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General form of α-resolution principle for linguistic truth-valued lattice-valued logic

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Abstract

This paper is focused on resolution-based automated reasoning theory in linguistic truth-valued lattice-valued logic based on linguistic truth-valued lattice implication algebra. Concretely, the general form of α-resolution principle based on the above lattice-valued logic is equivalently transformed into another simpler lattice-valued logic system. Firstly, the general form of α-resolution principle for lattice-valued propositional logic \( ({\fancyscript{L}}_{n} \times {\fancyscript{L}}_{2}){\text{P(X)}} \) is equivalently transformed into that for lattice-valued propositional logic \( \fancyscript{L}_{n} \)P(X). A similar conclusion is obtained between the general form of α-resolution principle for linguistic truth-valued lattice-valued propositional logic \({\fancyscript{L}}_{V(n \times 2)}\)P(X) and that for lattice-valued propositional logic \({\fancyscript{L}}_{Vn} \)P(X). Secondly, the general form of α-resolution principle for lattice-valued first-order logic \( ({\fancyscript{L}}_{n} \times {\fancyscript{L}}_{2}) \)F(X) is equivalently transformed into that for \({\fancyscript{L}}_{n} \)P(X). Similarly, this conclusion also holds for linguistic truth-valued lattice-valued first-order \({\fancyscript{L}}_{V(n \times 2)} \)F(X) and \({\fancyscript{L}}_{Vn} \)P(X). The presented work provides a key theoretical support for automated reasoning approaches and algorithms in linguistic truth-valued logic, which can further support linguistic information processing for decision making, i.e., reasoning with words.

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Acknowledgments

This work is partially supported by the National Natural Science Foundation of P. R. China (Grant No. 60875034, 61175055, 61100046); the project TIN-2009-0828; Sichuan Key Technology Research and Development Program of China (Grant No. 2011FZ0051) and Wireless Administration of Ministry of Industry and Information Technology of China ([2011]146).

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Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan, 610031, People’s Republic of China

    Xiaomei Zhong & Yang Xu

  2. School of Computing and Mathematics, University of Ulster, Jordanstown, Northern Ireland, UK

    Jun Liu & Shuwei Chen

  3. School of Electrical Engineering, Zhengzhou University, Zhengzhou, 450001, Henan, People’s Republic of China

    Shuwei Chen

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  1. Xiaomei Zhong
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  2. Yang Xu
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  3. Jun Liu
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  4. Shuwei Chen
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Correspondence to Jun Liu.

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Zhong, X., Xu, Y., Liu, J. et al. General form of α-resolution principle for linguistic truth-valued lattice-valued logic. Soft Comput 16, 1767–1781 (2012). https://doi.org/10.1007/s00500-012-0860-2

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