A Logic for the Schema Calculus
نویسندگان
چکیده
In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z 's popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations thus far have either failed to provide a calculus (e.g. the draft standard 3]) or have fallen back on informal descriptions at a syntactic level (most text books e.g. 7]). Alongside the calculus we introduce a derived equa-tional logic which enables us to formalise properly the informal notions of schema expression equality to be found in the literature.
منابع مشابه
Implications-as-Rules vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus
The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form. The introduction schema for implicati...
متن کاملLogic and Algebraic Languages Forinteroperability in Multidatabasesystemslaks
Developing a declarative approach to interoperability in the context of multidatabase systems is a major goal of this research. We take a rst step toward this goal in this paper, by developing a simple logic called SchemaLog which is syntactically higher-order but has a rst-order semantics. SchemaLog can provide for interoperability among multiple relational databases in a federation of databas...
متن کاملDiagonal arguments and fixed points
A universal schema for diagonalization was popularized by N.S. Yanofsky (2003), based on a pioneering work of F.W. Lawvere (1969), in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function. It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema. Here, we fi...
متن کاملOperation Refinement and Monotonicity in the Schema Calculus
The schema calculus of Z provides a means for expressing structured, modular specifications. Extending this modularity to program development requires the monotonicity of these operators with respect to refinement. This paper provides a thorough mathematical analysis of monotonicity with respect to four schema operations for three notions of operation refinement. The mathematical connection bet...
متن کاملInvestigating Z : the Schema Calculus
In this paper we introduce and investigate an improved kernel logic ZC for the specii-cation language Z. Unlike the standard accounts 8] 4] 1] 3] this logic is consistent and is easily shown to be sound. We show how a complete schema calculus can be derived within this logic and in doing so we reveal a high degree of logical organisation within the language. Finally, our approach eschews all no...
متن کامل