Physical Sciences and Mathematics Commons^™

Generalized Ultrametrics, Domains And An Application To Computational Logic, Anthony K. Seda, Pascal Hitzler

Computer Science and Engineering Faculty Publications

Fixed points of functions and operators are of fundamental importance in programming language semantics in giving meaning to recursive definitions and to constructs which involve self-reference. It follows therefore that fixed-point theorems are also of fundamental importance in theoretical computer science. Often, order-theoretic arguments are available in which case the well-known Knaster-Tarski theorem can be used to obtain fixed-points. Sometimes, however, analytical arguments are needed involving the Banach contraction mapping theorem as is the case for example in studying concurrency and communicating systems. Situations arise also in computational logic in the presence of negation which force non-monotonicity of the operators …