Related papers: Importing SMT and Connection proofs as expansion t…
Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key…
The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical…
We describe an extension to the TLA+ specification language with constructs for writing proofs and a proof environment, called the Proof Manager (PM), to checks those proofs. The language and the PM support the incremental development and…
Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in…
Multi-source translation systems translate from multiple languages to a single target language. By using information from these multiple sources, these systems achieve large gains in accuracy. To train these systems, it is necessary to have…
The origins of proof-theoretic semantics lie in the question of what constitutes the meaning of the logical connectives and its response: the rules of inference that govern the use of the connective. However, what if we go a step further…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
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…
Ordinals can help prove termination for dependently typed programs. Brouwer trees are a particular ordinal notation that make it very easy to assign sizes to higher order data structures. They extend natural numbers with a limit…
Proof scores can be regarded as outlines of the formal verification of system properties. They have been historically used by the OBJ family of specification languages. The main advantage of proof scores is that they follow the same syntax…
Large language models (LLMs) are increasingly used to generate software artifacts across many software engineering (SE) tasks, yet ensuring the semantic validity of these artifacts remains a fundamental challenge. Existing constrained…
Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…
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,…
Building on their demonstrated ability to perform a variety of tasks, we investigate the application of large language models (LLMs) to enhance in-depth analytical reasoning within the context of intelligence analysis. Intelligence analysts…
The ability to precisely derive mathematical objects is a core requirement for downstream STEM applications, including mathematics, physics, and chemistry, where reasoning must culminate in formally structured expressions. Yet, current LM…
Decision tree models, including random forests and gradient-boosted decision trees, are widely used in machine learning due to their high predictive performance. However, their complex structures often make them difficult to interpret,…
Masked diffusion models (MDMs) for text offer a compelling alternative to traditional autoregressive language models. Parallel generation makes them efficient, but their computational capabilities and the limitations inherent in their…
Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming…
Boosted trees is a dominant ML model, exhibiting high accuracy. However, boosted trees are hardly intelligible, and this is a problem whenever they are used in safety-critical applications. Indeed, in such a context, rigorous explanations…
In this paper, we show how to interpret a language featuring concurrency, references and replication into proof nets, which correspond to a fragment of differential linear logic. We prove a simulation and adequacy theorem. A key element in…