Finding the Most Similar Concepts in Two Different Ontologies

Abstract. A concise manner to send information from agent A to B is to use phrases constructed with the concepts of A: to use the concepts as the atomic tokens to be transmitted. Unfortunately, tokens from A are not understood by (they do not map into) the ontology of B, since in general each ontology has its own address space. Instead, A and B need to use a common communication language, such as English: the transmission tokens are English words. An algorithm is presented that finds the concept cB in OB (the ontology of B) most closely resembling a given concept cA. That is, given a concept from ontology OA, a method is provided to find the most similar concept in OB, as well as the similarity sim between both concepts. Examples are given. 1 Introduction an

Understanding constraint expressions in large conceptual schemas by automatic filtering

Human understanding of constraint expressions (also called schema rules) in large conceptual schemas is very di cult. This is due to the fact that the elements (entity types, attributes, relationship types) involved in an expression are de ned in di fferent places in the schema, which may be very distant from each other and embedded in an intricate web of irrelevant elements. The problem is insignifi cant when the conceptual schema is small, but very signi cant when it is large. In this paper we describe a novel method that, given a set of constraint expressions and a large conceptual schema, automatically filters the conceptual schema, obtaining a smaller one that contains the elements of interest for the understanding of the expressions. We also show the application of the method to the important case of understanding the specication of event types, whose constraint expressions consists of a set of pre and postconditions. We have evaluated the method by means of its application to a set of large conceptual schemas. The results show that the method is eff ective and e cient. We deal with conceptual schemas in UML/OCL, but the method can be adapted to other languages.Peer ReviewedPreprin

Cumulants and the moment algebra: tools for analysing weak measurements

Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call the moment algebra. Apart from resulting in simpler proofs, the flexibility of this structure allows generalizations of the original results to a number of weak measurement scenarios, including one where the weakly interacting pointers reach thermal equilibrium with the probed system.Comment: Journal reference added, minor correction

Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

The algebra of lexical semantics

Abstract. The current generative theory of the lexicon relies primar-ily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the gener-ative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of de-scribing discrepancies between syntactic type (lexical category) and se-mantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR. 1 Problem Statement In developing a formal theory of lexicography our starting point will be the informal practice of lexicography, rather than the more immediately related for-mal theories of Artificial Intelligence (AI) and Knowledge Representation (KR). Lexicography is a relatively mature field, with centuries of work experience an