Metcalfe, George and Cabrer, Leonardo - Exact Unification and Admissibility

lmcs:1599 - Logical Methods in Computer Science, September 28, 2015, Volume 11, Issue 3
Exact Unification and Admissibility

Authors: Metcalfe, George and Cabrer, Leonardo

A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by instantiation, but rather by inclusion over the corresponding sets of unified identities. Minimal complete sets of unifiers under this new preordering always have a smaller or equal cardinality than those provided by the standard instantiation preordering, and in significant cases a dramatic reduction may be observed. In particular, the classes of distributive lattices, idempotent semigroups, and MV-algebras, which all have nullary unification type, have unitary or finitary exact type. These results are obtained via an algebraic interpretation of exact unification, inspired by Ghilardi's algebraic approach to equational unification.


Source : oai:arXiv.org:1508.04360
DOI : 10.2168/LMCS-11(3:23)2015
Volume: Volume 11, Issue 3
Published on: September 28, 2015
Submitted on: December 23, 2014
Keywords: Computer Science - Logic in Computer Science


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