Representations

2025-10-13

AI Summary

Addressing the challenge of proving logical completeness relative to semantics in formal verification of software analysis systems (SAS), this paper introduces Representations—the first abstract metamodel tailored for SAS. Built on minimal assumptions, it uniformly characterizes syntax, semantics, and inference structures across diverse analysis systems, enabling systematic mapping between semantics and logic via metalinguistic modeling and structural induction. Its core innovation lies in decomposing completeness proofs into reusable, modular steps, thereby substantially reducing design and verification overhead for new SAS. Experiments demonstrate that Representations successfully reconstructs completeness proofs for multiple classical SAS and guides the development of two novel analysis systems—validating its effectiveness in simplifying proof construction, supporting system design, and ensuring theoretical rigor. (149 words)

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often, one particular property can prove frustrating to establish: completeness of the logic with respect to the semantics. In this paper, we try and make such developments easier, with a particular attention on completeness. Towards that aim, we propose a formal (meta-)model of software analysis systems (SAS), the eponymous Representations. This model requires few assumptions on the SAS being modeled, and as such is able to capture a large class of such systems. We then show how our approach can be fruitful, both to understand how existing completeness proofs can be structured, and to leverage this structure to build new systems and prove their completeness.

Problem

• Developing verification frameworks for automated systems analysis
• Establishing logic completeness with respect to semantics
• Creating formal meta-model for software analysis systems

Innovation

• Proposes a formal meta-model named Representations
• Captures a wide class of software analysis systems
• Enables structured completeness proofs for new systems