Computational aspects of elementary theories of classes of probability spaces

The talk will be devoted to algorithmic issues for elementary theories of various classes of probability spaces (finite, discrete, arbitrary, atomless). We shall consider both theories in a one-sorted language with variables over events, and theories in a two-sorted language that contains, in addition, variables over real numbers. Moreover, we shall pay attention to ‘weak’ spaces, in which measures are assumed to be finitely additive, but not necessarily countably additive; spaces of this kind are used in the semantics of many probabilistic logical systems arising in theoretical computer science. It should be noted that although we shall focus mainly on languages that are close to the traditionally studied elementary languages of fields and lattices, practically all the related results have natural analogues for the so-called ‘first-order logics of probability’, which emerged from J. Halpern's works and whose varians are still extensively studied (for example, by Z. Ognjanović's group in Belgrade).