Automated Deduction for Projection Elimination
Projection is a logic operation which allows to express tasks in knowledge representation. These tasks involve extraction or removal of knowledge concerning a given sub-vocabulary. It is a generalization of second-order quantification, permitting, so to speak, to ‘quantify’ upon an arbitrary set of ground literals instead of just (all ground literals with) a given predicate symbol.
In Automated Deduction for Projection Elimination, a semantic characterization of projection for first-order logic is presented. On this basis, properties underlying applications and processing methods are derived. The computational processing of projection, called projection elimination in analogy to quantifier elimination, can be performed by adapted theorem proving methods. This is shown for resolvent generation and, more in depth, tableau construction.
An abstract framework relates projection elimination with knowledge compilation and shows the adaption of key features of high performance tableau systems. As a prototypical instance, an adaption of a modern DPLL method, such as underlying state-of-the-art SAT solvers, is worked out. It generalizes various recent knowledge compilation methods and utilizes the interplay with projection elimination for efficiency improvements.