Tableau Calculus for Only-knowing and Abduction: A Preliminary Report
Resumo
Introduced by Hector Levesque in the 1990s, the logic of only-knowing (OL) has proven to be a rich framework for knowledge representation, a central topic in Artificial Intelligence. Since then, various extensions of OL have been explored by different authors. More recently, S. Molick and V. Belle extended OL to incorporate abductive reasoning, resulting in the logic of only-knowing and abduction (AOL). In this paper, we present sound and complete tableau rules for AOL, providing a preliminary step toward the development of an adequate proof-theoretic foundation for abductive reasoning within this extended logic.
Referências
Aliseda, A. (2000). Abduction as epistemic change: A peircean model in artificial intelligence. In Abduction and induction: Essays on their relation and integration, pages 45–58. Springer.
Belle, V. and Lakemeyer, G. (2010). Multi-agent only-knowing revisited. In Twelfth International Conference on the Principles of Knowledge Representation and Reasoning.
Belle, V. and Lakemeyer, G. (2015). Only knowing meets common knowledge. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, pages 2755–2761.
Levesque, H. J. (1989). A knowledge-level account of abduction. In IJCAI, pages 1061–1067.
Levesque, H. J. (1990). All i know: a study in autoepistemic logic. Artificial intelligence, 42(2-3):263–309.
Molick, S. and Belle, V. (2025). Propositional abduction via only-knowing: a nonmonotonic approach. On-line.Unpublished.
Nepomuceno-Fernández, A. (2002). Scientific explanation and modified semantic tableaux. In Logical and Computational Aspects of Model-Based Reasoning, pages 181–198. Springer.
Priest, G. (2008). An introduction to non-classical logic: From if to is. Cambridge University Press.
Belle, V. and Lakemeyer, G. (2010). Multi-agent only-knowing revisited. In Twelfth International Conference on the Principles of Knowledge Representation and Reasoning.
Belle, V. and Lakemeyer, G. (2015). Only knowing meets common knowledge. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015, pages 2755–2761.
Levesque, H. J. (1989). A knowledge-level account of abduction. In IJCAI, pages 1061–1067.
Levesque, H. J. (1990). All i know: a study in autoepistemic logic. Artificial intelligence, 42(2-3):263–309.
Molick, S. and Belle, V. (2025). Propositional abduction via only-knowing: a nonmonotonic approach. On-line.Unpublished.
Nepomuceno-Fernández, A. (2002). Scientific explanation and modified semantic tableaux. In Logical and Computational Aspects of Model-Based Reasoning, pages 181–198. Springer.
Priest, G. (2008). An introduction to non-classical logic: From if to is. Cambridge University Press.
Publicado
20/07/2025
Como Citar
MOLICK, Sanderson; FURTADO, Manuella.
Tableau Calculus for Only-knowing and Abduction: A Preliminary Report. In: WORKSHOP BRASILEIRO DE LÓGICA (WBL), 6. , 2025, Maceió/AL.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2025
.
p. 9-15.
ISSN 2763-8731.
DOI: https://doi.org/10.5753/wbl.2025.7468.
