Related papers: Importing SMT and Connection proofs as expansion t…

This paper presents an approach to lemma synthesis to support advanced inductive entailment procedures based on separation logic. We first propose a mechanism where lemmas are automatically proven and systematically applied. The lemmas may…

The CEGAR loop in software model checking notoriously diverges when the abstraction refinement procedure does not derive a loop invariant. An abstraction refinement procedure based on an SMT solver is applied to a trace, i.e., a restricted…

Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…

Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. As more taxa are added, the new source trees may begin to tell a different evolutionary story when…

While neural machine translation (NMT) models provide improved translation quality in an elegant, end-to-end framework, it is less clear what they learn about language. Recent work has started evaluating the quality of vector…

Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results,…

Abstract interpreters are complex pieces of software: even if the abstract interpretation theory and companion algorithms are well understood, their implementations are subject to bugs, that might question the soundness of their…

We are interested in understanding how well Transformer language models (TLMs) can perform reasoning tasks when trained on knowledge encoded in the form of natural language. We investigate their systematic generalization abilities on a…

A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…

We further develop the theoretical framework of proof mining, a program in mathematical logic that seeks to quantify and extract computational information from prima facie `non-computational' proofs from the mainstream mathematical…

Trustworthy Artificial Intelligence solutions are essential in today's data-driven applications, prioritizing principles such as robustness, safety, transparency, explainability, and privacy among others. This has led to the emergence of…

The use of logical systems for problem-solving may be as diverse as in proving theorems in mathematics or in figuring out how to meet up with a friend. In either case, the problem solving activity is captured by the search for an…

According to the Test-Time Scaling, the integration of External Slow-Thinking with the Verify mechanism has been demonstrated to enhance multi-round reasoning in large language models (LLMs). However, in the multimodal (MM) domain, there is…

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is,…

Although end-to-end Neural Machine Translation (NMT) has achieved remarkable progress in the past two years, it suffers from a major drawback: translations generated by NMT systems often lack of adequacy. It has been widely observed that…

Commutativity of data structure methods is of ongoing interest, with roots in the database community. In recent years commutativity has been shown to be a key ingredient to enabling multicore concurrency in contexts such as parallelizing…

Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to…

In this paper, we compare different existing approaches employed in data mining of big proof libraries in automated and interactive theorem proving.

We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…

Pre-trained Language Models (PLMs) have achieved great success on Machine Reading Comprehension (MRC) over the past few years. Although the general language representation learned from large-scale corpora does benefit MRC, the poor support…