The paper identifies necessary steps to create a national information system for management and preservation of cultural heritage documentation. The Republic of Serbia, where the digitization of cultural heritage is recognized as a segment of cultural development and officially accepted as one of the methods for preservation and presentation of heritage documentation, is taken as a case study. The paper describes the evolutionary path of the digitization process in Serbia and analyzes the importance of the adoption of a legal framework and establishment of national standards in the process of achieving the uniqueness in cultural heritage long-term sustainable documentation management and preservation across cultural institutions.

We present a prepositional probability logic which allows making formulas that speak about imprecise and conditional probabilities. A class of Kripke-like probabilistic models is defined to give semantics to probabilistic formulas. Every possible world of such a model is equipped with a probability space. The corresponding probabilities may have nonstandard values. The proposition "the probability is close to r" means that there is an infinitesimal ε, such that the probability is equal to r – ε (or r + ε). We provide an infinitary axiomatization and prove the corresponding extended completeness theorem.

We present two complex valued probabilistic logics, LCOMPB and LCOMPS, which extend classical propositional logic. In LCOMPB one can express formulas of the form Bz,?? meaning that the probability of ? is in the complex ball with the center z and the radius ?, while in LCOMPS one can make statements of the form Sz,?? with the intended meaning - the probability of propositional formula ? is in the complex square with the center z and the side 2?. The corresponding strongly complete axiom systems are provided. Decidability of the logics are proved by reducing the satisfiability problem for LCOMPB (LCOMPS) to the problem of solving systems of quadratic (linear) inequalities.

In this paper we provide a strongly complete axiomatization of a temporal epistemic logic in which non-rigid sets of agents are allowed. Using this framework, we prove a number of properties of the blockchain protocol with respect to the given set of axioms and premises.

In this article, we present the probability logic LFOCP which is suitable to formalize statements about conditional probabilities of first order formulas. The logical language contains formulas such as CP_≥s(ϕ, θ) and CP_≤s(ϕ, θ) with the intended meaning ‘the conditional probability of ϕ given θ is at least s’ and ‘at most s’, respectively, where ϕ and θ are first-order formulas. We introduce a class of first order Kripke-like models that combine properties of the usual Kripke models and finitely additive probabilities. We propose an infinitary axiom system and prove that it is sound and strongly complete with respect to the considered class of models. In this article, the terms finitary and infinitary concern meta language only, i.e. the logical language is countable, formulas are finite, while only proofs are allowed to be infinite. We analyse decidability of LFOCP and provide a procedure which decides satisfiability of a given conditional probability formula, in the case when the underlying first-order theory is decidable. Relationships to other systems and possible extensions of the presented approach are discussed.