A Higher-Order Calculus for Categories

A calculus for a fragment of category theory is presented. The types in the language denote categories and the expressions functors. The judgements of the calculus systematise categorical arguments such as: an expression is functorial in its free variables; two expressions are naturally isomorphic in their free variables. There are special binders for limits and more general ends. The rules for limits and ends support an algebraic manipulation of universal constructions as opposed to a more traditional diagrammatic approach. Duality within the calculus and applications in proving continuity are discussed with examples. The calculus gives a basis for mechanising a theory of categories in a generic theorem prover like Isabelle

Library Cataloguing and Role and Reference Grammar for Natural Language processing Applications

Several potential application of natural language processing have proven to be intractable. In this paper, we provide and overview of methods from library cataloguing and linguistics that have not yet been adopted by the natural language processing community and which could be used to help solve some of these problems

Content Differences in Syntactic and Semantic Representations

Syntactic analysis plays an important role in semantic parsing, but the nature of this role remains a topic of ongoing debate. The debate has been constrained by the scarcity of empirical comparative studies between syntactic and semantic schemes, which hinders the development of parsing methods informed by the details of target schemes and constructions. We target this gap, and take Universal Dependencies (UD) and UCCA as a test case. After abstracting away from differences of convention or formalism, we find that most content divergences can be ascribed to: (1) UCCA's distinction between a Scene and a non-Scene; (2) UCCA's distinction between primary relations, secondary ones and participants; (3) different treatment of multi-word expressions, and (4) different treatment of inter-clause linkage. We further discuss the long tail of cases where the two schemes take markedly different approaches. Finally, we show that the proposed comparison methodology can be used for fine-grained evaluation of UCCA parsing, highlighting both challenges and potential sources for improvement. The substantial differences between the schemes suggest that semantic parsers are likely to benefit downstream text understanding applications beyond their syntactic counterparts.Comment: NAACL-HLT 2019 camera read

Are seismic waiting time distributions universal?

We show that seismic waiting time distributions in California and Iceland have many features in common as, for example, a power-law decay with exponent $\alpha \approx 1.1$ for intermediate and with exponent $\gamma \approx 0.6$ for short waiting times. While the transition point between these two regimes scales proportionally with the size of the considered area, the full distribution is not universal and depends in a non-trivial way on the geological area under consideration and its size. This is due to the spatial distribution of epicenters which does \emph{not} form a simple mono-fractal. Yet, the dependence of the waiting time distributions on the threshold magnitude seems to be universal.Comment: 5 pages, 4 figures, accepted for publication in Geophys. Res. Let

A Universal Machine for Biform Theory Graphs

Broadly speaking, there are two kinds of semantics-aware assistant systems for mathematics: proof assistants express the semantic in logic and emphasize deduction, and computer algebra systems express the semantics in programming languages and emphasize computation. Combining the complementary strengths of both approaches while mending their complementary weaknesses has been an important goal of the mechanized mathematics community for some time. We pick up on the idea of biform theories and interpret it in the MMTt/OMDoc framework which introduced the foundations-as-theories approach, and can thus represent both logics and programming languages as theories. This yields a formal, modular framework of biform theory graphs which mixes specifications and implementations sharing the module system and typing information. We present automated knowledge management work flows that interface to existing specification/programming tools and enable an OpenMath Machine, that operationalizes biform theories, evaluating expressions by exhaustively applying the implementations of the respective operators. We evaluate the new biform framework by adding implementations to the OpenMath standard content dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final publication is available at http://link.springer.com