Nominal Logic with Equations Only

Autor: Ranald Clouston
Jazyk: angličtina
Rok vydání: 2011
Předmět:
Zdroj: Electronic Proceedings in Theoretical Computer Science, Vol 71, Iss Proc. LFMTP 2011, Pp 44-57 (2011)
Druh dokumentu: article
ISSN: 2075-2180
DOI: 10.4204/EPTCS.71.4
Popis: 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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