# Sound and Complete Sort Encodings for First-Order Logic

 Title: Sound and Complete Sort Encodings for First-Order Logic Authors: Jasmin Christian Blanchette (j /dot/ c /dot/ blanchette /at/ vu /dot/ nl) and Andrei Popescu Submission date: 2013-06-27 Abstract: This is a formalization of the soundness and completeness properties for various efficient encodings of sorts in unsorted first-order logic used by Isabelle's Sledgehammer tool. Essentially, the encodings proceed as follows: a many-sorted problem is decorated with (as few as possible) tags or guards that make the problem monotonic; then sorts can be soundly erased. The development employs a formalization of many-sorted first-order logic in clausal form (clauses, structures and the basic properties of the satisfaction relation), which could be of interest as the starting point for other formalizations of first-order logic metatheory. BibTeX: @article{Sort_Encodings-AFP, author = {Jasmin Christian Blanchette and Andrei Popescu}, title = {Sound and Complete Sort Encodings for First-Order Logic}, journal = {Archive of Formal Proofs}, month = jun, year = 2013, note = {\url{https://isa-afp.org/entries/Sort_Encodings.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.