383 research outputs found
Category Theory and Model-Driven Engineering: From Formal Semantics to Design Patterns and Beyond
There is a hidden intrigue in the title. CT is one of the most abstract
mathematical disciplines, sometimes nicknamed "abstract nonsense". MDE is a
recent trend in software development, industrially supported by standards,
tools, and the status of a new "silver bullet". Surprisingly, categorical
patterns turn out to be directly applicable to mathematical modeling of
structures appearing in everyday MDE practice. Model merging, transformation,
synchronization, and other important model management scenarios can be seen as
executions of categorical specifications.
Moreover, the paper aims to elucidate a claim that relationships between CT
and MDE are more complex and richer than is normally assumed for "applied
mathematics". CT provides a toolbox of design patterns and structural
principles of real practical value for MDE. We will present examples of how an
elementary categorical arrangement of a model management scenario reveals
deficiencies in the architecture of modern tools automating the scenario.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Two Forms of Inconsistency in Quantum Foundations
Recently, there has been some discussion of how Dutch Book arguments might be
used to demonstrate the rational incoherence of certain hidden variable models
of quantum theory (Feintzeig and Fletcher 2017). In this paper, we argue that
the 'form of inconsistency' underlying this alleged irrationality is deeply and
comprehensively related to the more familiar 'inconsistency' phenomenon of
contextuality. Our main result is that the hierarchy of contextuality due to
Abramsky and Brandenburger (2011) corresponds to a hierarchy of
additivity/convexity-violations which yields formal Dutch Books of different
strengths. We then use this result to provide a partial assessment of whether
these formal Dutch Books can be interpreted normatively.Comment: 26 pages, 5 figure
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