Grounded Circumscription in Description Logics

Master's thesis by Efstathios Delivorias

Supervisor Sebastian Rudolph
Computational Logic
15 Oktober 2014 – 9 April 2015
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Circumscription is a paradigm of non-monotonic logic meant to formalize the common sense understanding that among competing theories that represent phenomena equally well, the one with the fewest assumptions should be selected. Description Logics are knowledge representation formalisms designed to describe and reason about qualitative properties and aspects of a system. In this essay we aim to fuse Description Logics, which traditionally are monotonic, with a restricted version of Circumscription, called Grounded Circumscription. The work is based on a 2011 publication by K. Sengupta, A.A. Krisnadhi and P. Hitzler, which throughout this study we will refer to as "the original paper". The paper introduces the main idea of grounded circumscription along with algorithms for certain decision problems. We have optimized and modified these ideas. The optimization was our initial aim, in particular we wanted (and largely achieved) to transfer a big part of the reasoning to standard Description Logics, for which tools and results already exist. But in the process we uncovered some insufficiencies in the original paper, hence we have modified the main definition to one that is more effective and seems more intuitive.