相关论文: A Divergence Critic for Inductive Proof

As the first step of automatic fact checking, claim check-worthiness detection is a critical component of fact checking systems. There are multiple lines of research which study this problem: check-worthiness ranking from political speeches…

We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…

In logic programming, dynamic scheduling refers to a situation where the selection of the atom in each resolution (computation) step is determined at runtime, as opposed to a fixed selection rule such as the left-to-right one of Prolog.…

Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…

Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…

"Theorem proving is similar to the game of Go. So, we can probably improve our provers using deep learning, like DeepMind built the super-human computer Go program, AlphaGo." Such optimism has been observed among participants of AITP2017.…

Dilemma is intended to enhance quality and increase productivity of expert human translators by presenting to the writer relevant lexical information mechanically extracted from comparable existing translations, thus replacing - or…

Large language models have demonstrated impressive performance across a variety of reasoning tasks. However, their problem-solving ability often declines on more complex tasks due to hallucinations and the accumulation of errors within…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…

We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…

In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…

A policy maker faces a sequence of unknown outcomes. At each stage two (self-proclaimed) experts provide probabilistic forecasts on the outcome in the next stage. A comparison test is a protocol for the policy maker to (eventually) decide…

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

Recent advances in program synthesis offer means to automatically debug student submissions and generate personalized feedback in massive programming classrooms. When automatically generating feedback for programming assignments, a key…

The problem of checking whether two programs are semantically equivalent or not has a diverse range of applications, and is consequently of substantial importance. There are several techniques that address this problem, chiefly by…

Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities,…