36,561 research outputs found
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
Abstract Canonical Inference
An abstract framework of canonical inference is used to explore how different
proof orderings induce different variants of saturation and completeness.
Notions like completion, paramodulation, saturation, redundancy elimination,
and rewrite-system reduction are connected to proof orderings. Fairness of
deductive mechanisms is defined in terms of proof orderings, distinguishing
between (ordinary) "fairness," which yields completeness, and "uniform
fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi
Formalization of the fundamental group in untyped set theory using auto2
We present a new framework for formalizing mathematics in untyped set theory
using auto2. Using this framework, we formalize in Isabelle/FOL the entire
chain of development from the axioms of set theory to the definition of the
fundamental group for an arbitrary topological space. The auto2 prover is used
as the sole automation tool, and enables succinct proof scripts throughout the
project.Comment: 17 pages, accepted for ITP 201
Intermediates, Catalysts, Persistence, and Boundary Steady States
For dynamical systems arising from chemical reaction networks, persistence is
the property that each species concentration remains positively bounded away
from zero, as long as species concentrations were all positive in the
beginning. We describe two graphical procedures for simplifying reaction
networks without breaking known necessary or sufficient conditions for
persistence, by iteratively removing so-called intermediates and catalysts from
the network. The procedures are easy to apply and, in many cases, lead to
highly simplified network structures, such as monomolecular networks. For
specific classes of reaction networks, we show that these conditions for
persistence are equivalent to one another. Furthermore, they can also be
characterized by easily checkable strong connectivity properties of a related
graph. In particular, this is the case for (conservative) monomolecular
networks, as well as cascades of a large class of post-translational
modification systems (of which the MAPK cascade and the -site futile cycle
are prominent examples). Since one of the aforementioned sufficient conditions
for persistence precludes the existence of boundary steady states, our method
also provides a graphical tool to check for that.Comment: The main result was made more general through a slightly different
approach. Accepted for publication in the Journal of Mathematical Biolog
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