scholarly journals Plausible Reasoning about EL-Ontologies using Concept Interpolation

2020 ◽  
Author(s):  
Yazmín Ibáñez-García ◽  
Víctor Gutiérrez-Basulto ◽  
Steven Schockaert
Keyword(s):  
Computational Complexity ◽  
Knowledge Representation ◽  
Deductive Reasoning ◽  
Inductive Inference ◽  
Description Logics ◽  
Data Driven ◽  
Commonsense Reasoning ◽  
Inference Mechanism ◽  
Complexity Bounds ◽  
Reasoning Mechanism

Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and time-consuming to encode manually. As a result, ontologies for broad domains are almost inevitably incomplete. In recent years, several data-driven approaches have been proposed for automatically extending such ontologies. One family of methods rely on characterizations of concepts that are derived from text descriptions. While such characterizations do not capture ontological knowledge directly, they encode information about the similarity between different concepts that can be exploited for filling in the gaps in existing ontologies. To this end, several inductive inference mechanisms have already been proposed, but these have been defined and used in a heuristic fashion. In this paper, we instead propose an inductive inference mechanism which is based on a clear model-theoretic semantics, and can thus be tightly integrated with standard deductive reasoning. We particularly focus on interpolation, a powerful commonsense reasoning mechanism which is closely related to cognitive models of category-based induction. Apart from the formalization of the underlying semantics, as our main technical contribution we provide computational complexity bounds for reasoning in EL with this interpolation mechanism.

scholarly journals Keys, Nominals, and Concrete Domains

2005 ◽  
Vol 23 ◽  
pp. 667-726 ◽  
Author(s):  
L. Carsten ◽  
C. Areces ◽  
I. Horrocks ◽  
U. Sattler
Keyword(s):  
Computational Complexity ◽  
Social Security ◽  
Knowledge Representation ◽  
Detailed Analysis ◽  
Description Logics ◽  
Social Security Number ◽  
Database Models ◽  
Natural Description ◽  
Concrete Domains

Many description logics (DLs) combine knowledge representation on an abstract, logical level with an interface to 'concrete' domains like numbers and strings with built-in predicates such as >, +, and prefix-of. These hybrid DLs have turned out to be useful in several application areas, such as reasoning about conceptual database models. We propose to further extend such DLs with key constraints that allow the expression of statements like 'US citizens are uniquely identified by their social security number'. Based on this idea, we introduce a number of natural description logics and perform a detailed analysis of their decidability and computational complexity. It turns out that naive extensions with key constraints easily lead to undecidability, whereas more careful extensions yield NExpTime-complete DLs for a variety of useful concrete domains.

scholarly journals DatalogMTL: Computational Complexity and Expressive Power

2019 ◽  
Author(s):  
Przemysław A. Wałęga ◽  
Bernardo Cuenca Grau ◽  
Mark Kaminski ◽  
Egor V. Kostylev
Keyword(s):  
Computational Complexity ◽  
Knowledge Representation ◽  
Data Access ◽  
Expressive Power ◽  
Data Complexity ◽  
Complexity Bounds ◽  
Metric Temporal Logic ◽  
Stream Reasoning ◽  
Knowledge Representation Language ◽  
Representation Language

We study the complexity and expressive power of DatalogMTL - a knowledge representation language that extends Datalog with operators from metric temporal logic (MTL) and which has found applications in ontology-based data access and stream reasoning. We establish tight PSpace data complexity bounds and also show that DatalogMTL extended with negation on input predicates can express all queries in PSpace; this implies that MTL operators add significant expressive power to Datalog. Furthermore, we provide tight combined complexity bounds for the forward-propagating fragment of DatalogMTL, which was proposed in the context of stream reasoning, and show that it is possible to express all PSpace queries in the fragment extended with the falsum predicate.

scholarly journals Knowledge Representation of Highly Dynamic Ontologies Using Defeasible Logic

2021 ◽  
Vol 10 (2) ◽  
pp. 948-954
Keyword(s):  
Computational Complexity ◽  
Knowledge Representation ◽  
Knowledge Base ◽  
Description Logic ◽  
Defeasible Logic ◽  
Small Domain ◽  
Automated Support ◽  
Logical Rules

Description logic gives us the ability of reasoning with acceptable computational complexity with retaining the power of expressiveness. The power of description logic can be accompanied by the defeasible logic to manage non-monotonic reasoning. In some domains, we need flexible reasoning and knowledge representation to deal the dynamicity of such domains. In this paper, we present a DL representation for a small domain that describes the connections between different entities in a university publication system to show how could we deal with changeability in domain rules. An automated support can be provided on the basis of defeasible logical rules to represent the typicality in the knowledge base and to solve the conflicts that might happen.

scholarly journals Unifying Class-Based Representation Formalisms

1999 ◽  
Vol 11 ◽  
pp. 199-240 ◽  
Author(s):  
D. Calvanese ◽  
M. Lenzerini ◽  
D. Nardi
Keyword(s):  
Knowledge Representation ◽  
Description Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Finite Model ◽  
Functional Dependencies ◽  
Semantic Data ◽  
Representation Systems ◽  
Frame Systems ◽  
Essential Set

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically well-founded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world domains. We are able to show that it is precisely such combination of constructs that makes our logic powerful enough to model the essential set of features for defining class structures that are common to frame systems, object-oriented database languages, and semantic data models. As a consequence of the established correspondences, several significant extensions of each of the above formalisms become available. The high expressiveness of the logic we propose and the need for capturing the reasoning in different contexts forces us to distinguish between unrestricted and finite model reasoning. A notable feature of our proposal is that reasoning in both cases is decidable. We argue that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, our logic provides a common core for class-based representation formalisms.

A Review of Fuzzy Models for the Semantic Web

2011 ◽  
pp. 63-77
Author(s):  
Hailong Wang ◽  
Zongmin Ma ◽  
Li Yan ◽  
Jingwei Cheng
Keyword(s):  
Computational Complexity ◽  
Semantic Web ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Description Logics ◽  
Expressive Power ◽  
Semantic Knowledge ◽  
Context Information ◽  
Semantic Knowledge Base

In the Semantic Web context, information would be retrieved, processed, shared, reused and aligned in the maximum automatic way possible. Our experience with such applications in the Semantic Web has shown that these are rarely a matter of true or false but rather procedures that require degrees of relatedness, similarity, or ranking. Apart from the wealth of applications that are inherently imprecise, information itself is many times imprecise or vague. In order to be able to represent and reason with such type of information in the Semantic Web, different general approaches for extending semantic web languages with the ability to represent imprecision and uncertainty has been explored. In this chapter, we focus our attention on fuzzy extension approaches which are based on fuzzy set theory. We review the existing proposals for extending the theoretical counterpart of the semantic web languages, description logics (DLs), and the languages themselves. The following statements will include the expressive power of the fuzzy DLs formalism and its syntax and semantic, knowledge base, the decidability of the tableaux algorithm and its computational complexity etc. Also the fuzzy extension to OWL is discussed in this chapter.

scholarly journals On the computational complexity of dynamic slicing problems for program schemas

2011 ◽  
Vol 21 (6) ◽  
pp. 1339-1362 ◽  
Author(s):  
SEBASTIAN DANICIC ◽  
ROBERT. M. HIERONS ◽  
MICHAEL R. LAURENCE
Keyword(s):  
Computational Complexity ◽  
Structural Properties ◽  
Program Slicing ◽  
Np Hard ◽  
Complexity Bounds ◽  
Dynamic Slicing ◽  
Original Program ◽  
Control Dependence ◽  
Definition Of ◽  
Restrictive Definition

Given a program, a quotient can be obtained from it by deleting zero or more statements. The field of program slicing is concerned with computing a quotient of a program that preserves part of the behaviour of the original program. All program slicing algorithms take account of the structural properties of a program, such as control dependence and data dependence, rather than the semantics of its functions and predicates, and thus work, in effect, with program schemas. The dynamic slicing criterion of Korel and Laski requires only that program behaviour is preserved in cases where the original program follows a particular path, and that the slice/quotient follows this path. In this paper we formalise Korel and Laski's definition of a dynamic slice as applied to linear schemas, and also formulate a less restrictive definition in which the path through the original program need not be preserved by the slice. The less restrictive definition has the benefit of leading to smaller slices. For both definitions, we compute complexity bounds for the problems of establishing whether a given slice of a linear schema is a dynamic slice and whether a linear schema has a non-trivial dynamic slice, and prove that the latter problem is NP-hard in both cases. We also give an example to prove that minimal dynamic slices (whether or not they preserve the original path) need not be unique.

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