Preferences are not always expressible via complete linear orders: sometimes it is more natural to allow for the presence of incomparable outcomes. This may hold both in the agents’ preference ordering and in the social order. In this article, we consider this scenario and study what properties it may have. In particular, we show that, despite the added expressivity and ability to resolve confl...

Modal logic is extended by partially ordering the modalities. The modalities are normal, i.e., commute with either conjunctions or disjunctions and preserve either Truth or Falsity (respectively). The partial order does not conflict with type of modality (K, S4, etc.) although this paper will concentrate on S4 since partially ordered S4 systems appear to be numerous. The partially-ordered norma...

‎in this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.

We generalize the matroid intersection theorem to distributive supermatroids, a structure that extends the matroid to the partially ordered ground set. Distributive supermatroids are special cases of both supermatroids and greedoids, and they generalize polymatroids. This is the first good characterization proved for the intersection problem of an independence system where the ground set is par...

In this paper, we introduce a new class of (semi)hypergroup from a given (partially) quasi-ordered (semi)hypergroup as a generalization of {it "$El$--hyperstructures"}. Then, we study some basic properties and important elements belong to this class.}

The purpose of this paper is to establish fixed point results for a single mapping in a partially ordered modular metric space, and to prove a common fixed point theorem for two self-maps satisfying some weak contractive inequalities.

Mathematical concepts of order and ordering relations play multiple roles in semantic technologies. Discrete totally ordered data characterize both input streams and top-k rank-ordered recommendations and query output, while temporal attributes establish numerical total orders, either over time points or in the more complex case of startend temporal intervals. But also of note are the fully par...