IDSRadar: a real-time visualization framework for IDS alerts

In this paper, we establish the graded syntax theory of lattice-valued propositional logic based on finite lattice implication algebras, define the notions of syntactic consequence operation and formal proof, and develop a kind of graded finite lattice-valued propositional calculus. By generalizing classic provable equivalence relation, we present a kind of generalized provable equivalence relation, and establish the corresponding quotient algebra. Finally, we establish the generalized deduction theorem by syntactic consequence operation, and establish the completeness in Pavelka’s sense based on finite chains.