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Hidden Markov Models, HMM's, are mathematical models of Markov processes whose state is hidden but from which information can leak via channels. They are typically represented as 3-way joint probability distributions. We use HMM's as denotations of probabilistic hidden-state sequential programs, after recasting them as 'abstract' HMM's, i.e. Computations in the Giry monad D, and equipping them with a partial order of increasing security. However to encode the monadic type with hiding over state X we use DX→D2X rather than the conventional X→DX. We illustrate this construction with a very small Haskell prototype. We then present uncertainty measures as a generalisation of the extant diversity of probabilistic entropies, and we propose characteristic analytic properties for them. Based on that, we give a 'backwards', uncertainty-transformer semantics for HMM's, dual to the 'forwards' abstract HMM's. Finally, we discuss the Dalenius desideratum for statistical databases as an issue in semantic compositionality, and propose a means for taking it into account.
|Title of host publication||Proceedings - 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015|
|Place of Publication||Picataway, NJ|
|Publisher||Institute of Electrical and Electronics Engineers (IEEE)|
|Number of pages||12|
|Publication status||Published - 31 Jul 2015|
|Event||30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015 - Kyoto, Japan|
Duration: 6 Jul 2015 → 10 Jul 2015
|Name||Annual Symposium on Logic in Computer Science|
|Publisher||IEEE Computer Society|
|Other||30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015|
|Period||6/07/15 → 10/07/15|
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