# SLD-Resolution Reduction of Second-Order Horn Fragments -- technical report --

## TL;DR

This paper investigates the derivation reduction problem for SLD-resolution in second-order Horn logic, exploring its decidability and implications for Inductive Logic Programming and standard resolution.

## Contribution

It introduces the derivation reduction problem for SLD-resolution, analyzes its reducibility in second-order Horn fragments, and discusses extensions to standard resolution.

## Key findings

- Derivation reduction problem is undecidable in general.
- Certain second-order Horn fragments are reducible, enabling finite derivations.
- Results have implications for Inductive Logic Programming and resolution methods.

## Abstract

We present the derivation reduction problem for SLD-resolution, the undecidable problem of finding a finite subset of a set of clauses from which the whole set can be derived using SLD-resolution. We study the reducibility of various fragments of second-order Horn logic with particular applications in Inductive Logic Programming. We also discuss how these results extend to standard resolution.