Decomposable negation normal form
Journal of the ACM (JACM)
Computing Circumscription Revisited: A Reduction Algorithm
Journal of Automated Reasoning
Applying SAT Methods in Unbounded Symbolic Model Checking
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
MPTP 0.2: Design, Implementation, and Initial Experiments
Journal of Automated Reasoning
Propositional independence: formula-variable independence and forgetting
Journal of Artificial Intelligence Research
DPLL with a trace: from SAT to knowledge compilation
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Second Order Quantifier Elimination: Foundations, Computational Aspects and Applications
Tableaux for Projection Computation and Knowledge Compilation
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Projection and scope-determined circumscription
Journal of Symbolic Computation
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The computation of literal projection generalizes predicate quantifier elimination by permitting, so to speak, quantifying upon an arbitrary sets of ground literals, instead of just (all ground literals with) a given predicate symbol. Literal projection allows, for example, to express predicate quantification upon a predicate just in positive or negative polarity. Occurrences of the predicate in literals with the complementary polarity are then considered as unquantified predicate symbols. We present a formalization of literal projection and related concepts, such as literal forgetting, for first-order logic with a Herbrand semantics, which makes these notions easy to access, since they are expressed there by means of straightforward relationships between sets of literals. With this formalization, we show properties of literal projection which hold for formulas that are free of certain links, pairs of literals with complementary instances, each in a different conjunct of a conjunction, both in the scope of a universal first-order quantifier, or one in a subformula and the other in its context formula. These properties can justify the application of methods that construct formulas without such links to the computation of literal projection. Some tableau methods and direct methods for second-order quantifier elimination can be understood in this way.