Implementing the First-Order Logic of Here and There
This work addresses the need for automated reasoning tools in non-classical logics, specifically HT, which is incremental as it builds on existing intuitionistic logic methods.
The authors tackled the problem of automated theorem proving for first-order logic of here and there (HT) by developing provers based on a native sequent calculus and an embedding into intuitionistic logic, achieving evaluation on a large benchmark set to establish a foundation for future efficiency improvements.
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic proof search in the sequent calculus is optimized by using free variables and skolemization. The embedding is used in combination with sequent, tableau and connection calculi for intuitionistic first-order logic. All provers are evaluated on a large benchmark set of first-order formulas, providing a foundation for the development of more efficient HT provers.