Lambda the Ultimate

Axiomatic language is a formal system for specifying recursively enumerable sets of hierarchical symbolic expressions. But axiomatic language does not have negation. Extended axiomatic language is based on the idea that when one specifies a recursively enumerable set, one is simultaneously specifying the complement of that set (which may not be recursively enumerable). This complement set can be useful for specification. Extended axiomatic language makes use of this complement set and can be considered a form of logic programming negation. The web page defines the language and gives examples.