We propose a novel method to review K⊢ϕ when K and ϕ are both in Conjunctive Normal Forms (CF). We extend our method to solve the incremental satisfiablity problem (ISAT), and we present different cases where ISAT can be solved in polynomial time. Especially, we present an algorithm for 2-ISAT. Our last algorithm allow us to establish an upper bound for the time-complexity of 2-ISAT, as well as to establish some tractable cases for the 2-ISAT problem.
De Ita Luna, G., Marcial-Romero, J. R., & Hernández, J. A. (2016). The Incremental Satisfiability Problem for a Two Conjunctive Normal Form. Electronic Notes in Theoretical Computer Science, 328, 31–45. https://doi.org/10.1016/j.entcs.2016.11.004