The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of inform...

In this paper, we first extend the concept of arity in crisp convex spaces to case fuzzification and give some related properties. From view hull operator, study relations between disjoint sum M-fuzzifying its factor spaces. We also examine additivity degree separability (S0,S1,S2,S3,S4). Finally, show that every space is JHC iff corresponding JHC.

We propose an axiomatic framework for updating complete preference orderings without the monotonicity axiom. The induced preference reversals are justified on the basis of a normative interpretation that reconciles consequentialism with adequate forms of choice consistency. We conclude that preferences need not, and in some contexts even should not be recursive, thus confirming the intuition of...

The purpose of this note is to demonstrate that a weak form of club guessing on ω1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for ω-proper forcings.

The non-dictatorial asymmetric Nash bargaining solution is characterized on the basis of independence of irrelevant alternatives, independence of equivalent utility representations, and a new axiom—moderate collective rationality. The latter is logically weaker than Roth’s (1977) strong individual rationality and logically stronger than Anbarci and Sun’s (2011) weakest collective rationality.

Recently Dress andWenzel introduced the concept of valuated matroid in terms of a quantitative extension of the basis exchange axiom for matroids. This paper gives two sets of cryptomorphically equivalent axioms of valuated matroids in terms of a function defined on the family of the independent sets of the underlying matroid.

We study under which conditions the domain of-terms () and the equality theory of the-calculus () form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom , and the formula language must depart from Horn clauses and accept universal quantiications and implications in goals. In short, CLP(,) must be close to Prolog.

In this article we introduce a new axiom for bargaining solutions, named Proportional Concession Monotonicity (PCM), which imposes that no player benefit when all players collectively make proportional concessions with respect to their respective utopia values. We reconsider the leximin solution (Imai, 1983), and obtain an alternative characterization on the basis of PCM. JEL-Classification: C78