The equational logic of fixed points

Equational properties of stratified least fixed points

Recently, a novel fixed point operation has been introduced over certain non-monotonic functions between stratified complete lattices and used to give semantics to logic programs with negation and boolean context-free grammars. We prove that this new operation satisfies ‘the standard’ identities of fixed point operations as described by the axioms of iteration theories. We also study this new f...

Fixed Points in the Ambient Logic

We present an extension of the ambient logic with fixed points operators in the style of the μ-calculus. We give a simple syntactic condition for the equivalence between minimal and maximal fixpoint formulas and show how to subsume spatial analogues of the usual box and diamond operators.

Equational Logic and Equational Theories of Algebras

Survey of the Equational Logic

In 1975 I started a small project to explore the consequences of implementing equational programs with no semantic compromises. Latest results include a compiler that executes exactly the logical consequences of an equa-tional program, with run-time speed comparable to compiled Franz LISP. This paper surveys the development of the project, through theoretical foundations , algorithm development...

The Equational Theory of Fixed Points with Applications to Generalized Language Theory

We review the rudiments of the equational logic of (least) fixed points and provide some of its applications for axiomatization problems with respect to regular languages, tree languages, and synchronization trees.