In this paper we study two-sided, one-to-one matching problems and consider the most wellknown solution concept: the men-optimal solution. The men-optimal solution fails to satisfy consistency as well as converse consistency. Thanks to Sasaki and Toda (1992), we know that the minimal consistent extension of the men-optimal solution equals the core (Thomson, 1994a). In this paper, we compute the...

A study is presented on solutions of the Yule-Walker equations for singular AR processes that are stationary outputs of a given AR system. If the Yule-Walker equations admit more than one solution and the order of the AR system is no less than two, the solution set includes solutions which define unstable AR systems. The solution set also includes one solution, the minimal norm solution, which ...

The paper presents a preliminary solution to a long-standing problem in the foundations of well-founded semantics for logic programs. The problem addressed is this: which logic can be considered adequate for well-founded semantics (WFS) in the sense that its minimal models (appropriately defined) coincide with the partial stable models of a logic program? We approach this problem by identifying...

We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, encompassing the top cycle, the uncovered set, the Banks set, the minimal covering set, and the tournament equilibrium set. Moreover, the hi...