Automatic Concept Formation in Pure Mathematics

The HR program forms concepts and makes conjectures in domains of pure mathematics and uses theorem prover OTTER and model generator MACE to prove or disprove the conjectures. HR measures properties of concepts and assesses the theorems and proofs involving them to estimate the interestingness of each concept and employ a best first search. This approach has led HR to the discovery of interesting new mathematics and enables it to build theories from just the axioms of finite algebras

HR: A System for Machine Discovery in Finite Algebras

We describe the HR concept formation program which invents mathematical definitions and conjectures in finite algebras such as group theory and ring theory. We give the methods behind and the reasons for the concept formation in HR, an evaluation of its performance in its training domain, group theory, and a look at HR in domains other than group theory

Agent based cooperative theory formation in pure mathematics

The HR program, Colton et al. (1999), performs theory formation in domains of pure mathematics. Given only minimal information about a domain, it invents concepts, make conjectures, proves theorems and finds counterexamples to false conjectures. We present here a multi-agent version of HR which may provide a model for how individual mathematicians perform separate investigations but communicate their results to the mathematical community, learning from others as they do. We detail the exhaustive categorisation problem to which we have applied a multi-agent approach.

A Word Sense-Oriented User Interface for Interactive Multilingual Text Retrieval

In this paper we present an interface for supporting a user in an interactive cross-language search process using semantic classes. In order to enable users to access multilingual information, different problems have to be solved: disambiguating and translating the query words, as well as categorizing and presenting the results appropriately. Therefore, we first give a brief introduction to word sense disambiguation, cross-language text retrieval and document categorization and finally describe recent achievements of our research towards an interactive multilingual retrieval system. We focus especially on the problem of browsing and navigation of the different word senses in one source and possibly several target languages. In the last part of the paper, we discuss the developed user interface and its functionalities in more detail

A Taxonomy for Attack Patterns on Information Flows in Component-Based Operating Systems

We present a taxonomy and an algebra for attack patterns on component-based operating systems. In a multilevel security scenario, where isolation of partitions containing data at different security classifications is the primary security goal and security breaches are mainly defined as undesired disclosure or modification of classified data, strict control of information flows is the ultimate goal. In order to prevent undesired information flows, we provide a classification of information flow types in a component-based operating system and, by this, possible patterns to attack the system. The systematic consideration of informations flows reveals a specific type of operating system covert channel, the covert physical channel, which connects two former isolated partitions by emitting physical signals into the computer's environment and receiving them at another interface.Comment: 9 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

Optimized imaging using non-rigid registration

The extraordinary improvements of modern imaging devices offer access to data with unprecedented information content. However, widely used image processing methodologies fall far short of exploiting the full breadth of information offered by numerous types of scanning probe, optical, and electron microscopies. In many applications, it is necessary to keep measurement intensities below a desired threshold. We propose a methodology for extracting an increased level of information by processing a series of data sets suffering, in particular, from high degree of spatial uncertainty caused by complex multiscale motion during the acquisition process. An important role is played by a nonrigid pixel-wise registration method that can cope with low signal-to-noise ratios. This is accompanied by formulating objective quality measures which replace human intervention and visual inspection in the processing chain. Scanning transmission electron microscopy of siliceous zeolite material exhibits the above-mentioned obstructions and therefore serves as orientation and a test of our procedures