HoCHC: a Refutationally-complete and Semantically-invariant System of Higher-order Logic Modulo Theories

02/27/2019
by   C. -H. Luke Ong, et al.
0

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-Schonfinkel-Ramsey fragment of HoCHC modulo a restricted form of Linear Integer Arithmetic.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/10/2021

Reducing Higher-order Recursion Scheme Equivalence to Coinductive Higher-order Constrained Horn Clauses

Higher-order constrained Horn clauses (HoCHC) are a semantically-invaria...
04/28/2022

On Quantitative Algebraic Higher-Order Theories

We explore the possibility of extending Mardare et al. quantitative alge...
01/23/2018

Higher-Order Equational Pattern Anti-Unification [Preprint]

We consider anti-unification for simply typed lambda terms in associativ...
04/21/2020

The Imandra Automated Reasoning System (system description)

We describe Imandra, a modern computational logic theorem prover designe...
06/17/2011

Extensional Higher-Order Logic Programming

We propose a purely extensional semantics for higher-order logic program...
11/18/2020

Efficient Full Higher-Order Unification

We developed a procedure to enumerate complete sets of higher-order unif...
04/29/2021

Initial Limit Datalog: a New Extensible Class of Decidable Constrained Horn Clauses

We present initial limit Datalog, a new extensible class of constrained ...