Non-clausal Multi-ary alpha-Generalized Resolution Principle for a Lattice-Valued First-Order Logic

The present paper focuses on a resolution-based automated reasoning theory in a lattice-valued logic system with truth-values defined in a lattice-valued algebraic structure - lattice implication algebras (LIA) in order to handle automated deduction under an uncertain environment. Particularly, as a continuation and extension of the established work on binary resolution at a certain truth-value level α (called α-resolution), a non-clausal multi-ary α-generalized resolution principle and deduction are introduced in this paper for a lattice-valued first-order logic LF(X) based on LIA, which is essentially non-clausal generalized resolution avoiding the reduction to normal clausal form. Non-clausal multi-ary α-generalized resolution deduction in LF(X) is then proved to be sound and complete. The present work is expected to provide a theoretical foundation of more efficient resolution based automated reasoning in lattice-valued logic.