Volume 8, Issue 1, January 2015, Pages 34 - 43
α-Minimal Resolution Principle For A Lattice-Valued Logic
Hairui Jia, Yang Xu, Yi Liu, Jun Liu
Received 16 October 2013, Accepted 2 April 2014, Available Online 1 January 2015.
- https://doi.org/10.2991/ijcis.2015.8.1.3How to use a DOI?
- Automated reasoning, lattice-valued propositional logic LP(X), lattice-valued first-order logic LF(X), Î±-minimal resolution principle, Î±-minimal resolution group
- Based on the academic ideas of resolution-based automated reasoning and the previously established research work on binary α-resolution based automated reasoning schemes in the framework of lattice-valued logic with truth-values in a lattice algebraic structure-lattice implication algebra (LIA), this paper is focused on investigating α-n(t)-ary resolution based dynamic automated reasoning system based on lattice-valued logic based in LIA. One of key issues for α-n(t)-ary resolution dynamic automated reasoning is how to choose generalized literals in each resolution. In this paper, the definition of α-minimal resolution principle which determines how to choose generalized literals in LP(X) is introduced firstly, as well as its soundness and completeness being proved. α-minimal resolution principle is then further established in the corresponding lattice-valued first-order logic LF(X) along with its soundness theorem, lifting lemma and completeness theorem. These results lay the theoretical foundation for research of α-n(t)-ary resolution dynamic automated reasoning.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Hairui Jia AU - Yang Xu AU - Yi Liu AU - Jun Liu PY - 2015 DA - 2015/01/01 TI - α-Minimal Resolution Principle For A Lattice-Valued Logic JO - International Journal of Computational Intelligence Systems SP - 34 EP - 43 VL - 8 IS - 1 SN - 1875-6883 UR - https://doi.org/10.2991/ijcis.2015.8.1.3 DO - https://doi.org/10.2991/ijcis.2015.8.1.3 ID - Jia2015 ER -