Related papers: A Scalable Module System
The MMT language has been developed as a scalable representation and interchange language for formal mathematical knowledge. It permits natural representations of the syntax and semantics of virtually all declarative languages while making…
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…
One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human.…
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…
Large language models (LLMs) have substantially advanced machine learning research, including natural language processing, computer vision, data mining, etc., yet they still exhibit critical limitations in explainability, reliability,…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Logical frameworks are meta-formalisms in which the syntax and semantics of object logics and related formal systems can be defined. This allows object logics to inherit implementations from the framework including, e.g., parser, type…
Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study…
Huge language models (LMs) have ushered in a new era for AI, serving as a gateway to natural-language-based knowledge tasks. Although an essential element of modern AI, LMs are also inherently limited in a number of ways. We discuss these…
Despite their ability to understand chemical knowledge, large language models (LLMs) remain limited in their capacity to propose novel molecules with desired functions (e.g., drug-like properties). In addition, the molecules that LLMs…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for…
As the shortage of skilled workers continues to be a pressing issue, exacerbated by demographic change, it is becoming a critical challenge for organizations to preserve the knowledge of retiring experts and to pass it on to novices. While…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
The progress of Large Language Models (LLMs) like ChatGPT raises the question of how they can be integrated into education. One hope is that they can support mathematics learning, including word-problem solving. Since LLMs can handle…
Large language models (LLMs) have shown limitations in tasks requiring complex logical reasoning and multi-step problem-solving. To address these challenges, researchers have employed carefully designed prompts and flowcharts, simulating…
Before we can get the whole potential of employing computers in the process of managing mathematical `knowledge', we have to convert informal knowledge into machine-oriented representations. How exactly to support this process so that it…
Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…
Machine translation is the discipline concerned with developing automated tools for translating from one human language to another. Statistical machine translation (SMT) is the dominant paradigm in this field. In SMT, translations are…