16,301 research outputs found
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
Modal logics are coalgebraic
Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility
Modelling Learning as Modelling
Economists tend to represent learning as a procedure for estimating the parameters of the "correct" econometric model. We extend this approach by assuming that agents specify as well as estimate models. Learning thus takes the form of a dynamic process of developing models using an internal language of representation where expectations are formed by forecasting with the best current model. This introduces a distinction between the form and content of the internal models which is particularly relevant for boundedly rational agents. We propose a framework for such model development which use a combination of measures: the error with respect to past data, the complexity of the model, the cost of finding the model and a measure of the model's specificity The agent has to make various trade-offs between them. A utility learning agent is given as an example
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
Combining Spatial and Temporal Logics: Expressiveness vs. Complexity
In this paper, we construct and investigate a hierarchy of spatio-temporal
formalisms that result from various combinations of propositional spatial and
temporal logics such as the propositional temporal logic PTL, the spatial
logics RCC-8, BRCC-8, S4u and their fragments. The obtained results give a
clear picture of the trade-off between expressiveness and computational
realisability within the hierarchy. We demonstrate how different combining
principles as well as spatial and temporal primitives can produce NP-, PSPACE-,
EXPSPACE-, 2EXPSPACE-complete, and even undecidable spatio-temporal logics out
of components that are at most NP- or PSPACE-complete
Challenges for Efficient Query Evaluation on Structured Probabilistic Data
Query answering over probabilistic data is an important task but is generally
intractable. However, a new approach for this problem has recently been
proposed, based on structural decompositions of input databases, following,
e.g., tree decompositions. This paper presents a vision for a database
management system for probabilistic data built following this structural
approach. We review our existing and ongoing work on this topic and highlight
many theoretical and practical challenges that remain to be addressed.Comment: 9 pages, 1 figure, 23 references. Accepted for publication at SUM
201
PSPACE Reasoning for Graded Modal Logics
We present a PSPACE algorithm that decides satisfiability of the graded modal
logic Gr(K_R)---a natural extension of propositional modal logic K_R by
counting expressions---which plays an important role in the area of knowledge
representation. The algorithm employs a tableaux approach and is the first
known algorithm which meets the lower bound for the complexity of the problem.
Thus, we exactly fix the complexity of the problem and refute an
ExpTime-hardness conjecture. We extend the results to the logic Gr(K_(R \cap
I)), which augments Gr(K_R) with inverse relations and intersection of
accessibility relations. This establishes a kind of ``theoretical benchmark''
that all algorithmic approaches can be measured against
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