The Logical Syntax of (IT) Architectures
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Despite several (accepted) standards, core notions typically employed in information technology (IT) architectures lack the precise and exact foundations encountered in logic, algebra, and other branches of mathematics. In this contribution we define the term "architecture" in a mathematically rigorous way. We motivate our particular choice by demonstrating (i) how commonly understood and expected properties of an architecture can be suitably defined or derived within our formalization, and (ii) how our concept is fully compatible with real life (business) architectures. Based on our fundamental definitions we further develop a rigorous notion of architectural similarity based on the notion of "homomorphisms" between architectures. We demonstrate the (theoretical) applicability by deriving some theorems on the characterization n-tier architectures.
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