We investigate the computational complexity of axiom pinpointing, which is the task of finding minimal subsets of a Description Logic knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results...

The Pasch axiom is a strong geometric property which was noted and discussed even from the period of Euclid. Modern geometers followed the study of the Pasch axiom and in the context of axiomatic convexity this axiom was widely studied by pioneers in convexity theory. The connected graphs G for which the geodesic interval function I satisfies the Pasch axiom were characterized by Chepoi in 1994...

We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category. Moreover, the functors belonging to the stable derivator can be turned into exact functors with respect to these triangulated structures. Along the way, we give a ...

The concept of valuated matroids was introduced by Dress and Wenzel as a quantitative extension of the base exchange axiom for matroids. This paper gives several sets of cryptomorphically equivalent axioms of valuated matroids in terms of (R[f 1g)-valued vectors de ned on the circuits of the underlying matroid, where R is a totally ordered additive group. The dual of a valuated matroid is chara...

Starting from a generalization of the standard axioms for a monoid we present a stepwise development of various, mutually equivalent foundational axiom systems for category theory. Our axiom sets have been formalized in the Isabelle/HOL interactive proof assistant, and this formalization utilizes a semantically correct embedding of free logic in classical higher-order logic. The modeling and fo...

Both the Continuum Hypothesis and Martin's Axiom allow induc-tive constructions to continue in circumstances where the inductive hypothesis might otherwise fail. The search for useful related axioms procedes naturally in two directions: towards "Super Martin's Axioms ," which extend MA to broader classes of orders; and towards "Anti-Martin's Axioms" (AMA's) which are strictly weaker than CH, bu...

This research used MiChat and SayHi as materials for forensic investigations using three different tools, namely MOBILedit, Magnet Axiom, Belkasoft. These tools will show each performance in the process. We also added a rooting process an option if data cannot be extracted optimally even when these applications. The result of this study shows that cases studied with processes without root acces...

Although an increasing number of RDF knowledge bases are published, many of those consist primarily of instance data and lack sophisticated schemata. Having such schemata allows more powerful querying, consistency checking and debugging as well as improved inference. One of the reasons why schemata are still rare is the effort required to create them. In this article, we propose a semi-automati...

This study was designed to examine the biomechanical and physiological responses between cycling on the Axiom stationary ergometer (Axiom, Elite, Fontaniva, Italy) vs. field conditions for both uphill and level ground cycling. Nine cyclists performed cycling bouts in the laboratory on an Axiom stationary ergometer and on their personal road bikes in actual road cycling conditions in the field w...

Only-knowing was originally introduced by Levesque to capture the beliefs of an agent in the sense that its knowledge base is all the agent knows. When a knowledge base contains defaults Levesque also showed an exact correspondence between only-knowing and autoepistemic logic. Later these results were extended by Lakemeyer and Levesque to also capture a variant of autoepistemic logic proposed b...