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On α-satisfiability and its α-lock resolution in a finite lattice-valued propositional logic

(2012) LOGIC JOURNAL OF THE IGPL. 20(3). p.579-588
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Abstract
Automated reasoning issues are addressed for a finite lattice-valued propositional logic LnP(X) with truth-values in a finite lattice-valued logical algebraic structure—lattice implication algebra. We investigate extended strategies and rules from classical logic to LnP(X) to simplify the procedure in the semantic level for testing the satisfiability of formulas in LnP(X) at a certain truth-value level α (α-satisfiability) while keeping the role of truth constant formula played in LnP(X). We propose a lock resolution method at a certain truth-value level α (α-lock resolution) in LnP(X) and have proved its theorems of soundness and weak completeness, respectively. We provide more efficient resolution based automated reasoning in LnP(X) and key supports for α-resolution-based automated reasoning approaches and algorithms in lattice based linguistic truth-valued logic.
Keywords
finite lattice-valued propositional logic, PRINCIPLE, α-lock resolution method, α-satisfiability, Lattice-valued logic, α-resolution principle, LP(X)

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Chicago
He, Xingxing, Jun Liu, Yang Xu, Luis Martínez, and Da Ruan. 2012. “On Α-satisfiability and Its Α-lock Resolution in a Finite Lattice-valued Propositional Logic.” Logic Journal of the Igpl 20 (3): 579–588.
APA
He, Xingxing, Liu, J., Xu, Y., Martínez, L., & Ruan, D. (2012). On α-satisfiability and its α-lock resolution in a finite lattice-valued propositional logic. LOGIC JOURNAL OF THE IGPL, 20(3), 579–588.
Vancouver
1.
He X, Liu J, Xu Y, Martínez L, Ruan D. On α-satisfiability and its α-lock resolution in a finite lattice-valued propositional logic. LOGIC JOURNAL OF THE IGPL. 2012;20(3):579–88.
MLA
He, Xingxing, Jun Liu, Yang Xu, et al. “On Α-satisfiability and Its Α-lock Resolution in a Finite Lattice-valued Propositional Logic.” LOGIC JOURNAL OF THE IGPL 20.3 (2012): 579–588. Print.
@article{2918385,
  abstract     = {Automated reasoning issues are addressed for a finite lattice-valued propositional logic LnP(X) with truth-values in a finite lattice-valued logical algebraic structure---lattice implication algebra. We investigate extended strategies and rules from classical logic to LnP(X) to simplify the procedure in the semantic level for testing the satisfiability of formulas in LnP(X) at a certain truth-value level \ensuremath{\alpha} (\ensuremath{\alpha}-satisfiability) while keeping the role of truth constant formula played in LnP(X). We propose a lock resolution method at a certain truth-value level \ensuremath{\alpha} (\ensuremath{\alpha}-lock resolution) in LnP(X) and have proved its theorems of soundness and weak completeness, respectively. We provide more efficient resolution based automated reasoning in LnP(X) and key supports for \ensuremath{\alpha}-resolution-based automated reasoning approaches and algorithms in lattice based linguistic truth-valued logic.},
  author       = {He, Xingxing and Liu, Jun and Xu, Yang and Mart{\'i}nez, Luis and Ruan, Da},
  issn         = {1367-0751},
  journal      = {LOGIC JOURNAL OF THE IGPL},
  keyword      = {finite lattice-valued propositional logic,PRINCIPLE,\ensuremath{\alpha}-lock resolution method,\ensuremath{\alpha}-satisfiability,Lattice-valued logic,\ensuremath{\alpha}-resolution principle,LP(X)},
  language     = {eng},
  number       = {3},
  pages        = {579--588},
  title        = {On \ensuremath{\alpha}-satisfiability and its \ensuremath{\alpha}-lock resolution in a finite lattice-valued propositional logic},
  url          = {http://dx.doi.org/10.1093/jigpal/jzr007},
  volume       = {20},
  year         = {2012},
}

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