31,495 research outputs found
A unified theory of cone metric spaces and its applications to the fixed point theory
In this paper we develop a unified theory for cone metric spaces over a solid
vector space. As an application of the new theory we present full statements of
the iterated contraction principle and the Banach contraction principle in cone
metric spaces over a solid vector space.Comment: 51 page
A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time
In this paper we provide a flexible framework allowing for a unified study of
time consistency of risk measures and performance measures (also known as
acceptability indices). The proposed framework not only integrates existing
forms of time consistency, but also provides a comprehensive toolbox for
analysis and synthesis of the concept of time consistency in decision making.
In particular, it allows for in depth comparative analysis of (most of) the
existing types of time consistency -- a feat that has not be possible before
and which is done in the companion paper [BCP2016] to this one. In our approach
the time consistency is studied for a large class of maps that are postulated
to satisfy only two properties -- monotonicity and locality. The time
consistency is defined in terms of an update rule. The form of the update rule
introduced here is novel, and is perfectly suited for developing the unifying
framework that is worked out in this paper. As an illustration of the
applicability of our approach, we show how to recover almost all concepts of
weak time consistency by means of constructing appropriate update rules
A General Bargaining Model of Legislative Policy-making
We present a general model of legislative bargaining in which the status quo is an arbitrary point in a multidimensional policy space. In contrast to other bargaining models, the status quo is not assumed to be bad for all legislators, and delay may be Pareto efficient. We prove existence of stationary equilibria. We show that if all legislators are risk averse or if even limited transfers are possible, then delay is only possible if the status quo lies in the core. Thus, we expect immediate agreement in multidimensional models, where the core is typically empty. In one dimension, delay is possible if and only if the status quo lies in the core of the voting rule, and then it is the only possible outcome. Our comparative statics analysis yield two noteworthy insights: moderate status quos imply moderate policy outcomes, and legislative patience implies policy moderation
An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces
This paper explores new notions of approximate minimality in set optimization using a set approach. We propose characterizations of several approximate minimal elements of families of sets in real linear spaces by means of general functionals, which can be unified in an inequality approach. As particular cases, we investigate the use of the prominent Tammer–Weidner nonlinear scalarizing functionals, without assuming any topology, in our context. We also derive numerical methods to obtain approximate minimal elements of families of finitely many sets by means of our obtained results
The Expressive Power of k-ary Exclusion Logic
In this paper we study the expressive power of k-ary exclusion logic, EXC[k],
that is obtained by extending first order logic with k-ary exclusion atoms. It
is known that without arity bounds exclusion logic is equivalent with
dependence logic. By observing the translations, we see that the expressive
power of EXC[k] lies in between k-ary and (k+1)-ary dependence logics. We will
show that, at least in the case of k=1, the both of these inclusions are
proper.
In a recent work by the author it was shown that k-ary inclusion-exclusion
logic is equivalent with k-ary existential second order logic, ESO[k]. We will
show that, on the level of sentences, it is possible to simulate inclusion
atoms with exclusion atoms, and this way express ESO[k]-sentences by using only
k-ary exclusion atoms. For this translation we also need to introduce a novel
method for "unifying" the values of certain variables in a team. As a
consequence, EXC[k] captures ESO[k] on the level of sentences, and we get a
strict arity hierarchy for exclusion logic. It also follows that k-ary
inclusion logic is strictly weaker than EXC[k].
Finally we will use similar techniques to formulate a translation from ESO[k]
to k-ary inclusion logic with strict semantics. Consequently, for any arity
fragment of inclusion logic, strict semantics is more expressive than lax
semantics.Comment: Preprint of a paper in the special issue of WoLLIC2016 in Annals of
Pure and Applied Logic, 170(9):1070-1099, 201
A general unified framework for pairwise comparison matrices in multicriterial methods
In a Multicriteria Decision Making context, a pairwise comparison matrix is a helpful tool to determine the weighted
ranking on a set of alternatives or criteria. The entry of the matrix can assume different meanings: can be a preference ratio (multiplicative case) or a preference difference (additive case) or belongs to and measures the
distance from the indifference that is expressed by 0.5 (fuzzy
case). For the multiplicative case, a consistency index for the
matrix has been provided by T.L. Saaty in terms of maximum eigenvalue.
We consider pairwise comparison matrices over an abelian linearly
ordered group and, in this way, we provide a general framework
including the mentioned cases. By introducing a more general notion
of metric, we provide a consistency index that has a natural
meaning and it is easy to compute in the additive and multiplicative cases; in the other cases, it can be computed easily starting from a suitable additive or multiplicative matrix
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