Technical Foundations of a DPLL-Based SAT Solver for Propositional Gödel Logic

Hyperresolution for Gödel logic with truth constants

“…An output equivalent CNF may be of exponential size with respect to the size of the input formula; we had laid no restrictions on use of the distributivity law (4) during translation to conjunctive normal form. To avoid this disadvantage, we have devised translation to CNF via interpolation using new atoms, which produces an output CNF of linear size at the cost of being only equivalent satisfiable to the input formula [1]. A similar approach exploiting the renaming subformulae technique can be found in [14], [15], [16], [17], [18], [19].…”

“…Notice that if the estimated upper bound on the space complexity is equal to the estimated upper bound on the time complexity for some algorithm, then it will not be explicitly stated. Since our computational framework is only slightly different from that in [1], analogous considerations will be shorten. Let n s ∈ N (n s can be viewed as an offset in the memory) and E be either a term or a formula or an order clause or a finite theory or a finite order clausal theory.…”

“…This paper is a continuation of [1], mainly aiming at theoretical results concerning the logical and computational foundations of multi-step fuzzy inference. In [2], [3], [4], [5], [6], [7], [8], [9], [10], we have generalised the well-known hyperresolution principle to the first-order Gödel logic for the general case.…”

Automated Deduction in Propositional Product Logic

“…The procedure of Davis, Putnam, Logemann, and Loveland (algorithm) (DPLL) [15][16][17][18] is a prominent algorithm for solving the SAT problem in propositional calculus. In [19], we have extended DPLL procedure to Gödel logic. In Introduction to [19], we have briefly described the history of DPLL procedure together with its extensions to signed logic.…”

“…In [19], we have extended DPLL procedure to Gödel logic. In Introduction to [19], we have briefly described the history of DPLL procedure together with its extensions to signed logic. The underlying rule of the DPLL procedure has a branching nature.…”