Sound and Complete Sort Encodings for First-Order Logic

 

Title: Sound and Complete Sort Encodings for First-Order Logic
Authors: Jasmin Christian Blanchette (jasmin /dot/ blanchette /at/ gmail /dot/ com) and Andrei Popescu (uuomul /at/ yahoo /dot/ com)
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{http://isa-afp.org/entries/Sort_Encodings.shtml},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License