A logical framework with a graph meta-language

TL;DR

This paper introduces a graph-based logical framework with a simplified meta-language aimed at making logical systems easier to implement and use, leveraging graph databases for performance and proof management.

Contribution

The paper presents a novel graph-based logical framework that simplifies meta-language complexity and enhances proof system implementation and performance.

Findings

Implemented nine propositional logic systems including Fitch-style and Natural Deduction.

Utilized graph databases for optimized performance and proof compression.

Supported interactive and semi-automatic proof modes through a web interface.

Abstract

We conjecture that the relative unpopularity of logical frameworks among practitioners is partly due to their complex meta-languages, which often demand both programming skills and theoretical knowledge of the meta-language in question for them to be fruitfully used. We present ongoing work on a logical framework with a meta-language based on graphs. A simpler meta-language leads to a shallower embedding of the object language, but hopefully leads to easier implementation and usage. A graph-based logical framework also opens up interesting possibilities in time and space performance by using heavily optimized graph databases as backends and by proof compression algorithms geared towards graphs. Deductive systems can be specified using simple domain-specific languages built on top of the graph database's query language. There is support for interactive (through a web-based interface) and semiautomatic (following user-defined tactics specified by a domain-specific language) proof modes. We have so far implemented nine systems for propositional logic, including Fitch-style and backward-directed Natural Deduction systems for intuitionistic and classical logic (with the classical systems reusing the rules of the intuitionistic ones), and a Hilbert-style system for the K modal logic.