Exact Unification and Admissibility

Metcalfe, George; Cabrer, Leonardo Manuel (2015). Exact Unification and Admissibility. Logical methods in computer science, 11(3), pp. 1-15. Department of Theoretical Computer Science, Technical University of Braunschweig 10.2168

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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.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Metcalfe, George and Cabrer, Leonardo Manuel

Subjects:

500 Science > 510 Mathematics

ISSN:

1860-5974

Publisher:

Department of Theoretical Computer Science, Technical University of Braunschweig

Language:

English

Submitter:

George Metcalfe

Date Deposited:

07 Jan 2016 15:31

Last Modified:

07 Jan 2016 15:31

Publisher DOI:

10.2168

BORIS DOI:

10.7892/boris.74480

URI:

https://boris.unibe.ch/id/eprint/74480

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