Tableaux for Lattices
We formally derive tableau calculi for various lattices. They solve the word problem for the free algebra in the respective class. They are developed in and integrated into the ordered resolution theorem proving framework as special-purpose procedures. Theory-specific and procedural information is included by rewriting techniques and by imposing the subformula property on the ordering constraints. Intended applications include modal logic and the automated proof support for set-based formal methods. Our algebraic study also contributes to the foundations of tableau and sequent calculi, explaining the connection of distributivity with the data-structure of sequents and with cut-elimination.
KeywordsDistributive Lattice Word Problem Inference Rule Horn Clause Sequent Calculus
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