scholarly journals The Complexity of Reasoning with Cardinality Restrictions and Nominals in Expressive Description Logics

2000 ◽  
Vol 12 ◽  
pp. 199-217 ◽  
Author(s):  
S. Tobies
Keyword(s):  
Predicate Logic ◽  
Description Logics ◽  
Optimal Solution ◽  
Complete Problem ◽  
Pure Concept

We study the complexity of the combination of the Description Logics ALCQ and ALCQI with a terminological formalism based on cardinality restrictions on concepts. These combinations can naturally be embedded into C^2, the two variable fragment of predicate logic with counting quantifiers, which yields decidability in NExpTime. We show that this approach leads to an optimal solution for ALCQI, as ALCQI with cardinality restrictions has the same complexity as C^2 (NExpTime-complete). In contrast, we show that for ALCQ, the problem can be solved in ExpTime. This result is obtained by a reduction of reasoning with cardinality restrictions to reasoning with the (in general weaker) terminological formalism of general axioms for ALCQ extended with nominals. Using the same reduction, we show that, for the extension of ALCQI with nominals, reasoning with general axioms is a NExpTime-complete problem. Finally, we sharpen this result and show that pure concept satisfiability for ALCQI with nominals is NExpTime-complete. Without nominals, this problem is known to be PSpace-complete.

A Framework for Managing Consistency of Evolving UML Models

2011 ◽  
pp. 1-30 ◽  
Author(s):  
Tom Mens ◽  
Ragnhild Van Der Straeten ◽  
Jocelyn Simmonds
Keyword(s):  
Impact Analysis ◽  
Software Evolution ◽  
Predicate Logic ◽  
Description Logics ◽  
Unified Modeling Language ◽  
Tool Support ◽  
Unified Modeling ◽  
Inconsistency Management ◽  
Decidable Fragment ◽  
Uml Metamodel

As the standard for object-oriented analysis and design, the UML (Unified Modeling Language) metamodel, as well as contemporary CASE (Computer-Aided Software Engineering) tools, must provide adequate and integrated support for all essential aspects of software evolution. This includes version control, traceability, impact analysis, change propagation, inconsistency management, and model refactorings. This chapter focuses on the latter two aspects, and shows how tool support for these aspects can be provided. First, we extend the UML metamodel with support for versioning. Second, we make a classification of the possible inconsistencies of UML design models. Finally, we use the formalism of description logics, a decidable fragment of first-order predicate logic, to express logic rules that can detect and resolve these inconsistencies. We also show how the logic rules are used to propose model refactorings. As a proof of concept, we report on the results of initial experiments with a prototype tool we developed for this approach.

scholarly journals Applying Neural Networks to Find the Minimum Cost Coverage of a Boolean Function

VLSI Design ◽  
1995 ◽  
Vol 3 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Pong P. Chu
Keyword(s):  
Neural Network ◽  
Boolean Function ◽  
Input Data ◽  
Selection Process ◽  
Optimal Solution ◽  
Minimum Cost ◽  
Hopfield Network ◽  
Neural Network Approach ◽  
Complete Problem ◽  
Np Complete

To find a minimal expression of a boolean function includes a step to select the minimum cost cover from a set of implicants. Since the selection process is an NP-complete problem, to find an optimal solution is impractical for large input data size. Neural network approach is used to solve this problem. We first formalize the problem, and then define an “energy function” and map it to a modified Hopfield network, which will automatically search for the minima. Simulation of simple examples shows the proposed neural network can obtain good solutions most of the time.

Review on Multiobjective Task Scheduling in Cloud Computing using Nature Inspired Algorithms

2018 ◽  
Vol 6 (8) ◽  
pp. 282
Author(s):  
Shikha Chaudhary ◽  
Saroj Hiranwal ◽  
C. P. Gupta
Keyword(s):  
Cloud Computing ◽  
Optimal Solution ◽  
Computing System ◽  
Ant Colony Optimization Algorithm ◽  
New Class ◽  
Complete Problem ◽  
Nature Inspired Algorithm ◽  
Cloud Computing System ◽  
Np Complete ◽  
Nature Inspired Algorithms

In cloud computing huge pool of resources are available and shared through internet. The scheduling is a core technique which determines the performance of a cloud computing system. The goal of scheduling is to allocate task to appropriate machine to achieve one or more QOS. To find the suitable resource among pool of resources to achieve the goal is an NP Complete problem. A new class of algorithm called nature inspired algorithm came into existence to find optimal solution.  In this paper we provide a survey as well as a comparative analysis of various existing nature inspired scheduling algorithms which are based on genetic algorithm and ant colony optimization algorithm. 

scholarly journals A Multiobjective Particle Swarm Optimization Algorithm Based on Multipopulation Coevolution for Weapon-Target Assignment

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Guangyuan Fu ◽  
Chao Wang ◽  
Daqiao Zhang ◽  
Jiufen Zhao ◽  
Hongqiao Wang
Keyword(s):  
Particle Swarm Optimization ◽  
Particle Swarm Optimization Algorithm ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Swarm Optimization ◽  
Complete Problem ◽  
Multiobjective Particle Swarm Optimization ◽  
Optimal Solution Set ◽  
Target Assignment ◽  
Slave Population

Weapon-target assignment (WTA) is critical to command and decision making in modern battlefields and is a typical nondeterministic polynomial complete problem. To solve WTA problems with multiple optimization objectives, a multipopulation coevolution-based multiobjective particle swarm optimization (MOPSO) algorithm is proposed to realize the rapid search for the globally optimal solution. The algorithm constructs a master-slave population coevolution model. Each slave population corresponds to an objective function and is used to search for noninferior solutions. The master population receives all the noninferior solutions from the slave populations, repairs the gaps between the noninferior solutions, and generates a relatively optimal Pareto optimal solution set. In addition, to accelerate the slave populations searching for noninferior solutions and master population repairing the gaps between noninferior solutions, the particle velocity update method is improved. The simulation results show that the proposed algorithm has higher computational efficiency and achieves better solutions than existing algorithms capable of providing a good solution. The method is suitable for rapidly solving multiobjective WTA (MOWTA) problems.

scholarly journals Hierarchical Expertise Level Modeling for User Specific Contrastive Explanations

2018 ◽  
Author(s):  
Sarath Sreedharan ◽  
Siddharth Srivastava ◽  
Subbarao Kambhampati
Keyword(s):  
Greedy Algorithm ◽  
Autonomous Systems ◽  
Optimal Solution ◽  
Research Community ◽  
Domain Model ◽  
Human Model ◽  
Research Attention ◽  
Complete Problem ◽  
Expertise Level ◽  
Different Levels

There is a growing interest within the AI research community in developing autonomous systems capable of explaining their behavior to users. However, the problem of computing explanations for users of different levels of expertise has received little research attention. We propose an approach for addressing this problem by representing the user's understanding of the task as an abstraction of the domain model that the planner uses. We present algorithms for generating minimal explanations in cases where this abstract human model is not known. We reduce the problem of generating an explanation to a search over the space of abstract models and show that while the complete problem is NP-hard, a greedy algorithm can provide good approximations of the optimal solution. We also empirically show that our approach can efficiently compute explanations for a variety of problems.

scholarly journals A Game Theoretical Approach for Solving Winner Determination Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Chen-Kun Tsung ◽  
Hann-Jang Ho ◽  
Sing-Ling Lee
Keyword(s):  
Evolutionary Game ◽  
Optimal Solution ◽  
Computation Time ◽  
Winner Determination ◽  
Complete Problem ◽  
The Game Theory ◽  
Game Theoretical Approach ◽  
Np Complete ◽  
The Stability ◽  
Self Learning

Determining the winners in combinatorial auctions to maximize the auctioneer's revenue is an NP-complete problem. Computing an optimal solution requires huge computation time in some instances. In this paper, we apply three concepts of the game theory to design an approximation algorithm: the stability of the Nash equilibrium, the self-learning of the evolutionary game, and the mistake making of the trembling hand assumption. According to our simulation results, the proposed algorithm produces near-optimal solutions in terms of the auctioneer's revenue. Moreover, reasonable computation time is another advantage of applying the proposed algorithm to the real-world services.

scholarly journals Configuration knowledge representations for Semantic Web applications

2003 ◽  
Vol 17 (1) ◽  
pp. 31-50 ◽  
Author(s):  
ALEXANDER FELFERNIG ◽  
GERHARD FRIEDRICH ◽  
DIETMAR JANNACH ◽  
MARKUS STUMPTNER ◽  
MARKUS ZANKER
Keyword(s):  
Problem Solving ◽  
Semantic Web ◽  
Knowledge Representation ◽  
Web Applications ◽  
Description Logic ◽  
Predicate Logic ◽  
Description Logics ◽  
Formal Semantics ◽  
Problem Definition ◽  
Configuration Problem

Today's economy exhibits a growing trend toward highly specialized solution providers cooperatively offering configurable products and services to their customers. This paradigm shift requires the extension of current standalone configuration technology with capabilities of knowledge sharing and distributed problem solving. In this context a standardized configuration knowledge representation language with formal semantics is needed in order to support knowledge interchange between different configuration environments. Languages such as Ontology Inference Layer (OIL) and DARPA Agent Markup Language (DAML+OIL) are based on such formal semantics (description logic) and are very popular for knowledge representation in the Semantic Web. In this paper we analyze the applicability of those languages with respect to configuration knowledge representation and discuss additional demands on expressivity. For joint configuration problem solving it is necessary to agree on a common problem definition. Therefore, we give a description logic based definition of a configuration problem and show its equivalence with existing consistency-based definitions, thus joining the two major streams in knowledge-based configuration (description logics and predicate logic/constraint based configuration).

scholarly journals Description Logics That Count, and What They Can and Cannot Count

10.29007/ltzn ◽  
2020 ◽  
Author(s):  
Franz Baader ◽  
Filippo De Bortoli
Keyword(s):  
Boolean Algebra ◽  
Natural Number ◽  
Predicate Logic ◽  
Description Logics ◽  
Expressive Power ◽  
Cardinality Constraints ◽  
Presburger Arithmetic ◽  
First Order ◽  
First Order Predicate Logic

Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restriction on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning.In the present paper, we investigate the expressive power of the DLs obtained this way, using appropriate bisimulation characterizations and 0--1 laws as tools for distinguishing the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these logics are no longer expressible in first-order predicate logic (FOL), and we characterize their first-order fragments. In most of our previous work on DLs with QFBAPA-based set and cardinality constraints we have employed finiteness restrictions on interpretations to ensure that the obtained sets are finite. Here we dispense with these restrictions to make the comparison with classical DLs, where one usually considers arbitrary models rather than finite ones, easier. It turns out that doing so does not change the complexity of reasoning.

Identifying Measurement Invariant Item Sets in Cross-Cultural Settings Using an Automated Item Selection Procedure

Methodology ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 177-188 ◽  
Author(s):  
Martin Schultze ◽  
Michael Eid
Keyword(s):  
Measurement Invariance ◽  
Optimal Solution ◽  
Selection Procedure ◽  
Cross Cultural ◽  
Item Selection ◽  
Ant System ◽  
Item Quality ◽  
Ant System Algorithm ◽  
Selection For ◽  
Selection Of

Abstract. In the construction of scales intended for the use in cross-cultural studies, the selection of items needs to be guided not only by traditional criteria of item quality, but has to take information about the measurement invariance of the scale into account. We present an approach to automated item selection which depicts the process as a combinatorial optimization problem and aims at finding a scale which fulfils predefined target criteria – such as measurement invariance across cultures. The search for an optimal solution is performed using an adaptation of the [Formula: see text] Ant System algorithm. The approach is illustrated using an application to item selection for a personality scale assuming measurement invariance across multiple countries.

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