Related papers: Proof Simplification and Automated Theorem Proving
Automated theorem provers are used in extended static checking, where they are the performance bottleneck. Extended static checkers are run typically after incremental changes to the code. We propose to exploit this usage pattern to improve…
Interactive theorem provers (ITPs) are powerful tools for the formal verification of mathematical proofs down to the axiom level. However, their lack of a natural language interface remains a significant limitation. Recent advancements in…
We explore the idea of using automatic and similar kind of presentations of structures to deal with the conceptual problem of natural proof-theoretic ordinal notations. We conclude that this approach still does not meet the goals.
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…
This paper attempts to address the question of how best to assure the correctness of saturation-based automated theorem provers using our experience developing the theorem prover Vampire. We describe the techniques we currently employ to…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…
Proof engineering is notoriously labor-intensive: proofs that are straightforward on paper often require lengthy scripts in theorem provers. Recent advances in large language models (LLMs) create new opportunities for proof automation:…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…
This paper reports on an exploration of Boolos' Curious Inference, using higher-order automated theorem provers (ATPs). Surprisingly, only suitable shorthand notations had to be provided by hand for ATPs to find a short proof. The…
In the context of interactive theorem provers based on a dependent type theory, automation tactics (dedicated decision procedures, call of automated solvers, ...) are often limited to goals which are exactly in some expected logical…
Automatic text simplification (TS) aims to automate the process of rewriting text to make it easier for people to read. A pre-requisite for TS to be useful is that it should convey information that is consistent with the meaning of the…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
Improvements in text generation technologies such as machine translation have necessitated more costly and time-consuming human evaluation procedures to ensure an accurate signal. We investigate a simple way to reduce cost by reducing the…
Background. Reproducibility is essential to the scientific method, but reproduction is often a laborious task. Recent works have attempted to automate this process and relieve researchers of this workload. However, due to varying…
Grading of examination papers is a hectic, time-labor intensive task and is often subjected to inefficiency and bias in checking. This research project is a primitive experiment in the automation of grading of theoretical answers written in…