The Possibilistic Horn Non-Clausal Knowledge Bases

Possibilistic logic is the most popular approach to represent and reason with uncertain and partially inconsistent knowledge. Regarding normal forms, the encoding of real-world problems does usually not result in a clausal formula and although a possibility nonclausal formula is theoretically equivalent to some possibilistic clausal formula [26, 22], approaches needing clausal form transformations are practically infeasible or have experimentally shown to be highly inefficient as discussed below. Two kinds of clausal form transformation are known: (1) one is based on the repetitive application of the distributive laws to the input non-clausal formula until a logically equivalent clausal formula is obtained; and (2) the other transformation, Tsetin-transformation [59], is based on recursively substituting sub-formulas in the input non-clausal formula by fresh literals until obtaining an equi-satisfiable, but not equivalent, clausal formula.