340 research outputs found
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
Living with Paradoxes
AbstractA good knowledge representation system has to find a balance between expressive power on the one hand and efficient reasoning on the other. Furthermore it is necessary to understand its limitations and problems. A logic which contains strings is very expressive and allows for very natural representations, which in turn allow for appropriate reasoning patterns. However, such a system has the feature that it is possible to formulate self-referential paradoxes in it. This can be considered as a strength and as a weakness at the same time. On the one hand it is a positive aspect that it is possible to represent paradoxes, which can be formulated in natural language. On the other hand it is necessary to be careful and not to trivialise the logical system. In the paper different aspects of knowledge representation which allows self-referentiality will be discussed. A system will be presented which is a pragmatic compromise between expressive power on the one hand and simplicity and efficiency of the reasoning process on the other hand. It is built on a three-valued system that makes it possible to use reasoning techniques from classical first-order logic
Formal representation and proof for cooperative games
In this contribution we present some work we have been doing in representing and proving theorems from the area of economics, and mainly we present work we will do in a project in which we will apply mechanised theorem proving tools to a class of economic problems for which very few general tools currently exist. For mechanised theorem proving, the research introduces the field to a new application domain with a large user base; more specifically, the researchers are collaborating with developers working on state-of-the-art theorem provers. For economics, the research will provide tools for handling a hard class of problems; more generally, as the first application of mechanised theorem proving to centrally involve economic theorists, it aims to properly introduce mechanised theorem proving techniques to the discipline.\u
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
Some Aspects of Analogy in Mathematical Reasoning
An important research problem is the incorporation of âdeclarativeâ knowledge into an automated theorem prover that can be utilized in the search for a proof. An interesting proposal in this direction is Alan Bundyâs approach of using explicit proof plans that encapsulate the general form of a proof and is instantiated into a particular proof for the case at hand. We give some examples that show how a âdeclarativeâ highlevel description of a proof can be used to ïŹnd proofs of apparently âsimiliarâ theorems by analogy. This âanalogicalâ information is used to select the appropriate axioms from the database so that the theorem can be proved. This information is also used to adjust some options of a resolution theorem prover. In order to get a powerful tool it is necessary to develop an epistemologically appropriate language to describe proofs, for which a large set of examples should be used as a testbed. We present some ideas in this direction
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
Computer Algebra and Mechanized Reasoning: Selected St. Andrews' ISSAC/Calculemus 2000 Contributions. Foreword from the Editors
Proving soundness of combinatorial Vickrey auctions and generating verified executable code
Using mechanised reasoning we prove that combinatorial Vickrey auctions are
soundly specified in that they associate a unique outcome (allocation and
transfers) to any valid input (bids). Having done so, we auto-generate verified
executable code from the formally defined auction. This removes a source of
error in implementing the auction design. We intend to use formal methods to
verify new auction designs. Here, our contribution is to introduce and
demonstrate the use of formal methods for auction verification in the familiar
setting of a well-known auction
Towards formal analysis of insider threats for auctions
This paper brings together the world of insider threats and auctions. For online-auction systems, like eBay, but also for high-value one-off auction algorithms as they are used for selling radio wave frequencies, the use of rigorous machine supported modelling and verification techniques is meaningful to prove correctness and scrutinize vulnerability to security and privacy attacks. Surveying the threats in auctions and insider collusions, we present an approach to model and analyze auction protocols for insider threats using the interactive theorem prover Isabelle. As a case study, we use the cocaine auction protocol that represents a nice combination of cryptographic techniques, protocols, and privacy goals suitable for highlighting insider threats for auctions
Insider threats for auctions: formalization, mechanized proof, and code generation
This paper applies machine assisted formal methods to explore insider threats for auctions. Auction systems, like eBay, are an important problem domain for formal analysis because they challenge modelling concepts as well as analysis methods. We use machine assisted formal modelling and proof in Isabelle to demonstrate how security and privacy goals of auction protocols can be formally verified. Applying the costly scrutiny of formal methods is justified for auctions since privacy and trust are prominent issues and auctions are sometimes designed for one-off occasions where high bids are at stake. For example, when radio wave frequencies are on sale, auctions are especially created for just one occasion where fair and consistent behaviour is required. Investigating the threats in auctions and insider collusions, we model and analyze auction protocols for insider threats using the interactive theorem prover Isabelle. We use the existing example of a fictitious cocaine auction protocol from the literature to develop and illustrate our approach. Combining the Isabelle Insider framework with the inductive approach to verifying security protocols in Isabelle, we formalize the cocaine auction protocol, prove that this formal definition excludes sweetheart deals, and also that collusion attacks cannot generally be excluded. The practical implication of the formalization is demonstrated by code generation. Isabelle allows generating code from constructive specifications into the programming language Scala. We provide constructive test functions for cocaine auction traces, prove within Isabelle that these functions conform to the protocol definition, and apply code generation to produce an implementation of the executable test predicate for cocaine auction traces in Scala
- âŠ