Related papers: Sequencelib: A Computational Platform for Formaliz…
The chase is a sound, complete, but possibly non-terminating algorithm for reasoning with existential rules (aka. tuple-generating dependencies), a highly expressive knowledge representation language. Although the procedure appears simple,…
Chemical theory can be made more rigorous using the Lean theorem prover, an interactive theorem prover for complex mathematics. We formalize the Langmuir and BET theories of adsorption, making each scientific premise clear and every step of…
Data curation tasks that prepare data for analytics are critical for turning data into actionable insights. However, due to the diverse requirements of applications in different domains, generic off-the-shelf tools are typically…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Formal synthesis is the process of generating a program satisfying a high-level formal specification. In recent times, effective formal synthesis methods have been proposed based on the use of inductive learning. We refer to this class of…
The resolution of intelligence tests, in particular numerical sequences, has been of great interest in the evaluation of AI systems. We present a new computational model called KitBit that uses a reduced set of algorithms and their…
The deployment of Large Language Models (LLMs) for code debugging (e.g., C and Python) is widespread, benefiting from their ability to understand and interpret intricate concepts. However, in the semiconductor industry, utilising LLMs to…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
Computational complexity is a key limitation of genomic analyses. Thus, over the last 30 years, researchers have proposed numerous fast heuristic methods that provide computational relief. Comparing genomic sequences is one of the most…
While the ecosystem of Lean and Mathlib has enjoyed celebrated success in formal mathematical reasoning with the help of large language models (LLMs), the absence of many folklore lemmas in Mathlib remains a persistent barrier that limits…
We present Reelay, a unified online temporal logic monitoring framework designed for the rigorous analysis and runtime verification of cyber-physical systems. Reelay addresses the fragmentation of existing logical formalisms and tools by…
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…
We introduce a self-learning algorithm for synthesizing programs for OEIS sequences. The algorithm starts from scratch initially generating programs at random. Then it runs many iterations of a self-learning loop that interleaves (i)…
Open Information Extraction (OIE) is a structured prediction (SP) task in Natural Language Processing (NLP) that aims to extract structured $n$-ary tuples - usually subject-relation-object triples - from free text. The word embeddings in…
Large language models are transforming all areas of academia and industry, attracting the attention of researchers, professionals, and the general public. In the trek for more powerful architectures, Mixture-of-Experts, inspired by ensemble…
Background: With the rapid growth of massively parallel sequencing technologies, still more laboratories are utilizing sequenced DNA fragments for genomic analyses. Interpretation of sequencing data is, however, strongly dependent on…
Open Information Extraction (OIE) systems seek to compress the factual propositions of a sentence into a series of n-ary tuples. These tuples are useful for downstream tasks in natural language processing like knowledge base creation,…
Integrating Internet of Things (IoT) data with business process event logs is crucial for analysing IoT-enhanced processes, yet remains challenging due to differences in abstraction levels and the separation of data sources. Simply…
We present a case study where an automatic AI system formalizes a textbook with more than 500 pages of graduate-level algebraic combinatorics to Lean. The resulting formalization represents a new milestone in textbook formalization scale…
Geometry problems are a crucial testbed for AI reasoning capabilities. Most existing geometry solving systems cannot express problems within a unified framework, thus are difficult to integrate with other mathematical fields. Besides, since…