PCC in terms of cognitive centers is that of an informational switcher, mainly operating with Iknow/Iwant to explore the self-status reflected in Iam, within day-dreaming/imaginary virtual sceneries. (shrink)