Logike sa integralima u uslovnim očekivanjima

It could say that the research of logical systems in the dissertation goes in two directions: the first one is related to probability theory i.e. measure theory, while the other direction is related to topology. The main subject of this dissertation is extending the classical logic to formal systems which will be adequate for describing and concluding in the mentioned mathematical environments. The first part represents follow-up of works by M. Rašković and R. Đorđević in the area of probability logics and especially in the area of biprobability logics. The focus is on the logics with integral operators and logics with conditional expectation operators. The topological class logic [11, 12], which is adequate for studying the notions of topological product and continuous functions on topological class-spaces, is presented in the second part of this dissertation

Logike sa metričkim operatorima

The aim of this paper is to combine distance functions and Boolean proposi­ tions by developing a formalism suitable for speaking about distances between Boolean formulas. We introduce and investigate a formal language that is an extension of classical propositional language obtained by adding new binary (modal -like) operators of t he form D≤ s and D≥ s , seQt, Our language all­ ows making formulas such as D≤ s(a , (3 ) with the intended meaning 'distance between formulas a and (3 is less than or equal to s'. The semantics of the proposed language consists of possible worlds with a distanc e function defined between sets of worlds. Our main concern is a complete axiomatization that is sound and strongly complete with respect to the given semantics

Constraining the T2K neutrino oscillation parameter results using data from the off-axis near detector, ND280:Implementation of a nucleon removal energy systematic uncertainty treatment in the BANFF fit

Presented in this thesis are the results of the BANFF near-detector fit as part of the T2K 2020 neutrino oscillation parameter constraint, with a focus on the implementation of four nucleon-removal energy parameters, $\Delta E_{\mathrm{rmv}}$. These parameters correspond to the systematic uncertainty associated with the energetic cost, $E_{\mathrm{rmv}}$, of liberating a bound nucleon from the ground state of a nucleus in quasielastic neutrino scattering. Previously the dominant source of systematic uncertainty on the extraction of the neutrino mass splitting term $\Delta m^2_{32}$(NO)/$|\Delta m^2_{31}|$(IO), an update of the nuclear model used for CCQE interactions at T2K from a relativistic Fermi gas model to a spectral function model and a new treatment of the systematic uncertainty on $E_{\mathrm{rmv}}$ has allowed the total bias on $\Delta m^2_{32}$ to be reduced by a factor of 2.8, and does not impact T2K's ability to exclude leptonic CP-conservation. The fit to the ND280 data is an essential stage of the extraction of the PMNS mixing parameters from T2K's data in which the beam and interaction cross-section models common to ND280 and Super-Kamiokande are constrained by sampling the unoscillated beam. The ND280 data are shown to be consistent with the T2K model, reporting a p-value of $p=0.74$, an improvement on the previous ND280 fit $p=0.5$. A study of the postfit model shows an improved consistency with a p-value of $p=0.82$. The impact of propagating biases in the fits to the ND280 data to the fits to Super-Kamiokande data on the constraints on $\Delta m^2_{32}$ and $\delta_{CP}$ are investigated, shown to be small, and covered by an additional uncertainty term in the likelihood driven by fits to alternative models. The overall contribution of the $E_{\mathrm{rmv}}$ systematic uncertainty to the total variance on $\Delta m^2_{32}$ using the 2020 (2018) T2K implementation was estimated to be $\sigma_{E_{\text{rmv}}}^2/\sigma_{\Delta m^2}^2=1(6)\%$