Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Residuated Park Theories (1102.1139v1)

Published 6 Feb 2011 in cs.LO and math.LO

Abstract: When $L$ is a complete lattice, the collection $\Mon_L$ of all monotone functions $Lp \to Ln$, $n,p \geq 0$, forms a Lawvere theory. We enrich this Lawvere theory with the binary supremum operation $\vee$, an operation of (left) residuation $\res$ and the parameterized least fixed point operation $\dagger$. We exhibit a system of \emph{equational} axioms which is sound and proves all valid equations of the theories $\Mon_L$ involving only the theory operations, $\vee$ and $\dagger$, i.e., all valid equations not involving residuation. We also present an alternative axiomatization, where $\dagger$ is replaced by a star operation, and provide an application to regular tree languages.

Citations (8)

Summary

We haven't generated a summary for this paper yet.