---
title: "OI-implication: Soundness and Refutation Completeness"
authors:
  - "Floriana Esposito"
  - "Nicola Fanizzi"
  - "Stefano Ferilli"
  - "Giovanni Semeraro"
doi: ""
url: "https://ijcai.org/proceedings/2001/116"
pdf: "https://ijcai.org/proceedings/2001/0116.pdf"
venue: "Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence"
year: 2001
pages: "847-851"
track: ""
keywords:
---

# OI-implication: Soundness and Refutation Completeness

Floriana Esposito, Nicola Fanizzi, Stefano Ferilli, Giovanni Semeraro

*Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence*, pages 847-851.

## Abstract

Weakening implication by assuming the object identity bias allows for both a model-theoretical and a proof-theoretical definition of a novel and more manageable ordering relationship over clausal spaces. In this paper, we give two important results, namely the soundness and the refutation completeness (through a subsumption theorem) of the underlying derivation procedure, that make this relationship particularly appealing for inducing a generalization model for clausal search spaces.