Abstract
This article presents a relational formalization of axiomatic set theory, including so-called ZFC and the anti-foundation axiom (AFA) due to P. Aczel. The relational framework of set theory provides a general methodology for the fundamental study on computer and information sciences such as theory of graph transformation, situation semantics and analysis of knowledge dynamics in distributed systems. To demonstrate the feasibility of relational set theory some fundamental theorems of set theory, for example, Cantor-Bernstein-Schroder theorem, Cantor's theorem, Rieger's theorem and Mostowski's collapsing lemma are proved.
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