## On Proof-Search in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid E-Unification (1996)

Venue: | Automated Deduction --- CADE-13 |

Citations: | 17 - 9 self |

### BibTeX

@INPROCEEDINGS{Voronkov96onproof-search,

author = {Andrei Voronkov},

title = {On Proof-Search in Intuitionistic Logic with Equality, or Back to Simultaneous Rigid E-Unification},

booktitle = {Automated Deduction --- CADE-13},

year = {1996},

pages = {32--46}

}

### Years of Citing Articles

### OpenURL

### Abstract

We characterize provability in intuitionistic logic with equality in terms of a constraint calculus. This characterization uncovers close connections between provability in intuitionistic logic with equality and solutions to simultaneous rigid E-unification. We show that the problem of existence of a sequent proof with a given skeleton is polynomial-time equivalent to simultaneous rigid E-unifiability. This gives us a proof procedure for intuitionistic logic with equality modulo simultaneous rigid E-unification. We also show that simultaneous rigid E-unifiability is polynomial-time reducible to intuitionistic logic with equality. Thus, any proof procedure for intuitionistic logic with equality can be considered as a procedure for simultaneous rigid E-unifiability. In turn, any procedure for simultaneous rigid E-unifiability gives a procedure for establishing provability in intuitionistic logic with equality. 2 2 Copyright c fl 1995, 1996 Andrei Voronkov. This technical report and ot...