Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-26T04:36:08.499Z Has data issue: false hasContentIssue false
  • English
  • Français

Semantics for a basic relevant logic with intensional conjunction and disjunction (and some of its extensions)

Published online by Cambridge University Press:  01 February 2008

YING GAO  and
JINGDE CHENG
YING GAO
Affiliation:
Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, 338-8570, Japan Email: gaoying@aise.ics.saitama-u.ac.jp, cheng@aise.ics.saitama-u.ac.jp
JINGDE CHENG
Affiliation:
Department of Information and Computer Sciences, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama, 338-8570, Japan Email: gaoying@aise.ics.saitama-u.ac.jp, cheng@aise.ics.saitama-u.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper proposes a new relevant logic B+⊓⊔, which is obtained by adding two binary connectives, intensional conjunction ⊓ and intensional disjunction ⊔, to Meyer–Routley minimal positive relevant logic B+, where ⊓ and ⊔ are weaker than fusion ˚ and fission +, respectively. We give Kripke-style semantics for B+⊓⊔, with →, ⊓ and ⊔ modelled by ternary relations. We prove the soundness and completeness of the proposed semantics. A number of axiomatic extensions of B+⊓⊔, including negation-extensions, are also considered, together with the corresponding semantic conditions required for soundness and completeness to be maintained.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 1: in memory of Sauro Tulipani , February 2008 , pp. 145 - 164
Copyright
Copyright © Cambridge University Press2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, A. R. and Belnap, N. D. (1975) Entailment: The Logic of Relevance and Necessity, vol. I, Princeton University Press.Google Scholar
Anderson, A. R., Belnap, N. D. and Dunn, J. M. (1992) Entailment: The Logic of Relevance and Necessity, vol. II, Princeton University Press.Google Scholar
Brady, R. (ed.) (2003) Relevant Logics and their Rivals, vol. II, Ashgate Publishing Company.Google Scholar
Cheng, J. (2006) Strong Relevant Logic as the Universal Basis of Various Applied Logics for Knowledge Representation and Reasoning. In: Kiyoki, Y., Henno, J., Jaakkola, H. and Kangassalo, H. (eds.) Information Modelling and Knowledge Bases XVII, Frontiers in Artificial Intelligence and Applications 136 310–320.Google Scholar
Dunn, J. M. (1990) Gaggle Theory: An Abstraction of Galois Connections and Residuation with Applications to Negation and Various Logical Operations. In: van Eijk, J. (ed.) Logics in AI: European Workshop JELIA 1990. Springer-Verlag Lecture Notes in Computer Science 478 31–51.CrossRefGoogle Scholar
Fine, K. (1974) Models for Entailment. Journal of Philosophical Logic 3 347–372.CrossRefGoogle Scholar
Gao, Y. and Cheng, J. (2007) Semantics for a Basic Relevant Logic with Intensional Conjunction and Disjunction. Proceedings of the AILA Workshop on Logic, Model and Computer Science 2006. Electronic Notes in Theoretical Computer Science 169 61–71.CrossRefGoogle Scholar
Priest, G. and Sylvan, R. (1992) Simplified Semantics for Basic Relevant Logics. Journal of Philosophical Logic 21 217–232.CrossRefGoogle Scholar
Restall, G. (1993) Simplified Semantics for Relevant Logics (and Some of Their Rivals). Journal of Philosophical Logic 22 481–511.CrossRefGoogle Scholar
Routley, R. and Meyer, R. K. (1972) The Semantics of Entailment - III. Journal of Philosophical Logic 1 192–208.CrossRefGoogle Scholar
Routley, R., Plumwood, V., Meyer, R. K. and Brady, R. T. (1982) Relevant Logics and their Rivals, vol I, Ridgeview Publishing Company.Google Scholar