=Paper=
{{Paper
|id=Vol-1624/inv1
|storemode=property
|title=None
|pdfUrl=https://ceur-ws.org/Vol-1624/inv1.pdf
|volume=Vol-1624
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==None==
<pdf width="1500px">https://ceur-ws.org/Vol-1624/inv1.pdf</pdf>
<pre>
Strictly Positive Fragments of Modal and
            Description Logic

                          Lev D. Beklemishev

Mathematical Institute of Russian Academy of Science, Moscow, Russia



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 built-up from T (truth) and the variables using
just conjunction and the diamond modalities. The interest towards such
fragments independently emerged around 2010 in two different areas: in
description logic and in the area of proof-theoretic 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 proof-theoretic 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 proof-theoretic 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.

Keywords: Modal Logic, Description Logic

</pre>