Abstract
Multi-adjoint logic programs were recently proposed as a generalization of monotonic and residuated logic programs, in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. In this work, the need of biresiduated pairs is justified through the study of a very intuitive family of operators, which turn out to be not necessarily commutative and associative and, thus, might have two different residuated implications; finally, we introduce the framework of biresiduated multi-adjoint logic programming and sketch some considerations on its fixpoint semantics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blok, W.J., la Falce, S.B.: Komori identities in algebraic logic. Reports on Mathematical Logic 34, 79–106 (2001)
Damásio, C.V., Moniz Pereira, L.: Monotonic and residuated logic programs. In: Benferhat, S., Besnard, P. (eds.) ECSQARU 2001. LNCS (LNAI), vol. 2143, pp. 748–759. Springer, Heidelberg (2001)
Dunn, J.M.: Partial gaggles applied to logics with restricted structural rules. In: Došen, K., Schroeder-Heister, P. (eds.) Substructural Logics, Studies in Logic and Computation, pp. 63–108. Oxford University Press, Oxford (1993)
Gottwald, S.: Fuzzy Sets and Fuzzy Logic. Vieweg (1993)
Hájek, P.: Metamathematics of Fuzzy Logic. In: Trends in Logic, Kluwer Academic, Dordrecht (1998)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer academic, Dordrecht (2000)
Medina, J., Ojeda-Aciego, M., Vojtáš, P.: Multi-adjoint logic programming with continuous semantics. In: Eiter, T., Faber, W., Truszczyński, M. (eds.) LPNMR 2001. LNCS (LNAI), vol. 2173, pp. 351–364. Springer, Heidelberg (2001)
Mesiar, R., Novak, V.: Operations fitting triangular-norm-based biresiduation. Fuzzy Sets and Systems 104(1), 77–84 (1999)
Morsi, N.N.: Propositional calculus under adjointness. Fuzzy Sets and Systems 132, 91–106 (2002)
Sularia, M.: A logical system for multicriteria decision analysis. Studies in Informatics and Control 7(3) (1998)
van Alten, C.J.: Representable biresiduated lattices. Journal of Algebra 247, 672–691 (2002)
Vojtáš, P.: Fuzzy logic programming. Fuzzy sets and systems 124(3), 361–370 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Medina, J., Ojeda-Aciego, M., Valverde, A., Vojtáš, P. (2004). Towards Biresiduated Multi-adjoint Logic Programming. In: Conejo, R., Urretavizcaya, M., Pérez-de-la-Cruz, JL. (eds) Current Topics in Artificial Intelligence. TTIA 2003. Lecture Notes in Computer Science(), vol 3040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25945-9_60
Download citation
DOI: https://doi.org/10.1007/978-3-540-25945-9_60
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22218-7
Online ISBN: 978-3-540-25945-9
eBook Packages: Springer Book Archive