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Proof theory for Kleene algebra

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1 Author(s)
Hardin, C. ; Dept. of Math., Cornell Univ., Ithaca, NY, USA

The universal Horn theory of relational Kleene algebra with tests (RKAT) is of practical interest, particularly for program semantics. We develop an (infinitary) proof system, based on well-founded trees of finite automata, which is sound and complete for this theory. A small modification of this system yields a proof system which is sound and complete for the universal Horn theory of *-continuous Kleene algebras with tests (KAT*). This sheds light on the relationship between RKAT and KAT*.

Published in:

Logic in Computer Science, 2005. LICS 2005. Proceedings. 20th Annual IEEE Symposium on

Date of Conference:

26-29 June 2005