

Colloquium of the Faculty of Computer Science
September 20, 2016 18:10–19:30, Moscow






Strictly positive fragments of modal and description logic
L. D. Beklemishev^{ab} ^{a} National Research University "Higher School of Economics" (HSE), Moscow
^{b} Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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Abstract:
In this talk we will advocate the use of weak systems of modal logic called strictly positive. These
can be seen as fragments of polymodal logic consisting of implications of the form A → B, where A and B are formulas builtup from T (truth) and the variables using just & and the diamond modalities. The interest towards such fragments emerged around 2010 independently in two different areas: in description logic and in the area of prooftheoretic applications of modal logic.
From the point of view of description logic, strictly positive fragments correspond to the OWL 2 EL profile of the OWL web ontology language, for which various properties of ontologies can be decided in polynomial time. In the area of prooftheortic applications, these fragments emerged under the name reflection calculi, as they proved to be a convenient tool to study the independent reflection principles in arithmetic and to calculate prooftheoretic ordinals of formal systems.
Thus, in two different areas strictly positive languages and logics proved to combine both efficiency and simplicity, and sufficient expressive power. In this talk we discuss general problems around weak systems of this kind and describe some of their applications.

