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

The use of data-mining for the automatic formation of tactics

This paper discusses the usse of data-mining for the automatic formation of tactics. It was presented at the Workshop on Computer-Supported Mathematical Theory Development held at IJCAR in 2004. The aim of this project is to evaluate the applicability of data-mining techniques to the automatic formation of tactics from large corpuses of proofs. We data-mine information from large proof corpuses to find commonly occurring patterns. These patterns are then evolved into tactics using genetic programming techniques

Mathematical proofs and scientific discovery

The idea that science can be automated is so deeply related to the view that the method of mathematics is the axiomatic method, that confuting the claim that mathematical knowledge can be extended by means of the axiomatic method is almost equivalent to confuting the claim that science can be automated. I argue that the axiomatic view is inadequate as a view of the method of mathematics and that the analytic view is to be preferred. But, if the method of mathematics and natural sciences is the analytic method, then the advancement of knowledge cannot be mechanized, since non-deductive reasoning plays a crucial role in the analytic method, and non-deductive reasoning cannot be fully mechanized

The Most Influential Paper Gerard Salton Never Wrote

Gerard Salton is often credited with developing the vector space model (VSM) for information retrieval (IR). Citations to Salton give the impression that the VSM must have been articulated as an IR model sometime between 1970 and 1975. However, the VSM as it is understood today evolved over a longer time period than is usually acknowledged, and an articulation of the model and its assumptions did not appear in print until several years after those assumptions had been criticized and alternative models proposed. An often cited overview paper titled ???A Vector Space Model for Information Retrieval??? (alleged to have been published in 1975) does not exist, and citations to it represent a confusion of two 1975 articles, neither of which were overviews of the VSM as a model of information retrieval. Until the late 1970s, Salton did not present vector spaces as models of IR generally but rather as models of specifi c computations. Citations to the phantom paper refl ect an apparently widely held misconception that the operational features and explanatory devices now associated with the VSM must have been introduced at the same time it was fi rst proposed as an IR model.published or submitted for publicatio

Technology assessment of advanced automation for space missions

Six general classes of technology requirements derived during the mission definition phase of the study were identified as having maximum importance and urgency, including autonomous world model based information systems, learning and hypothesis formation, natural language and other man-machine communication, space manufacturing, teleoperators and robot systems, and computer science and technology

07421 Abstracts Collection -- Formal Protocol Verification Applied

From 14/10/2007 to 19/10/2007, the Dagstuhl Seminar 07421 ``Formal Protocol Verification Applied\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available