### 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.

### License

BSD License

### Topics

- Logic/General logic/Mechanization of proofs

### Session Sort_Encodings

- Preliminaries
- TermsAndClauses
- Sig
- M
- CM
- Mono
- Mcalc
- T_G_Prelim
- Mcalc2
- Mcalc2C
- G
- T
- U
- CU
- E
- Encodings

## Cite

×

Sort_Encodings-AFP

    @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   = {June},
      year    = {2013},
      note    = {\url{https://isa-afp.org/entries/Sort_Encodings.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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