Determination of α-resolution in lattice-valued first-order logic LF(X)

  • Authors:

  • Yang Xu;Jun Liu;Da Ruan;Xiaobing Li

  • Affiliations:

  • School of Mathematics, Southwest Jiaotong University, Chengdu, Sichuan 610031, PR China;School of Computing and Mathematics, Faculty of Computing and Engineering, University of Ulster at Jordanstown, Newtownabbey BT37 0QB, Northern Ireland, UK;Belgian Nuclear Research Centre (SCKCEN), Mol, and Ghent University, Gent, Belgium;School of Management Science and Engineering, Dongbei University of Finance and Economics, Dalian, Liaoning 116025, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

Key issues for resolution-based automated reasoning in lattice-valued first-order logic LF(X) are investigated with truth-values in a lattice-valued logical algebraic structure-lattice implication algebra (LIA). The determination of resolution at a certain truth-value level (called @a-resolution) in LF(X) is proved to be equivalently transformed into the determination of @a-resolution in lattice-valued propositional logic LP(X) based on LIA. The determination of @a-resolution of any quasi-regular generalized literals and constants under various cases in LP(X) is further analyzed, specified, and subsequently verified. Hence the determination of @a-resolution in LF(X) can be accordingly solved to a very broad extent, which not only lays a foundation for the practical implementation of automated reasoning algorithms in LF(X), but also provides a key support for @a-resolution-based automated reasoning approaches and algorithms in LIA based linguistic truth-valued logics.