Related papers: Proof Mining with Dependent Types
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
Process mining is widely used to diagnose processes and uncover performance and compliance problems. It is also possible to see relations between different behavioral aspects, e.g., cases that deviate more at the beginning of the process…
Large language models have the potential to simplify formal theorem proving and make it more accessible. But how to get the most out of these models is still an open question. To answer this question, we take a step back and explore the…
Recently, we developed an automated theorem prover for projective incidence geometry. This prover, based on a combinatorial approach using matroids, proceeds by saturation using the matroid rules. It is designed as an independent tool,…
As new advancements in the field of quantum computing lead to the development of increasingly complex programs, approaches to validate and debug these programs are becoming more important. To this end, methods employed in classical…
One of the proposed solutions for improving the scalability of semantics of programming languages is Component-Based Semantics, introduced by Peter D. Mosses. It is expected that this framework can also be used effectively for modular meta…
Graded type theories are an emerging paradigm for augmenting the reasoning power of types with parameterizable, fine-grained analyses of program properties. There have been many such theories in recent years which equip a type theory with…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
We investigate here a new version of the Calculus of Inductive Constructions (CIC) on which the proof assistant Coq is based: the Calculus of Congruent Inductive Constructions, which truly extends CIC by building in arbitrary first-order…
A novel approach to the fully automated, unsupervised extraction of dependency grammars and associated syntax-to-semantic-relationship mappings from large text corpora is described. The suggested approach builds on the authors' prior work…
Fact verification based on structured data is challenging as it requires models to understand both natural language and symbolic operations performed over tables. Although pre-trained language models have demonstrated a strong capability in…
Recent advances in Automated Theorem Proving have shown the effectiveness of leveraging a (large) language model that generates tactics (i.e. proof steps) to search through proof states. The current model, while trained solely on successful…
There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we…
The Coq Platform is a continuously developed distribution of the Coq proof assistant together with commonly used libraries, plugins, and external tools useful in Coq-based formal verification projects. The Coq Platform enables reproducing…
As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…
Table-based reasoning has shown remarkable progress in combining deep models with discrete reasoning, which requires reasoning over both free-form natural language (NL) questions and structured tabular data. However, previous table-based…
What provides the highest level of assurance for correctness of execution within a programming language? One answer, and our solution in particular, to this problem is to provide a formalization for, if it exists, the denotational semantics…
Based on the concept of annotation-based agents, this report introduces tools and a formal notation for defining and running text mining experiments using a statically typed domain-specific language embedded in Scala. Using machine learning…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant. In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic…