arXiv subjects

Michael Kohlhase

Publications and source records attributed to Michael Kohlhase.

At least 19 recordsLinked to original sources

arXiv2024

The Potential of Answer Classes in Large-scale Written Computer-Science Exams -- Vol. 2

Students' answers to tasks provide a valuable source of information in teaching as they result from applying cognitive processes to a learning content addressed in the task. Due to steadily increasing course sizes, analyzing student answers is frequently the only means of obtaining evidence about student performance. However, in many cases, resources are limited, and when evaluating exams, the focus is solely on identifying correct or incorrect answers. This overlooks the value of analyzing incorrect answers, which can help improve teaching strategies or identify misconceptions to be addressed in the next cohort. In teacher training for secondary education, assessment guidelines are mandatory for every exam, including anticipated errors and misconceptions. We applied this concept to a university exam with 462 students and 41 tasks. For each task, the instructors developed answer classes -- classes of expected responses, to which student answers were mapped during the exam correction process. The experiment resulted in a shift in mindset among the tutors and instructors responsible for the course: after initially having great reservations about whether the significant additional effort would yield an appropriate benefit, the procedure was subsequently found to be extremely valuable. The concept presented, and the experience gained from the experiment were cast into a system with which it is possible to correct paper-based exams on the basis of answer classes. This updated version of the paper provides an overview and new potential in the course of using the digital version of the approach.

cs.CY↗

arXiv2024

Leveraging Large Language Models to Generate Course-specific Semantically Annotated Learning Objects

Background: Over the past few decades, the process and methodology of automated question generation (AQG) have undergone significant transformations. Recent progress in generative natural language models has opened up new potential in the generation of educational content. Objectives: This paper explores the potential of large language models (LLMs) for generating computer science questions that are sufficiently annotated for automatic learner model updates, are fully situated in the context of a particular course, and address the cognitive dimension understand. Methods: Unlike previous attempts that might use basic methods like ChatGPT, our approach involves more targeted strategies such as retrieval-augmented generation (RAG) to produce contextually relevant and pedagogically meaningful learning objects. Results and Conclusions: Our results show that generating structural, semantic annotations works well. However, this success was not reflected in the case of relational annotations. The quality of the generated questions often did not meet educational standards, highlighting that although LLMs can contribute to the pool of learning materials, their current level of performance requires significant human intervention to refine and validate the generated content.

cs.AI↗

arXiv2020

Context Graphs for Legal Reasoning and Argumentation

We propose a new, structured, logic-based framework for legal reasoning and argumentation: Instead of using a single, unstructured meaning space, theory graphs organize knowledge and inference into collections of modular meaning spaces organized by inheritance and interpretation. Context graphs extend theory graphs by attack relations and interpret theories as knowledge contexts of agents in argumentation. We introduce the context graph paradigm by modeling the well-studied case Popov v. Hayashi, concentrating on the role of analogical reasoning in context graphs.

cs.LO↗

arXiv2020

Experiences from Exporting Major Proof Assistant Libraries

The interoperability of proof assistants and the integration of their libraries is a highly valued but elusive goal in the field of theorem proving. As a preparatory step, in previous work, we translated the libraries of multiple proof assistants, specifically the ones of Coq, HOL Light, IMPS, Isabelle, Mizar, and PVS into a universal format: OMDoc/MMT. Each translation presented tremendous theoretical, technical, and social challenges, some universal and some system-specific, some solvable and some still open. In this paper, we survey these challenges and compare and evaluate the solutions we chose. We believe similar library translations will be an essential part of any future system interoperability solution and our experiences will prove valuable to others undertaking such efforts.

cs.LO↗

arXiv2020

Making Isabelle Content Accessible in Knowledge Representation Formats

The libraries of proof assistants like Isabelle, Coq, HOL are notoriously difficult to interpret by external tools: de facto, only the prover itself can parse and process them adequately. In the case of Isabelle, an export of the library into a FAIR (Findable, Accessible, Interoperable, and Reusable) knowledge exchange format was already envisioned by the authors in 1999 but had previously proved too difficult. After substantial improvements of the Isabelle Prover IDE (PIDE) and the OMDoc/Mmt format since then, we are now able to deliver such an export. Concretely we present an integration of PIDE and MMT that allows exporting all Isabelle libraries in OMDoc format. Our export covers the full Isabelle distribution and the Archive of Formal Proofs (AFP) -- more than 12 thousand theories and locales resulting in over 65GB of OMDoc/XML. Such a systematic export of Isabelle content to a well-defined interchange format like OMDoc enables many applications such as dependency management, independent proof checking, or library search.

cs.LO↗

arXiv2020

TGView3D System Description: 3-Dimensional Visualization of Theory Graphs

We describe TGView3D, an interactive 3D graph viewer optimized for exploring theory graphs. To exploit the three spatial dimensions, it extends a force-directed layout with a hierarchical component. Because of the limitations of regular displays, the system also supports the use of a head-mounted display and utilizes several virtual realty interaction concepts.

cs.HC↗

arXiv2020

The Space of Mathematical Software Systems -- A Survey of Paradigmatic Systems

Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of increasingly powerful but also diverging systems. To give researchers a guide to this space of systems, we devise a novel conceptualization of mathematical software that focuses on five aspects: inference covers formal logic and reasoning about mathematical statements via proofs and models, typically with strong emphasis on correctness; computation covers algorithms and software libraries for representing and manipulating mathematical objects, typically with strong emphasis on efficiency; concretization covers generating and maintaining collections of mathematical objects conforming to a certain pattern, typically with strong emphasis on complete enumeration; narration covers describing mathematical contexts and relations, typically with strong emphasis on human readability; finally, organization covers representing mathematical contexts and objects in machine-actionable formal languages, typically with strong emphasis on expressivity and system interoperability. Despite broad agreement that an ideal system would seamlessly integrate all these aspects, research has diversified into families of highly specialized systems focusing on a single aspect and possibly partially integrating others, each with their own communities, challenges, and successes. In this survey, we focus on the commonalities and differences of these systems from the perspective of a future multi-aspect system.

cs.MS↗

arXiv2019

GF + MMT = GLF -- From Language to Semantics through LF

These days, vast amounts of knowledge are available online, most of it in written form. Search engines help us access this knowledge, but aggregating, relating and reasoning with it is still a predominantly human effort. One of the key challenges for automated reasoning based on natural-language texts is the need to extract meaning (semantics) from texts. Natural language understanding (NLU) systems describe the conversion from a set of natural language utterances to terms in a particular logic. Tools for the co-development of grammar and target logic are currently largely missing. We will describe the Grammatical Logical Framework (GLF), a combination of two existing frameworks, in which large parts of a symbolic, rule-based NLU system can be developed and implemented: the Grammatical Framework (GF) and MMT. GF is a tool for syntactic analysis, generation, and translation with complex natural language grammars and MMT can be used to specify logical systems and to represent knowledge in them. Combining these tools is possible, because they are based on compatible logical frameworks: Martin-Löf type theory and LF. The flexibility of logical frameworks is needed, as NLU research has not settled on a particular target logic for meaning representation. Instead, new logics are developed all the time to handle various language phenomena. GLF allows users to develop the logic and the language parsing components in parallel, and to connect them for experimentation with the entire pipeline.

cs.CL↗

arXiv2019

Big Math and the One-Brain Barrier A Position Paper and Architecture Proposal

Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards "big mathematics", its relation to human cognition, and how machine support for big math can be organized. The central contribution of this position paper is an information model for "doing mathematics", which posits that humans very efficiently integrate four aspects: inference, computation, tabulation, and narration around a well-organized core of mathematical knowledge. The challenge for mathematical software systems is that these four aspects need to be integrated as well. We briefly survey the state of the art.

cs.MS↗

arXiv2019

The Theorem Prover Museum -- Conserving the System Heritage of Automated Reasoning

We present the Theorem Prover Museum, and initiative to conserve -- and make publicly available -- the sources and source-related artefacts of automated reasoning systems. Theorem provers have been at the forefront of Artificial Intelligence, stretching the limits of computation, and incubating many innovations we take for granted today. Without the systems themselves as preserved cultural artefacts, future historians will have difficulties to study the history of science and engineering in our discipline.

cs.LO↗

arXiv2016

Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach

OpenDreamKit --- "Open Digital Research Environment Toolkit for the Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015--2019, the ecosystem of open-source mathematical software systems. From that, OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications. An important step in the OpenDreamKit endeavor is to foster the interoperability between a variety of systems, ranging from computer algebra systems over mathematical databases to front-ends. This is the mission of the integration work package (WP6). We report on experiments and future plans with the \emph{Math-in-the-Middle} approach. This information architecture consists in a central mathematical ontology that documents the domain and fixes a joint vocabulary, combined with specifications of the functionalities of the various systems. Interaction between systems can then be enriched by pivoting off this information architecture.

cs.MS↗

arXiv2014

Realms: A Structure for Consolidating Knowledge about Mathematical Theories

Since there are different ways of axiomatizing and developing a mathematical theory, knowledge about a such a theory may reside in many places and in many forms within a library of formalized mathematics. We introduce the notion of a realm as a structure for consolidating knowledge about a mathematical theory. A realm contains several axiomatizations of a theory that are separately developed. Views interconnect these developments and establish that the axiomatizations are equivalent in the sense of being mutually interpretable. A realm also contains an external interface that is convenient for users of the library who want to apply the concepts and facts of the theory without delving into the details of how the concepts and facts were developed. We illustrate the utility of realms through a series of examples. We also give an outline of the mechanisms that are needed to create and maintain realms.

cs.MS↗

arXiv2014

XLSearch: A Search Engine for Spreadsheets

Spreadsheets are end-user programs and domain models that are heavily employed in administration, financial forecasting, education, and science because of their intuitive, flexible, and direct approach to computation. As a result, institutions are swamped by millions of spreadsheets that are becoming increasingly difficult to manage, access, and control. This note presents the XLSearch system, a novel search engine for spreadsheets. It indexes spreadsheet formulae and efficiently answers formula queries via unification (a complex query language that allows metavariables in both the query as well as the index). But a web-based search engine is only one application of the underlying technology: Spreadsheet formula export to web standards like MathML combined with formula indexing can be used to find similar spreadsheets or common formula errors.

cs.DB↗

arXiv2013

Towards Ontological Support for Principle Solutions in Mechanical Engineering

The engineering design process follows a series of standardized stages of development, which have many aspects in common with software engineering. Among these stages, the principle solution can be regarded as an analogue of the design specification, fixing as it does the way the final product works. It is usually constructed as an abstract sketch (hand-drawn or constructed with a CAD system) where the functional parts of the product are identified, and geometric and topological constraints are formulated. Here, we outline a semantic approach where the principle solution is annotated with ontological assertions, thus making the intended requirements explicit and available for further machine processing; this includes the automated detection of design errors in the final CAD model, making additional use of a background ontology of engineering knowledge. We embed this approach into a document-oriented design workflow, in which the background ontology and semantic annotations in the documents are exploited to trace parts and requirements through the design process and across different applications.

cs.SE↗

arXiv2013

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.

cs.LO↗

arXiv2012

The Planetary Project: Towards eMath3.0

The Planetary project develops a general framework - the Planetary system - for social semantic portals that support users in interacting with STEM (Science/Technology/Engineering/Mathematics) documents. Developed from an initial attempt to replace the aging portal of PlanetMath.org with a mashup of existing MKM technologies, the Planetary system is now in a state, where it can serve as a basis for various eMath3.0 portals, ranging from eLearning systems over scientific archives to semantic help systems.

cs.DL↗

arXiv2012

Reimplementing the Mathematical Subject Classification (MSC) as a Linked Open Dataset

The Mathematics Subject Classification (MSC) is a widely used scheme for classifying documents in mathematics by subject. Its traditional, idiosyncratic conceptualization and representation makes the scheme hard to maintain and requires custom implementations of search, query and annotation support. This limits uptake e.g. in semantic web technologies in general and the creation and exploration of connections between mathematics and related domains (e.g. science) in particular. This paper presents the new official implementation of the MSC2010 as a Linked Open Dataset, building on SKOS (Simple Knowledge Organization System). We provide a brief overview of the dataset's structure, its available implementations, and first applications.

cs.DL↗

arXiv2011

Licensing the Mizar Mathematical Library

The Mizar Mathematical Library (MML) is a large corpus of formalised mathematical knowledge. It has been constructed over the course of many years by a large number of authors and maintainers. Yet the legal status of these efforts of the Mizar community has never been clarified. In 2010, after many years of loose deliberations, the community decided to investigate the issue of licensing the content of the MML, thereby clarifying and crystallizing the status of the texts, the text's authors, and the library's long-term maintainers. The community has settled on a copyright and license policy that suits the peculiar features of Mizar and its community. In this paper we discuss the copyright and license solutions. We offer our experience in the hopes that the communities of other libraries of formalised mathematical knowledge might take up the legal and scientific problems that we addressed for Mizar.

cs.DL↗