253 research outputs found
The ForMaRE Project - Formal Mathematical Reasoning in Economics
The ForMaRE project applies formal mathematical reasoning to economics. We
seek to increase confidence in economics' theoretical results, to aid in
discovering new results, and to foster interest in formal methods, i.e.
computer-aided reasoning, within economics. To formal methods, we seek to
contribute user experience feedback from new audiences, as well as new
challenge problems. In the first project year, we continued earlier game theory
studies but then focused on auctions, where we are building a toolbox of
formalisations, and have started to study matching and financial risk.
In parallel to conducting research that connects economics and formal
methods, we organise events and provide infrastructure to connect both
communities, from fostering mutual awareness to targeted matchmaking. These
efforts extend beyond economics, towards generally enabling domain experts to
use mechanised reasoning.Comment: Conference on Intelligent Computer Mathematics, 8--12 July, Bath, UK.
Published as number 7961 in Lecture Notes in Artificial Intelligence,
Springe
Set Theory or Higher Order Logic to Represent Auction Concepts in Isabelle?
When faced with the question of how to represent properties in a formal proof
system any user has to make design decisions. We have proved three of the
theorems from Maskin's 2004 survey article on Auction Theory using the
Isabelle/HOL system, and we have produced verified code for combinatorial
Vickrey auctions. A fundamental question in this was how to represent some
basic concepts: since set theory is available inside Isabelle/HOL, when
introducing new definitions there is often the issue of balancing the amount of
set-theoretical objects and of objects expressed using entities which are more
typical of higher order logic such as functions or lists. Likewise, a user has
often to answer the question whether to use a constructive or a
non-constructive definition. Such decisions have consequences for the proof
development and the usability of the formalization. For instance, sets are
usually closer to the representation that economists would use and recognize,
while the other objects are closer to the extraction of computational content.
In this paper we give examples of the advantages and disadvantages for these
approaches and their relationships. In addition, we present the corresponding
Isabelle library of definitions and theorems, most prominently those dealing
with relations and quotients.Comment: Preprint of a paper accepted for the forthcoming CICM 2014 conference
(cicm-conference.org/2014): S.M. Watt et al. (Eds.): CICM 2014, LNAI 8543,
Springer International Publishing Switzerland 2014. 16 pages, 1 figur
Budget Imbalance Criteria for Auctions: A Formalized Theorem
We present an original theorem in auction theory: it specifies general
conditions under which the sum of the payments of all bidders is necessarily
not identically zero, and more generally not constant. Moreover, it explicitly
supplies a construction for a finite minimal set of possible bids on which such
a sum is not constant. In particular, this theorem applies to the important
case of a second-price Vickrey auction, where it reduces to a basic result of
which a novel proof is given. To enhance the confidence in this new theorem, it
has been formalized in Isabelle/HOL: the main results and definitions of the
formal proof are re- produced here in common mathematical language, and are
accompanied by an informal discussion about the underlying ideas.Comment: 6th Podlasie Conference on Mathematics 2014, 11 page
An Introduction to Mechanized Reasoning
Mechanized reasoning uses computers to verify proofs and to help discover new
theorems. Computer scientists have applied mechanized reasoning to economic
problems but -- to date -- this work has not yet been properly presented in
economics journals. We introduce mechanized reasoning to economists in three
ways. First, we introduce mechanized reasoning in general, describing both the
techniques and their successful applications. Second, we explain how mechanized
reasoning has been applied to economic problems, concentrating on the two
domains that have attracted the most attention: social choice theory and
auction theory. Finally, we present a detailed example of mechanized reasoning
in practice by means of a proof of Vickrey's familiar theorem on second-price
auctions
Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014
Preface
For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general
public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas.
As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities
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