Assumption set semantics (The procedures)
Our purpose is to extend logic programming semantics for programs with some form of denial statements  specifying that some sets of literals cannot all belong to the meaning of a program. Denials represent an intuitive form of knowledge representation extending the capabilities of logic programming as a tool for knowledge representation and reasoning. In  we defined the intended meaning of a program with a set of denials, and show that a set of denials is isomorphic to sets of assumption based denials. The model theory we introduce there is clearly general in the sense it does not rely on any particular semantics. A consequence is that satisfaction of (denials) may be seen as satisfaction w.r.t. to a smaller class of models (revised models) which are also stable under a suitable operator. Operationally, satisfaction of denials is equivalent to membership of the set of assumption based denials, thus avoiding the need for general consistency checking, which are more suitable (in some sense) for logic programming based implementations.
In  we introduce WFS⊥ and show an application of the use of denial rules to add a second form of negation in the spirit of  when the logic programming semantics being used is well founded semantics  and define the conditional meaning of the program. Here we present procedures 1 which are sound and complete (for ground programs) w.r.t. WFS⊥ and the conditional meaning of the program.
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