Papers on Knowledge Representation, Logic, and Algorithmic Methods
J. Hoffmann, J. Koehler:
A new Method to Query and Index Sets,
IJCAI-99, pages 462-467, Technical Report 108
Abstract: Let us consider the following problem: Given a (probably huge) set
of sets S and a query set q, is there some set s in S such
that s is a subset of q? This problem occurs in at least four
application areas: the matching of a large number (usually several
100,000s) of production rules, the processing of queries in data
bases supporting set-valued attributes, the identification of
inconsistent subgoals during artificial intelligence planning and
the detection of potential periodic chains in labeled tableau
systems for modal logics.
In this paper, we introduce a data structure and
algorithm that allow a compact representation of such a huge set of
sets and an efficient answering of subset and superset
queries. The algorithm has been used successfully in the IPP
system and enabled this planner to win the ADL track of
the first planning competition.
H. J. Ohlbach, J. Koehler:
Modal Logics, Description Logics and Arithmetic Reasoning,
Journal of Artificial Intelligence, 1-2/1999, pages 1-31
Abstract:
We introduce mathematical programming and atomic decomposition as the
basic modal (T-Box) inference techniques for a large class of modal and
description logics. The class of description logics suitable for the proposed
methods is strong on the arithmetical side. In particular there may be
complex arithmetical conditions on sets of accessible worlds (role fillers).
The atomic decomposition technique can deal with set constructors for
modal parameters (role terms)
and parameter (role) hierarchies specified in full propositional
logic. Besides the standard modal operators,
a number of other constructors can be added in a relatively
straightforward way. Examples are graded modalities
(qualified number restrictions) and also
generalized quantifiers like `most', `n%', `more' and `many'.
H. J. Ohlbach, J. Koehler:
Role Hierarchies and Number Restrictions,
DL-97
Abstract:
We introduce a new technique that translates cardinality information
about finite sets into simple arithmetic terms and thereby enables a
system to reason about such set cardinalities by solving arithmetic
equation problems. The atomic decomposition technique separates a
collection of sets into mutually disjoint smallest components
(``atoms'') such that the cardinality of the sets are just the sum of
the cardinalities of their atoms. With this idea it is possible to
have languages combining arithmetic formulae with set terms, and to
translate the formulae of this combined logic into pure arithmetical
formulae. As a particular application we show how this technique
yields new inference procedures for concept languages with so called
number restriction operators.
Extended technical report.
J. Koehler:
An Application of Terminological Logics to
Case-based Reasoning.
KR-94, pages 351-362.
Abstract:
A key problem in case-based reasoning is the representation,
organization and maintenance of case libraries. While current
approaches rely on heuristic and psychologically inspired formalisms,
terminological logics have emerged as a powerful representation
formalism with clearly defined formal semantics. This paper
demonstrates how the indexing of case libraries can be grounded on
terminological logics by using them as a kind of query language to the
case library. Indices of cases are represented as concepts in a
terminological logic. They are automatically constructed from the
symbolic representation of cases with the help of a well-defined
abstraction process. The retrieval of cases from the library is
grounded on concept classification.
J. Koehler, R. Treinen :
Constraint Deduction in an Interval-based Temporal Logic.
Lecture Notes in Computer Science 897, pages 103-117, Springer 1995
Abstract:
We describe reasoning methods for the interval-based modal
temporal logic LLP which employs the modal operators sometimes,
always, next, and chop. We propose a constraint deduction
approach and compare it with a sequent calculus, developed as the basic
machinery for the deductive planning system PHI which uses LLP
as underlying formalism.
Jana Koehler, 10/15/2006