Skip to main content
×
Home
    • Aa
    • Aa

Finite and infinite support in nominal algebra and logic: nominal completeness theorems for free

  • Murdoch J. Gabbay (a1)
Abstract
Abstract

By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal models, so the construction hinges on generating from an instance of the latter, some instance of the former in which sufficiently many inequalities are preserved between elements. We do this using an infinite generalisation of nominal atoms-abstraction.

The results are of interest in their own right, but also, we factor the mathematics so as to maximise the chances that it could be used off-the-shelf for other nominal reasoning systems too. Models with infinite support can be easier to work with, so it is useful to have a semi-automatic theorem to transfer results from classes of infinitely-supported nominal models to the more restricted class of models with finite support.

In conclusion, we consider different permissive-nominal syntaxes and nominal models and discuss how they relate to the results proved here.

Copyright
References
Hide All
[3] Gilles Dowek and Murdoch J. Gabbay , Permissive nominal logic, Proceedings of the 12th international ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming (PPDP 2010), 2010, pp. 165176.

[5] Gilles Dowek , Murdoch J. Gabbay , and Dominic P. Mulligan , Permissive nominal terms and their unification: an infinite, co-infinite approach to nominal techniques, Logic Journal of the IGPL, vol. 18 (2010), no. 6, pp. 769822, (journal version).

[7] Murdoch J. Gabbay , A general mathematics of names, Information and Computation, vol. 205 (2007), no. 7, pp. 9821011.

[8] Murdoch J. Gabbay , Nominal algebra and the HSP theorem, Journal of Logic and Computation, vol. 19 (2009), no. 2, pp. 341367.

[9] Murdoch J. Gabbay , Foundations of nominal techniques: logic and semantics of variables in abstract syntax, The Bulletin of Symbolic Logic, vol. 17 (2011), no. 2, pp. 161229.

[10] Murdoch J. Gabbay , Two-level nominal sets and semantic nominal terms: an extension of nominal set theory for handling meta-variables, Mathematical Structures in Computer Science, vol. 21 (2011), pp. 9971033.

[11] Murdoch J. Gabbay , Meta-variables as infinite lists in nominal terms unification and rewriting, Logic Journal of the IGPL, (2012), in press.

[14] Murdoch J. Gabbay , Nominal universal algebra: equational logic with names and binding, Journal of Logic and Computation, vol. 19 (2009), no. 6, pp. 14551508.

[15] Murdoch J. Gabbay and Andrew M. Pitts , A new approach to abstract syntax with variable binding, Formal Aspects of Computing, vol. 13 (2001), no. 3–5, pp. 341363.

[16] Wilfrid Hodges , Model theory, Cambridge University Press, 1993.

[18] M. H. A. Newman , On theories with a combinatorial definition of equivalence. Annals of Mathematics, vol. 43 (1942), no. 2, pp. 223243.

[19] Andrew M. Pitts , Nominal logic, a first order theory of names and binding, Information and Computation, vol. 186 (2003), no. 2, pp. 165193.

[20] Christian Urban , Andrew M. Pitts , and Murdoch J. Gabbay , Nominal unification, Theoretical Computer Science, vol. 323 (2004), no. 1–3, pp. 473497.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 4 *
Loading metrics...

Abstract views

Total abstract views: 36 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 17th October 2017. This data will be updated every 24 hours.