20 research outputs found
A Goal-Directed Implementation of Query Answering for Hybrid MKNF Knowledge Bases
Ontologies and rules are usually loosely coupled in knowledge representation
formalisms. In fact, ontologies use open-world reasoning while the leading
semantics for rules use non-monotonic, closed-world reasoning. One exception is
the tightly-coupled framework of Minimal Knowledge and Negation as Failure
(MKNF), which allows statements about individuals to be jointly derived via
entailment from an ontology and inferences from rules. Nonetheless, the
practical usefulness of MKNF has not always been clear, although recent work
has formalized a general resolution-based method for querying MKNF when rules
are taken to have the well-founded semantics, and the ontology is modeled by a
general oracle. That work leaves open what algorithms should be used to relate
the entailments of the ontology and the inferences of rules. In this paper we
provide such algorithms, and describe the implementation of a query-driven
system, CDF-Rules, for hybrid knowledge bases combining both (non-monotonic)
rules under the well-founded semantics and a (monotonic) ontology, represented
by a CDF Type-1 (ALQ) theory. To appear in Theory and Practice of Logic
Programming (TPLP
Complexity Results and Practical Algorithms for Logics in Knowledge Representation
Description Logics (DLs) are used in knowledge-based systems to represent and
reason about terminological knowledge of the application domain in a
semantically well-defined manner. In this thesis, we establish a number of
novel complexity results and give practical algorithms for expressive DLs that
provide different forms of counting quantifiers.
We show that, in many cases, adding local counting in the form of qualifying
number restrictions to DLs does not increase the complexity of the inference
problems, even if binary coding of numbers in the input is assumed. On the
other hand, we show that adding different forms of global counting restrictions
to a logic may increase the complexity of the inference problems dramatically.
We provide exact complexity results and a practical, tableau based algorithm
for the DL SHIQ, which forms the basis of the highly optimized DL system iFaCT.
Finally, we describe a tableau algorithm for the clique guarded fragment
(CGF), which we hope will serve as the basis for an efficient implementation of
a CGF reasoner.Comment: Ph.D. Thesi
Reasoning Algebraically with Description Logics
Semantic Web applications based on the Web Ontology Language (OWL) often
require the use of numbers in class descriptions for expressing
cardinality restrictions on properties or even classes. Some of these
cardinalities are specified explicitly, but quite a few are entailed and
need to be discovered by reasoning procedures. Due to the Description
Logic (DL) foundation of OWL, those reasoning services are offered by DL
reasoners. Existing DL reasoners employ reasoning procedures that are
arithmetically uninformed and substitute arithmetic reasoning by "don't
know" non-determinism in order to cover all possible cases. This lack of
information about arithmetic problems dramatically degrades the
performance of DL reasoners in many cases, especially with ontologies
relying on the use of Nominals and Qualied Cardinality Restrictions.
The contribution of this thesis is twofold: on the theoretical level, it
presents algebra�ic reasoning with DL (ReAl DL) using a sound, complete,
and terminating reasoning procedure for the DL SHOQ. ReAl DL combines
tableau reasoning procedures with algebraic methods, namely Integer
Programming, to ensure arithmetically better informed reasoning. SHOQ
extends the standard DL ALC with transitive roles, role hierarchies,
qualified cardinality restrictions (QCRs), and nominals, and forms an
expressive subset of OWL. Although the proposed algebraic tableau is
double exponential in the worst case, it deals with cardinalities with
an additional level of information and properties that make the calculus
amenable and well suited for optimizations. In order for ReAl DL to have
a practical merit, suited optimizations are proposed towards achieving
an efficient reasoning approach that addresses the sources of complexity
related to nominals and QCRs. On the practical level, a running
prototype reasoner (HARD) is implemented based on the proposed calculus
and optimizations. HARD is used to evaluate the practical merit of ReAl
DL, as well as the effectiveness of the proposed optimizations.
Experimental results based on real world and synthetic ontologies show
that ReAl DL outperforms existing reasoning approaches in handling the
interactions between nominals and QCRs. ReAl DL also comes with some
interesting features such as the ability to handle ontologies with
cyclic descriptions without adopting special blocking strategies. ReAl
DL can form a basis to provide more efficient reasoning support for
ontologies using nominals or QCRs
Derivation methods for hybrid knowledge bases with rules and ontologies
Trabalho apresentado no âmbito do Mestrado em Engenharia Informática, como requisito parcial para obtenção do grau de Mestre em Engenharia InformáticaFirst of all, I would like to thank my advisor, José Júlio Alferes, for his incredible support. Right from the start, during the first semester of this work, when we were 2700 km apart and meeting regularly via Skype, until the end of this dissertation, he was always committed and available for discussions, even when he had lots of other urgent things to do.
A really special thanks to Terrance Swift, whom acted as an advisor, helping me a lot in
the second implementation, and correcting all XSB’s and CDF’s bugs. This implementation
wouldn’t surely have reached such a fruitful end without his support.
I would also like to thank all my colleagues and friends at FCT for the great work environment and for not letting me take myself too serious. A special thanks to my colleagues from Dresden for encouraging me to work even when there were so many other interesting things to do as an Erasmus student.
I’m indebted to LuĂs Leal, Bárbara Soares, Jorge Soares and CecĂlia Calado, who kindly
accepted to read a preliminary version of this report and gave me their valuable comments.
For giving me working conditions and a partial financial support, I acknowledge the Departamento de Informática of the Faculdade de Ciências e Tecnologias of Universidade Nova de Lisboa.
Last, but definitely not least, I would like to thank my parents and all my family for their continuous encouragement and motivation. A special thanks to Bruno for his love, support and patience
A Customized ILP-Based Solver for Description Logic Reasoners
Artificial intelligence based systems are known for conveying knowledge through machines. This knowledge is often represented using logic representation languages. One of the well-known families of such languages is called Description Logic (DL) which formally reasons and represents knowledge on the concepts, roles and individuals of an application domain. DL reasoners have been evolving and upgraded through the years, however when it comes to handling more complicated ontologies with big values occurring in number restrictions, the current reasoners mostly fail to perform efficiently. One of the techniques used in DL reasoners is the so-called atomic decomposition technique which combines arithmetic and logical reasoning. This thesis presents a customized CPLEX-based solver for enhancing DL reasoners through optimizing the atomic decomposition technique. Furthermore, we provide evidence on how this method can improve the reasoning performance by optimizing atomic decomposition. For such purpose, an empirical evaluation of our system for a set of synthesized benchmarks is demonstrated
Modal Logics with Counting
International audienceWe present a modal language that includes explicit operators to count the number of elements that a model might include in the extension of a formula, and we discuss how this logic has been previously investigated under different guises. We show that the language is related to graded modalities and to hybrid logics. We illustrate a possible application of the language to the treatment of plural objects and queries in natural language. We investigate the expressive power of this logic via bisimulations, discuss the complexity of its satisfiability problem, define a new reasoning task that retrieves the cardinality bound of the extension of a given input formula, and provide an algorithm to solve it
Action, Time and Space in Description Logics
Description Logics (DLs) are a family of logic-based knowledge representation (KR) formalisms designed to represent and reason about static conceptual knowledge in a semantically well-understood way. On the other hand, standard action formalisms are KR formalisms based on classical logic designed to model and reason about dynamic systems. The largest part of the present work is dedicated to integrating DLs with action formalisms, with the main goal of obtaining decidable action formalisms with an expressiveness significantly beyond propositional. To this end, we offer DL-tailored solutions to the frame and ramification problem. One of the main technical results is that standard reasoning problems about actions (executability and projection), as well as the plan existence problem are decidable if one restricts the logic for describing action pre- and post-conditions and the state of the world to decidable Description Logics. A smaller part of the work is related to decidable extensions of Description Logics with concrete datatypes, most importantly with those allowing to refer to the notions of space and time
Adding Causal Relationships to DL-based Action Formalisms
In the reasoning about actions community, causal relationships have been proposed as a possible approach for solving the ramification problem, i. e., the problem of how to deal with indirect effects of actions. In this paper, we show that causal relationships can be added to action formalisms based on Description Logics without destroying the decidability of the consistency and the projection problem
Hypertableau Reasoning for Description Logics
We present a novel reasoning calculus for the description logic SHOIQ^+---a
knowledge representation formalism with applications in areas such as the
Semantic Web. Unnecessary nondeterminism and the construction of large models
are two primary sources of inefficiency in the tableau-based reasoning calculi
used in state-of-the-art reasoners. In order to reduce nondeterminism, we base
our calculus on hypertableau and hyperresolution calculi, which we extend with
a blocking condition to ensure termination. In order to reduce the size of the
constructed models, we introduce anywhere pairwise blocking. We also present an
improved nominal introduction rule that ensures termination in the presence of
nominals, inverse roles, and number restrictions---a combination of DL
constructs that has proven notoriously difficult to handle. Our implementation
shows significant performance improvements over state-of-the-art reasoners on
several well-known ontologies