General form of ?-resolution principle for linguistic truth-valued lattice-valued logic
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 ?-resolution principle based on the above lattice-valued logic is equivalently transformed into another simpler lattice-valued logic system. Firstly, the general form of ?-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 ?-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 ?-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.
general form of ?-resolution principle linguistic truth-valued lattice-valued logic resolution-based automated reasoning linguistic truth-valued lattice implication algebra