ETAPS 2019
Sat 6 - Thu 11 April 2019 Prague, Czech Republic
Sun 7 Apr 2019 10:00 - 10:30 at S4 (HCVS) - I Chair(s): Maurizio Proietti

We present a simple resolution proof system for higher-order constrained Horn clauses (HoCHC) - a system of higher-order logic modulo theories - and prove its soundness and refutational completeness w.r.t. the standard semantics. As corollaries, we obtain the compactness theorem and semi-decidability of HoCHC for semi-decidable background theories, and we prove that HoCHC satisfies a canonical model property. Moreover a variant of the well-known translation from higher-order to 1st-order logic is shown to be sound and complete for HoCHC in standard semantics. We illustrate how to transfer decidability results for (fragments of) 1st-order logic modulo theories to our higher-order setting, using as example the Bernays-Schönfinkel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic.

Slides for "HoCHC: A Refutationally Complete and Semantically Invariant System of Higher-order Logic Modulo Theories" (HCVS19-HoCHC.pdf)608KiB