Sound and Complete Sort Encodings for First-Order Logic

This is a formalization of the soundness and completeness proper-ties for various efficient encodings of sorts in unsorted first-order logicused by Isabelle’s Sledgehammer tool.The results are reported in [1, §2,3] and the formalization itself ispresented in [2, §3–5]. Essentially, the encodings proceed as follows:a many-sorted problem is decorated with (as few as possible) tags orguards that make the problem monotonic; then sorts can be soundlyerased. The proofs rely on monotonicity criteria recently introducedby Claessen, Lillieström and Smallbone [3].The development employs a formalization of many-sorted first-order logic in clausal form (clauses, structures and the basic propertiesof the satisfaction relation), which could be of interest as the startingpoint for other formalizations of first-order logic metatheory. References[1] J. C. Blanchette, S. Böhme, A. Popescu, and N. Smallbone. Encodingmonomorphic and polymorphic types. In N. Piterman and S. Smolka,editors, TACAS 2013, volume 7795 of LNCS, pages 493–507. Springer,2013.[2] J. C. Blanchette and A. Popescu. Mechanizing the metatheory of sledge-hammer. To be presented at FroCoS 2013.[3] K. Claessen, A. Lillieström, and N. Smallbone. Sort it out withmonotonicity—Translating between many-sorted and unsorted first-order logic. In N. Bjørner and V. Sofronie-Stokkermans, editors, CADE-23, volume 6803 of LNAI, pages 207–221. Springer, 2011.