Related papers: Bridging Syntax and Semantics of Lean Expressions …
Autoformalization, the process of transforming informal mathematical language into formal specifications and proofs remains a difficult task for state-of-the-art (large) language models. Existing works point to competing explanations for…
Large-scale formalization projects in Lean rely on blueprints: structured dependency graphs linking informal mathematical exposition to formal declarations. While blueprints are central to human collaboration, existing tooling treats the…
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…
We extend a semantic verification framework for hybrid systems with the Isabelle/HOL proof assistant by an algebraic model for hybrid program stores, a shallow expression model for hybrid programs and their correctness specifications, and…
Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
In Machine-Assisted Theorem Proving, a theorem proving agent searches for a sequence of expressions and tactics that can prove a conjecture in a proof assistant. In this work, we introduce several novel concepts and capabilities to address…
Mathematical reasoning remains a significant challenge for Large Language Models (LLMs) due to hallucinations. When combined with formal proof assistants like Lean, these hallucinations can be eliminated through rigorous verification,…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
Machine-learning automation tools, ranging from humble grid-search to hyperopt, auto-sklearn, and TPOT, help explore large search spaces of possible pipelines. Unfortunately, each of these tools has a different syntax for specifying its…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Hierarchical graph rewriting is a highly expressive computational formalism that manipulates graphs enhanced with box structures for representing hierarchies. It has provided the foundations of various graph-based modeling tools, but the…
Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite…
This paper describes the design and implementation of a new machine learning model for online learning systems. We aim at improving the intelligent level of the systems by enabling an automated math word problem solver which can support a…
Milner (1984) introduced a process semantics for regular expressions as process graphs. Unlike for the language semantics, where every regular (that is, DFA-accepted) language is the interpretation of some regular expression, there are…
One of the most attractive features of untyped languages is the flexibility in term creation and manipulation. However, with such power comes the responsibility of ensuring the correctness of these operations. A solution is adding run-time…
Evaluations of large language models (LLMs) primarily emphasize convergent logical reasoning, where success is defined by producing a single correct proof. However, many real-world reasoning problems admit multiple valid derivations,…
Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps…
Model execution allows us to prototype and analyse software engineering models by stepping through their possible behaviours, using techniques like animation and simulation. On the other hand, deductive verification allows us to construct…
Heterogeneous graphs are widely present in real-world complex networks, where the diversity of node and relation types leads to complex and rich semantics. Efforts for modeling complex relation semantics in heterogeneous graphs are…