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The combination of Large Language Models (LLMs), systematic evaluation, and evolutionary algorithms has enabled breakthroughs in combinatorial optimization and scientific discovery. We propose to extend this powerful combination to the…
Taxonomies represent hierarchical relations between entities, frequently applied in various software modeling and natural language processing (NLP) activities. They are typically subject to a set of structural constraints restricting their…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of…
Prompting and fine-tuning have emerged as two competing paradigms for augmenting language models with new capabilities, such as the use of tools. Prompting approaches are quick to set up but rely on providing explicit demonstrations of each…
Large language models (LLMs) often struggle with complex logical reasoning due to logical inconsistencies and the inherent difficulty of such reasoning. We use Lean, a theorem proving framework, to address these challenges. By formalizing…
In recent years the effectiveness of interactive theorem provers has increased to an extent that the bottleneck in the interactive process shifted to efficiency: while in principle large and complex theorems are provable (effectiveness), it…
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.…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
Large Language Models (LLMs) have emerged as powerful tools in mathematical theorem proving, particularly when utilizing formal languages such as LEAN. A prevalent proof method involves the LLM prover iteratively constructing the proof…
Interactive theorem provers, like Isabelle/HOL, Coq and Lean, have expressive languages that allow the formalization of general mathematical objects and proofs. In this context, an important goal is to reduce the time and effort needed to…
Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…
Existing studies have introduced method-based reasoning and scope extension as approaches to enhance Large Language Model (LLM) performance beyond direct matrix mappings. Building on these foundations, this paper summarizes and integrates…
Distilling robust reasoning capabilities from large language models (LLMs) into smaller, computationally efficient student models remains an unresolved challenge. Despite recent advances, distilled models frequently suffer from superficial…
Taxonomies play a crucial role in various applications by providing a structural representation of knowledge. The task of taxonomy expansion involves integrating emerging concepts into existing taxonomies by identifying appropriate parent…
Taxonomies are hierarchical knowledge graphs crucial for recommendation systems, and web applications. As data grows, expanding taxonomies is essential, but existing methods face key challenges: (1) discriminative models struggle with…
In this article we discuss how abstraction boundaries can help tame complexity in mathematical research, with the help of an interactive theorem prover. While many of the ideas we present here have been used implicitly by mathematicians for…
Formal proofs are challenging to write even for experienced experts. Recent progress in Neural Theorem Proving (NTP) shows promise in expediting this process. However, the formal corpora available on the Internet are limited compared to the…
Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast…