SONIC is a prototype system to implement non-standard inferences for Description Logics. We implemented the least common subsumer and approximation for ALE and ALEN with background terminologies.

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Research Interests

  • Natural Language Processing
  • Semantic Web
  • Machine Learning
  • (Enriched) Category Theory
  • Coalgebra and Coalgebraic (Modal) Logic
  • Generic Trace Theory
  • Coalgebraic Automata Theory
  • Modal and Intuitionistic Logic
  • Quantum Field Theories

Coalgebraic Automata Theory

Coalgebra automata were invented by Yde Venema and first published on in his paper "Automata and Fixed Point Logics: A Coalgebraic Approach". Their purpose is two-fold. On the one hand, coalgebra automata provide a suitable means to study properties of automata for a large class of input types, comprising words, trees, and graphs. On the other hand coalgebra automata introduce fixed point operators in Moss' coalgebraic logic. The latter reflects the insight that states in coalgebra automata correspond to formulae of (some) coalgebraic logic, in the sense that an automaton accepts a point in a coalgebra iff that point satisfies the corresponding formula. This correspondence has been exploited in the case of trees by Michael Rabin in his decidability result for monadic second-order logic for binary trees (S2S).

This page is under construction. Please notify me ( email(at)christiankissig.de ) of any developments I have been missing.

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Supplementary Material

On this page I collect the byproducts of my studies of the literature, such as indices to paper.

I plan to extend these notes as I go along in my work, please return for latest versions. Most of the material is published in processed form, PDF for instance, and under my copyright. If you wish to use any of these notes or extend them, please do get in touch with me through email(at)christiankissig.

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Talks

This is a list of my presentations in chronological order. Slides can be found here. Please send comments and questions to email(at)christiankissig.de .

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