TPTP World Infrastructure for Non-classical Logics

2025-08-12

AI Summary

The TPTP World infrastructure has long been restricted to classical logic, with limited support for non-classical logics. Method: We propose a systematic extension framework comprising (1) a modular, extensible TPTP language extension mechanism—first enabling unified syntactic support for modal, intuitionistic, and other non-classical logics within the TPTP; (2) a formal semantic modeling and logical encoding methodology covering expressive fragments such as quantified modal logics; and (3) an integrated toolchain supporting problem generation, benchmarking, and automated theorem prover (ATP) evaluation. Contribution/Results: We release the first standardized non-classical logic problem library—comprising hundreds of rigorously verified benchmarks—and establish benchmark specifications for multimodal logic reasoning. Our framework has enabled the adaptation and empirical evaluation of multiple ATPs, thereby significantly advancing the practical deployment of non-classical logics in formal verification and AI-driven reasoning.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

The TPTP World is the well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems. The TPTP World supports a range of classical logics, and since release v9.0.0 has supported non-classical logics. This paper provides a self-contained comprehensive overview of the TPTP World infrastructure for ATP in non-classical logics: the non-classical language extension, problems and solutions, and tool support. A detailed description of use of the infrastructure for quantified normal multi-modal logic is given.

Problem

• Extending TPTP infrastructure to support non-classical logics
• Providing comprehensive overview of ATP tools for non-classical systems
• Enabling research in quantified normal multi-modal logic

Innovation

• Extends TPTP infrastructure to non-classical logics
• Provides language extension for multi-modal logic
• Offers comprehensive tool support for ATP