scholarly journals Bounded Predicates in Description Logics with Counting

2021 ◽  
Author(s):  
Sanja Lukumbuzya ◽  
Mantas Simkus
Keyword(s):  
Integer Programming ◽  
Description Logics ◽  
Upper Bounds ◽  
Safety Condition ◽  
Supporting Tool

Description Logics (DLs) support so-called anonymous objects, which significantly contribute to the expressiveness of these KR languages, but also cause substantial computational challenges. This paper investigates reasoning about upper bounds on predicate sizes for ontologies written in the expressive DL ALCHOIQ extended with closed predicates. We describe a procedure based on integer programming that allows us to decide the existence of upper bounds on the cardinality of some predicate in the models of a given ontology in a data-independent way. Our results yield a promising supporting tool for constructing higher quality ontologies, and provide a new way to push the decidability frontiers. To wit, we define a new safety condition for Datalog-based queries over DL ontologies, while retaining decidability of query entailment.

scholarly journals Conservative Extensions in Horn Description Logics with Inverse Roles

2020 ◽  
Vol 68 ◽  
pp. 365-411
Author(s):  
Jean Christoph Jung ◽  
Carsten Lutz ◽  
Mauricio Martel ◽  
Thomas Schneider
Keyword(s):  
Computational Complexity ◽  
Decision Procedure ◽  
Description Logics ◽  
Upper Bounds ◽  
Standard Approach ◽  
Tree Automata ◽  
Conjunctive Queries ◽  
Universal Models ◽  
Conservative Extensions

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.

An ExpTime Upper Bound for ALC with Integers

2020 ◽  
Author(s):  
Nadia Labai ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Upper Bound ◽  
Description Logics ◽  
Upper Bounds ◽  
Worst Case ◽  
Exponential Time ◽  
Functional Roles ◽  
Case Complexity ◽  
Worst Case Complexity ◽  
Concrete Domains ◽  
Single Exponential

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual DLs while keeping the complexity of reasoning in check. For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called ω-admissible domains, which are required to be dense. Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension. The decidability of some extensions of ALC with non-dense domains has been shown, but existing results rely on powerful machinery that does not allow to infer any elementary bounds on the complexity of the problem. In this paper, we study an extension of ALC with a rich integer domain that allows for comparisons (between features, and between features and constants coded in unary), and prove that consistency can be solved using automata-theoretic techniques in single exponential time, and thus has no higher worst-case complexity than standard ALC. Our upper bounds apply to some extensions of DLs with concrete domains known from the literature, support general TBoxes, and allow for comparing values along paths of ordinary (not necessarily functional) roles.

scholarly journals On Finite Entailment of Non-Local Queries in Description Logics

2020 ◽  
Author(s):  
Tomasz Gogacz ◽  
Víctor Gutiérrez-Basulto ◽  
Albert Gutowski ◽  
Yazmín Ibáñez-García ◽  
Filip Murlak
Keyword(s):  
Lower Bound ◽  
Transitive Closure ◽  
Description Logics ◽  
Upper Bounds ◽  
Conjunctive Queries ◽  
Non Local

We study the problem of finite entailment of ontology-mediated queries. Going beyond local queries, we allow transitive closure over roles. We focus on ontologies formulated in the description logics ALCOI and ALCOQ, extended with transitive closure. For both logics, we show 2EXPTIME upper bounds for finite entailment of unions of conjunctive queries with transitive closure. We also provide a matching lower bound by showing that finite entailment of conjunctive queries with transitive closure in ALC is 2EXPTIME-hard

Penjadwalan Mesin dengan Metode Integer Linear Programming pada PT. XYZ

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Fransiskus Lauson Matondang ◽  
Rosnani Ginting
Keyword(s):  
Integer Programming ◽  
Time Delays ◽  
Parallel Machines ◽  
Research Concept ◽  
Total Settlement ◽  
Approach Method ◽  
Additional Costs ◽  
Maximum Completion Time ◽  
Completion Times ◽  
Better Than

PT XYZ sering mengalami keterlambatan waktu karena dalam setiap keterlambatan yang dilakukan selalu ada penalty yang diberikan kepada perusahaan dan hal ini mengakibatkan tambahan biaya , oleh karena itu hal ini harus dihindari dengan membuat penjadwalan yang efisien, dalam hal ini dilakukanlah perbaikan dengan meminimisasi waktu penyelesaian maksimum Cmax pada mesin paralel yang berpola aliran flowshop (dan tidak boleh dilakukan interupsi yang dilakukan pada pekerjaan yang sedang diproses, untuk melakukan pekerjaan lainnya, satu lintasan hanya memproduksi satu produk dan hanya satu produk juga yang dikerjakan secara langsung. Waktu penyelesaian yang berbeda dari setiap mesin dengan pengerjaannya juga adalah masalah yang dihadapi untuk menjadikan mesin mesin ini sesuai menjadi satu penjadwalan yang terintegrasi dengan metode integer programming yang membuat penjadwalan dengan konsep riset operasi dengan metode pendekatan 0-1 utuk menjadi lebih efisien lagi , dihasilkan minimisasi keterlambatan total penyelesaian order dengan 42,28 menit lebih baik dari sebelumnya.   PT XYZ often experiences time delays because in every delay made there is always a penalty given to the company and this results in additional costs, therefore this must be avoided by making efficient scheduling, in this case repairs are carried out by minimizing the maximum completion time of Cmax on parallel machines that are patterned with flowshop flow (and no interruptions should be carried out on the work being processed, to do other work, one track only produces one product and only one product is directly worked. Different completion times of each machine with the workmanship is also the problem faced to make this machine suitable to be one scheduling integrated with integer programming methods that makes scheduling with the operational research concept with the 0-1 approach method to be more efficient, resulting in minimization of the delay in the total settlement of orders with 42.28 minutes was better than before.

“EcoTOP” the Supporting Tool for Eco-Energy System Planning

2010 ◽  
Vol 130 (5) ◽  
pp. 536-537
Author(s):  
Shinichiro Oke ◽  
Shin Higashiyama ◽  
Hiroyuki Murata ◽  
Hirofumi Takikawa
Keyword(s):  
Energy System ◽  
System Planning ◽  
Supporting Tool ◽  
Energy System Planning
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