Abstract
In informal mathematical discourse (such as the text of a paper on theoretical computer science), we often reason about equalities involving binding of object-variables. We find ourselves writing assertions involving meta-variables and captureavoidance constraints on where object-variables can and cannot occur free. Formalizing such assertions is problematic because the standard logical frameworks cannot express capture-avoidance constraints directly.
In this article, we make the case for extending the logic of equality with meta-variables and capture-avoidance constraints, to obtain ‘nominal algebra’. We use nominal techniques that allow for a direct formalization of meta-level assertions, while remaining close to informal practice. We investigate proof-theoretical properties, we provide a sound and complete semantics in nominal sets and we compare and contrast our design decisions with other possibilities leading to similar systems.
Original language | English |
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Pages (from-to) | 1455-1508 |
Journal | Journal of Logic and Computation |
Volume | 19 |
Issue number | 6 |
DOIs | |
Publication status | Published - 2009 |