arXiv subjects

Michael Kohlhase

Publications and source records attributed to Michael Kohlhase.

33 records · Page 2Linked to original sources

arXiv2011

A Foundational View on Integration Problems

The integration of reasoning and computation services across system and language boundaries is a challenging problem of computer science. In this paper, we use integration for the scenario where we have two systems that we integrate by moving problems and solutions between them. While this scenario is often approached from an engineering perspective, we take a foundational view. Based on the generic declarative language MMT, we develop a theoretical framework for system integration using theories and partial theory morphisms. Because MMT permits representations of the meta-logical foundations themselves, this includes integration across logics. We discuss safe and unsafe integration schemes and devise a general form of safe integration.

cs.LO↗

arXiv2011

Workflows for the Management of Change in Science, Technologies, Engineering and Mathematics

Mathematical knowledge is a central component in science, engineering, and technology (documentation). Most of it is represented informally, and -- in contrast to published research mathematics -- subject to continual change. Unfortunately, machine support for change management has either been very coarse grained and thus barely useful, or restricted to formal languages, where automation is possible. In this paper, we report on an effort to extend change management to collections of semi-formal documents which flexibly intermix mathematical formulas and natural language and to integrate it into a semantic publishing system for mathematical knowledge. We validate the long-standing assumption that the semantic annotations in these flexiformal documents that drive the machine-supported interaction with documents can support semantic impact analyses at the same time. But in contrast to the fully formal setting, where adaptations of impacted documents can be automated to some degree, the flexiformal setting requires much more user interaction and thus a much tighter integration into document management workflows.

cs.DL↗

arXiv2011

A Scalable Module System

Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented mathematical knowledge that needs to be managed to use such systems effectively. While mathematical knowledge management (MKM) "in the small" is well-studied, scaling up to large, highly interconnected corpora remains difficult. We hold that in order to realize MKM "in the large", we need representation languages and software architectures that are designed systematically with large-scale processing in mind. Therefore, we have designed and implemented the MMT language -- a module system for mathematical theories. MMT is designed as the simplest possible language that combines a module system, a foundationally uncommitted formal semantics, and web-scalable implementations. Due to a careful choice of representational primitives, MMT allows us to integrate existing representation languages for formal mathematical knowledge in a simple, scalable formalism. In particular, MMT abstracts from the underlying mathematical and logical foundations so that it can serve as a standardized representation format for a formal digital library. Moreover, MMT systematically separates logic-dependent and logic-independent concerns so that it can serve as an interface layer between computation systems and MKM systems.

cs.LO↗

arXiv2011

The Planetary System: Executable Science, Technology, Engineering and Math Papers

Executable scientific papers contain not just layouted text for reading. They contain, or link to, machine-comprehensible representations of the scientific findings or experiments they describe. Client-side players can thus enable readers to "check, manipulate and explore the result space". We have realized executable papers in the STEM domain with the Planetary system. Semantic annotations associate the papers with a content commons holding the background ontology, the annotations are exposed as Linked Data, and a frontend player application hooks modular interactive services into the semantic annotations.

cs.DL↗

arXiv2010

What we understand is what we get: Assessment in Spreadsheets

In previous work we have studied how an explicit representation of background knowledge associated with a specific spreadsheet can be exploited to alleviate usability problems with spreadsheet-based applications. We have implemented this approach in the SACHS system to provide a semantic help system for spreadsheets applications. In this paper, we evaluate the (comprehension) coverage of SACHS on an Excel-based financial controlling system via a "Wizard-of-Oz" experiment. This shows that SACHS adds significant value, but systematically misses important classes of explanations. For judgements about the information contained in spreadsheets, we provide a first approach for an "assessment module" in SACHS.

cs.SE↗

arXiv2010

sTeX+ - a System for Flexible Formalization of Linked Data

We present the sTeX+ system, a user-driven advancement of sTeX - a semantic extension of LaTeX that allows for producing high-quality PDF documents for (proof)reading and printing, as well as semantic XML/OMDoc documents for the Web or further processing. Originally sTeX had been created as an invasive, semantic frontend for authoring XML documents. Here, we used sTeX in a Software Engineering case study as a formalization tool. In order to deal with modular pre-semantic vocabularies and relations, we upgraded it to sTeX+ in a participatory design process. We present a tool chain that starts with an sTeX+ editor and ultimately serves the generated documents as XHTML+RDFa Linked Data via an OMDoc-enabled, versioned XML database. In the final output, all structural annotations are preserved in order to enable semantic information retrieval services.

cs.SE↗

arXiv2010

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.

cs.OH↗

arXiv2010

sTeXIDE: An Integrated Development Environment for sTeX Collections

Authoring documents in MKM formats like OMDoc is a very tedious task. After years of working on a semantically annotated corpus of sTeX documents (GenCS), we identified a set of common, time-consuming subtasks, which can be supported in an integrated authoring environment. We have adapted the modular Eclipse IDE into sTeXIDE, an authoring solution for enhancing productivity in contributing to sTeX based corpora. sTeXIDE supports context-aware command completion, module management, semantic macro retrieval, and theory graph navigation.

cs.OH↗

arXiv2010

Dimensions of Formality: A Case Study for MKM in Software Engineering

We study the formalization of a collection of documents created for a Software Engineering project from an MKM perspective. We analyze how document and collection markup formats can cope with an open-ended, multi-dimensional space of primary and secondary classifications and relationships. We show that RDFa-based extensions of MKM formats, employing flexible "metadata" relationships referencing specific vocabularies for distinct dimensions, are well-suited to encode this and to put it into service. This formalized knowledge can be used for enriching interactive document browsing, for enabling multi-dimensional metadata queries over documents and collections, and for exporting Linked Data to the Semantic Web and thus enabling further reuse.

cs.DL↗

arXiv2010

Publishing Math Lecture Notes as Linked Data

We mark up a corpus of LaTeX lecture notes semantically and expose them as Linked Data in XHTML+MathML+RDFa. Our application makes the resulting documents interactively browsable for students. Our ontology helps to answer queries from students and lecturers, and paves the path towards an integration of our corpus with external sites.

cs.DL↗

arXiv2009

Cut-Simulation and Impredicativity

We investigate cut-elimination and cut-simulation in impredicative (higher-order) logics. We illustrate that adding simple axioms such as Leibniz equations to a calculus for an impredicative logic -- in our case a sequent calculus for classical type theory -- is like adding cut. The phenomenon equally applies to prominent axioms like Boolean- and functional extensionality, induction, choice, and description. This calls for the development of calculi where these principles are built-in instead of being treated axiomatically.

cs.LO↗

arXiv1997

Computing Parallelism in Discourse

Although much has been said about parallelism in discourse, a formal, computational theory of parallelism structure is still outstanding. In this paper, we present a theory which given two parallel utterances predicts which are the parallel elements. The theory consists of a sorted, higher-order abductive calculus and we show that it reconciles the insights of discourse theories of parallelism with those of Higher-Order Unification approaches to discourse semantics, thereby providing a natural framework in which to capture the effect of parallelism on discourse semantics.

cmp-lg↗

arXiv1996

Corrections and Higher-Order Unification

We propose an analysis of corrections which models some of the requirements corrections place on context. We then show that this analysis naturally extends to the interaction of corrections with pronominal anaphora on the one hand, and (in)definiteness on the other. The analysis builds on previous unification--based approaches to NL semantics and relies on Higher--Order Unification with Equivalences, a form of unification which takes into account not only syntactic beta-eta-identity but also denotational equivalence.

cmp-lg↗

arXiv1996

Higher-Order Coloured Unification and Natural Language Semantics

In this paper, we show that Higher-Order Coloured Unification - a form of unification developed for automated theorem proving - provides a general theory for modeling the interface between the interpretation process and other sources of linguistic, non semantic information. In particular, it provides the general theory for the Primary Occurrence Restriction which (Dalrymple, Shieber and Pereira, 1991)'s analysis called for.

cmp-lg↗

arXiv1996

Focus and Higher-Order Unification

Pulman has shown that Higher--Order Unification (HOU) can be used to model the interpretation of focus. In this paper, we extend the unification--based approach to cases which are often seen as a test--bed for focus theory: utterances with multiple focus operators and second occurrence expressions. We then show that the resulting analysis favourably compares with two prominent theories of focus (namely, Rooth's Alternative Semantics and Krifka's Structured Meanings theory) in that it correctly generates interpretations which these alternative theories cannot yield. Finally, we discuss the formal properties of the approach and argue that even though HOU need not terminate, for the class of unification--problems dealt with in this paper, HOU avoids this shortcoming and is in fact computationally tractable.

cmp-lg↗