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SOZL (structured methodology + object-oriented methodology + Z language) is a language that attempts to integrate structured method, object-oriented method and formal method. The core of this language is predicate data flow diagram (PDFD). In order to eliminate the ambiguity of predicate data flow diagrams and their associated textual specifications, a formalization of the syntax and semantics of predicate data flow diagrams is necessary. In this paper we use Z notation to define an abstract syntax and the related structural constraints for the PDFD notation, and provide it with an axiomatic semantics based on the concept of data availability and functionality of predicate operation. Finally, an example is given to establish functionality consistent decomposition on hierarchical PDFD (HPDFD).