Hierarchic Reasoning in Local Theory Extensions | Zendy

Viorica Sofronie-Stokkermans | Zendy

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Hierarchic Reasoning in Local Theory Extensions

Author(s) -

Viorica Sofronie-Stokkermans

Publication year - 2005

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-28005-7

DOI - 10.1007/11532231_16

Subject(s) - decidability , extension (predicate logic) , computer science , base (topology) , discrete mathematics , model theory , algebra over a field , mathematics , theoretical computer science , pure mathematics , programming language , mathematical analysis

We show that for special types of extensions of a base theory, which we call local, efficient hierarchic reasoning is possible. We identify situations in which it is possible, for an extension $\mathcal{T}_{1}$ of a theory $\mathcal{T}_{0}$, to express the decidability and complexity of the universal theory of $\mathcal{T}_{1}$ in terms of the decidability resp. complexity of suitable fragments of the theory $\mathcal{T}_{0}$ (universal or ∀∃). These results apply to theories related to data types, but also to certain theories of functions from mathematics.

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