An Extensible Logic Embedding Tool for Lightweight Non-Classical Reasoning

Abstract

The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets. When used as a pre-processor or library for higher-order theorem provers, the tool admits off-the-shelf automation for logics for which otherwise few to none provers are currently available.

Theorem Proving in Dependently-Typed Higher-Order Logic

“…We chose this ATP because its existing preprocessor infrastructure already includes a powerful logic embedding tool [21,22].However, with a little more effort, other HOL ATPs work as well.…”

“…We position our implementation close to an existing HOL ATP, namely the LEO-III system. From the LEO-III perspective, DHOL serves as an additional input language that is translated into HOL by an external logic embedding tool [21,22] in the LEO-III ecosystem. Because LEO-III already supports such embeddings and because the TPTP syntax [24] foresees the use of dependent types in ATPs and provides syntax for them (albeit without a normative semantics), we were able to implement the translation with no disruptions to existing workflows.…”