相关论文: Certified Connection Tableaux Proofs for HOL Light…

Network topology matrices are algebraic representations of graphs that are widely used in modeling and analysis of various applications including electrical circuits, communication networks and transportation systems. In this paper, we…

Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…

Language models have become increasingly powerful tools for formal mathematical reasoning. However, most existing approaches rely exclusively on either large general-purpose models or smaller specialized models, each with distinct…

Hierarchical proof trees (hiproofs for short) add structure to ordinary proof trees, by allowing portions of trees to be hierarchically nested. The additional structure can be used to abstract away from details, or to label particular…

Large Language Models (LLMs) have recently advanced the field of Automated Theorem Proving (ATP), attaining substantial performance gains through widely adopted test-time scaling strategies, notably reflective Chain-of-Thought (CoT)…

Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and in some cases more efficient than LP, CLP or LP + tabling. Previous designs of TCLP systems did not fully…

This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…

LPTP (Logic Program Theorem Prover) is an interactive natural-deduction-based theorem prover for pure Prolog programs with negation as failure, unification with the occurs check, and a restricted but extensible set of built-in predicates.…

We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We…

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…

We present a trustworthy connection between the Leon verification system and the Isabelle proof assistant. Leon is a system for verifying functional Scala programs. It uses a variety of automated theorem provers (ATPs) to check verification…

The synergy between deep learning models and traditional automation tools, such as built-in tactics of the proof assistant and off-the-shelf automated theorem provers, plays a crucial role in developing robust and efficient neural theorem…

The state-of-the-art in optimal control from timed temporal logic specifications, including Metric Temporal Logic (MTL) and Signal Temporal Logic (STL), is based on Mixed-Integer Convex Programming (MICP). The standard MICP approach is…

AI agents have shown initial promise in automating mathematical theorem proving in proof assistants such as Lean. The same proof assistants can be used to verify the correctness of code by pairing code with specifications and proofs that…

We present ML4PG - a machine learning extension for Proof General. It allows users to gather proof statistics related to shapes of goals, sequences of applied tactics, and proof tree structures from the libraries of interactive higher-order…

Solving mathematical problems using computer-verifiable languages like Lean has significantly impacted the mathematical and computer science communities. State-of-the-art methods utilize a single Large Language Model (LLM) to generate…

During the High Luminosity phase of LHC, up to 200 proton-proton collisions per bunch crossing will bring severe challenges for event reconstruction. To mitigate pileup effects, an extended upgrade program of the CMS experiment is expected.…

Connection calculi allow for very compact implementations of goal-directed proof search. We give an overview of our work related to connection tableaux calculi: First, we show optimised functional implementations of clausal and nonclausal…

We present a tool called HHLPar for verifying hybrid systems modelled in Hybrid Communicating Sequential Processes (HCSP). HHLPar is built upon a Hybrid Hoare Logic for HCSP, which is able to reason about continuous-time properties of…