Forms of Generic Common Knowledge

In multi-agent epistemic logics, common knowledge has been a central consideration of study. A generic common knowledge (G.C.K.) system is one that yields iterated knowledge I(ϕ): 'any agent knows that any agent knows that any agent knows. . . ϕ' for any number of iterations. Generic common knowledge yields iterated knowledge G.C.K.(ϕ) → I(ϕ) but is not necessarily logically equivalent to it. This contrasts with the most prevalent formulation of common knowledge C as equivalent to iterated knowledge. A spectrum of systems may satisfy the G.C.K. condition, of which C is just one. It has been shown that in the usual epistemic scenarios, G.C.K. can replace conventional common knowledge and Artemov has noted that such standard sources of common knowledge as public announcements of atomic sentences generally yield G.C.K. rather than C. In this dissertation we study mathematical properties of generic common knowledge and compare them to the traditional common knowledge notion. In particular, we contrast the modal G.C.K. logics of McCarthy (e.g. M4) and Artemov (e.g. [special characters omitted]) with C-systems (e.g. [special characters omitted]) and present a joint C/G.C.K. implicit knowledge logic [special characters omitted] as a conservative extension of both. We show that in standard epistemic scenarios in which common knowledge of certain premises is assumed, whose conclusion does not concern common knowledge (such as Muddy Children, Wise Men, Unfaithful Wives, etc.), a lighter G.C.K.can be used instead of the traditional, more complicated, common knowledge. We then present the first fully explicit G.C.K. system LP n(LP). This justification logic realizes the corresponding modal system [special characters omitted] so that G.C.K., along with individual knowledge modalities, can always be made explicit

Circulating leptin, soluble leptin receptor and free leptin index in critically ill patients with sepsis: a prospective observational study

BACKGROUND: Leptin, the prototype adipokine, exerts immunomodulatory actions being implicated in inflammatory responses during sepsis. Clinical evidence regarding its role in sepsis has been contradictory, while free leptin has not been studied. The aim of this study was to jointly investigate circulating total leptin, its soluble receptor (sOB-R), and free leptin, as well as their kinetics in critically ill patients with sepsis regarding their diagnostic and prognostic value. METHODS: In a prospective study, serum total leptin, sOB-R and free leptin index (FLI) were determined in 102 critically ill patients with sepsis within 48 hours from sepsis onset and one week after enrollment, and in 102 age and gender-matched healthy controls. RESULTS: Upon enrolment, total leptin, sOB-R and FLI were significantly higher in septic patients compared to controls and they were positively correlated with sepsis severity scores, while they presented a significant decrease during the first week (P<0.001). The decrease in total leptin and sOB-R was significantly higher in patients with sepsis compared to septic shock and in survivors compared to non-survivors at 28 days (P<0.001). Higher serum total leptin was independently associated with survival at 28 days (enrollment: HR 0.86, P=0.03; one week after: HR 0.77, P<0.001). Higher kinetics of total leptin (but not FLI) was independently associated with survival after adjustment (HR: 0.48, P=0.001). CONCLUSIONS: Higher circulating total leptin and its higher kinetics during the first week from sepsis onset independently predict 28-day survival in critically ill patients. Free leptin did not present any additional diagnostic and prognostic value in sepsis