Deriving tableau-based solutions to lattice word problems
- We derive tableau calculi as solutions to the word problem for the free semilattice, the free distributive lattice and the free boolean lattice with a new method introduced in [13]. The method uses ordered resolution as a logical framework. The theory-specific and procedural information about the goal, the subformula property, is encoded via the ordering. Completeness of the calculi follows from correctness of their construction. Besides demonstrating the power of the derivation method, our formal reconstruction of tableaux also concerns the algebraic foundations of tableau and sequent calculi, in particular the connection of distributivity with the data-structure of sequents and with cut-elimination.
