Related papers: Premise Selection and External Provers for HOL4
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…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
We present simple new Hoare logics and refinement calculi for hybrid systems in the style of differential dynamic logic. (Refinement) Kleene algebra with tests is used for reasoning about the program structure and generating verification…
Phishing detection systems are predominantly rely on statistical machine learning models, which often lack contextual reasoning and are vulnerable to adversarial manipulation. In this work, we propose a hybrid framework that integrates…
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, they did not have a systematic way to encode their expertise. To address this…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
This study presents the first examination of the ability of Large Language Models (LLMs) to follow reasoning strategies that are used to guide Automated Theorem Provers (ATPs). We evaluate the performance of GPT4, GPT3.5 Turbo and Google's…
Logical reasoning is a core challenge in natural language understanding and a fundamental capability of artificial intelligence, underpinning scientific discovery, mathematical theorem proving, and complex decision-making. Despite the…
Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…
Automated Theorem Proving (ATP) in formal languages remains a formidable challenge in AI, demanding rigorous logical deduction and navigating vast search spaces. While large language models (LLMs) have shown promising performance, existing…
Quantum Hoare Logic (QHL) was introduced in Ying's work to specify and reason about quantum programs. In this paper, we implement a theorem prover for QHL based on Isabelle/HOL. By applying the theorem prover, verifying a quantum program…
An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant…
Vampire has been for a long time the strongest first-order automatic theorem prover, widely used for hammer-style proof automation in ITPs such as Mizar, Isabelle, HOL, and Coq. In this work, we considerably improve the performance of…
We consider the problem of how to verify the security of probabilistic oblivious algorithms formally and systematically. Unfortunately, prior program logics fail to support a number of complexities that feature in the semantics and…
In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning…
The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…