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arXiv · 1111.0088

Nominal Logic with Equations Only

Ranald Clouston
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Abstract

Many formal systems, particularly in computer science, may be captured by equations modulated by side conditions asserting the "freshness of names"; these can be reasoned about with Nominal Equational Logic (NEL). Like most logics of this sort NEL employs this notion of freshness as a first class logical connective. However, this can become inconvenient when attempting to translate results from standard equational logic to the nominal setting. This paper presents proof rules for a logic whose only connectives are equations, which we call Nominal Equation-only Logic (NEoL). We prove that NEoL is just as expressive as NEL. We then give a simple description of equality in the empty NEoL-theory, then extend that result to describe freshness in the empty NEL-theory.

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Ranald Clouston. 2011-11-01. Nominal Logic with Equations Only. https://doi.org/10.4204/eptcs.71.4

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