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Abstract: We show how to axiomatize by equations the least prefixed point of an order preserving function and discuss the domain of application of the proposed method. Thus, we generalize the well known equational axiomatization of Propositional Dynamic Logic to a complete equational axiomatization of the Boolean Modal μ-Calculus. We show on the other hand that the existence of a term which does not preserve the order is an essential condition for the least prefixed point to be definable by equations. (Update)
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BibTeX entry: (Update)
L. Santocanale. On the equational definition of the least prefixed point. Theoretical Computer Science, 295(1-3):341--370, February 2003. http://citeseer.ist.psu.edu/article/santocanale03equational.html More
@article{ santocanale01equational,
author = "Luigi Santocanale",
title = "On the Equational Definition of the Least Prefixed Point",
journal = "Lecture Notes in Computer Science",
volume = "2136",
pages = "645+",
year = "2001",
url = "citeseer.ist.psu.edu/article/santocanale03equational.html" }
Citations (may not include all citations):190 Results on the propositional -calculus (context) - Kozen - 1983
40 Fixpoint induction and proofs of program properties (context) - Park - 1970
37 Action logic and pure induction - Pratt - 1990
31 An elementary proof of the completeness of PDL (context) - Kozen, Parikh - 1981
28 A completeness theorem in the modal logic of programs (context) - Segerberg - 1978
21 Iteration theories (context) - Bloom, Esik - 1993
20 Completeness of Kozen's axiomatisation of the propositional .. - Walukiewicz - 2000
20 Universal algebra (context) - Gr - 1979
17 Varieties of ordered algebras (context) - Bloom - 1976
13 Free lattices (context) - Whitman - 1942
11 A hierarchy theorem for the -calculus (context) - Lenzi - 1996
11 Dynamic algebras: examples (context) - Pratt - 1991
9 calculus alternation-depth hierarchy is strict on binary tre.. - Arnold - 1999
8 The modal mu-calculus alternation hierarchy is strict (context) - eld - 1998
7 The alternation hierarchy for the theory of -lattices (context) - Santocanale - 2000
6 Duality and the completeness of the modal -calculus (context) - Ambler, Kwiatkowska et al. - 1995
5 On xed-point clones (context) - Niwi - 1986
4 Duality for modal -logics (context) - Hartonas - 1998
4 Sur les -treillis libres (context) - Santocanale - 2000
2 egories exactes (context) - Barr - 1971
2 Completeness of Park induction (context) - Esik - 1997
2 Department of Computer Science (context) - Santocanale, -lattices et al. - 2000
2 Monadic logic of order over naturals has no nite base (context) - Beauquier, Rabinovich - 2001
1 Iteration algebras (context) - Bloom, Esik - 1992
Documents on the same site (http://www.labri.fr/Perso/~santocan/respapers.html): More
Ambiguous Classes in the Games μ-Calculus Hierarchy - Arnold, Santocanale (Correct)
From Parity Games to Circular Proofs - Santocanale (2002) (Correct)
μ-Bicomplete Categories and Parity Functors - Santocanale (2001) (Correct)
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