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Algebras of multiplace functions for signatures containing antidomain

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Abstract

We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or quasiequational axiomatisations for the representation class. We do the same for the question of representability by injective multiplace partial functions. For all our representation theorems, it is an immediate corollary of our proof that the finite representation property holds for the representation class. We show that for a large set of signatures, the representation classes have equational theories that are coNP-complete.

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Authors and Affiliations

  1. Department of Computer Science, University College London, Gower Street, London, WC1E 6BT, UK

    Brett McLean

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  1. Brett McLean
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Correspondence to Brett McLean.

Additional information

Presented by I. Hodkinson.

The author would like to thank his PhD supervisor Robin Hirsch for many helpful discussions.

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McLean, B. Algebras of multiplace functions for signatures containing antidomain. Algebra Univers. 78, 215–248 (2017). https://doi.org/10.1007/s00012-017-0452-1

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  • DOI: https://doi.org/10.1007/s00012-017-0452-1

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