We discuss some aspects of infinitely exchangeable partition-valued stochastic processes. In particular, we introduce the the cut-and-paste process on the state space of partitions of the natural numbers whose sample paths differ from previously studied exchangeable coalescent (Kingman, 1982) and fragmentation (Bertoin, 2001) processes. Though it evolves differently, the cut-and-paste process p...

In this paper, we consider R-valued integrable processes which are increasing in the convex order, i.e. R-valued peacocks in our terminology. After the presentation of some examples, we show that an R-valued process is a peacock if and only if it has the same one-dimensional marginals as an R-valued martingale. This extends former results, obtained notably by V. Strassen (1965), J.L. Doob (1968...

I adapt a reduction process introduced by Serrano and Volij (1998) so that the reduced games of convex-valued games are convex-valued. I use the corresponding consistency property and its converse to axiomatize the inner core for games that are convex-valued, non-level and smooth.

In this paper, we prove that a fuzzy set–valued Brownian motion Bt, as defined in [2], can be handle by an R–valued Wiener process bt, in the sense that Bt = Ibt ; i.e. it is actually the indicator function of a Wiener process.

In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called “jump-type Fleming-Viot processes”. Furthermore we a...

Closed classes of three-valued logic generated by periodic symmetric funtions that equal 1 in tuples from {1, 2} and equal 0 on the rest tuples are considered. Criteria for bases existence and finite bases existence for these classes is obtained. The problem of the bases existence for some families of closed classes of the three-valued logic functions is considered in the paper. E. Post [1] (se...

Partial functions are abundant in mathematics and program specifications. Unfortunately, their importance has been mostly ignored in automated theorem proving. In this paper, we develop a theorem proving strategy for Partial Classical Logic (PCL). Proof search takes place in Kleene Logic. We show that PCL theories can be translated into equivalent sets of formulas in Kleene logic. For proof sea...

Łukasiewicz three-valued logic Ł3 is often understood as the set of 3-valued valid formulas according to Łukasiewicz’s 3-valued matrices. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: “well-determined” Ł3a and “truth-preserving” Ł3b defined by two different consequence relations on the 3-valued matrices. The aim of this paper is to provide (by using D...