scholarly journals Towards closed world reasoning in dynamic open worlds

2010 ◽  
Vol 10 (4-6) ◽  
pp. 547-563 ◽  
Author(s):  
MARTIN SLOTA ◽  
JOÃO LEITE
Keyword(s):  
Semantic Web ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Static Case ◽  
First Order ◽  
Closed World ◽  
Hybrid Knowledge ◽  
First Time

AbstractThe need for integration of ontologies with nonmonotonic rules has been gaining importance in a number of areas, such as the Semantic Web. A number of researchers addressed this problem by proposing a unified semantics forhybrid knowledge basescomposed of both an ontology (expressed in a fragment of first-order logic) and nonmonotonic rules. These semantics have matured over the years, but only provide solutions for the static case when knowledge does not need to evolve.In this paper we take a first step towards addressing the dynamics of hybrid knowledge bases. We focus on knowledge updates and, considering the state of the art of belief update, ontology update and rule update, we show that current solutions are only partial and difficult to combine. Then we extend the existing work on ABox updates with rules, provide a semantics for such evolving hybrid knowledge bases and study its basic properties.To the best of our knowledge, this is the first time that an update operator is proposed for hybrid knowledge bases.

Principles and practice in verifying rule-based systems

1992 ◽  
Vol 7 (2) ◽  
pp. 115-141 ◽  
Author(s):  
Alun D. Preece ◽  
Rajjan Shinghal ◽  
Aïda Batarekh
Keyword(s):  
Expert System ◽  
Knowledge Base ◽  
State Of The Art ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Rule Based ◽  
First Order ◽  
Rule Bases ◽  
System Knowledge

AbstractThis paper surveys the verification of expert system knowledge bases by detecting anomalies. Such anomalies are highly indicative of errors in the knowledge base. The paper is in two parts. The first part describes four types of anomaly: redundancy, ambivalence, circularity, and deficiency. We consider rule bases which are based on first-order logic, and explain the anomalies in terms of the syntax and semantics of logic. The second part presents a review of five programs which have been built to detect various subsets of the anomalies. The four anomalies provide a framework for comparing the capabilities of the five tools, and we highlight the strengths and weaknesses of each approach. This paper therefore provides not only a set of underlying principles for performing knowledge base verification through anomaly detection, but also a survey of the state-of-the-art in building practical tools for carrying out such verification. The reader of this paper is expected to be familiar with first-order logic.

First-Order Logic Reasoning Support for the Semantic Web

2009 ◽  
Vol 19 (12) ◽  
pp. 3091-3099 ◽  
Author(s):  
Gui-Hong XU ◽  
Jian ZHANG
Keyword(s):  
Semantic Web ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Logic Reasoning

scholarly journals Characterizing Boundedness in Chase Variants

2020 ◽  
Vol 21 (1) ◽  
pp. 51-79
Author(s):  
STATHIS DELIVORIAS ◽  
MICHEL LECLÈRE ◽  
MARIE-LAURE MUGNIER ◽  
FEDERICO ULLIANA
Keyword(s):  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Universal Models ◽  
Knowing That ◽  
Significant Interest ◽  
Horn Rules ◽  
Boundedness Problem ◽  
Undecidable Problem

AbstractExistential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Logics for the Semantic Web

2011 ◽  
pp. 24-43
Author(s):  
J. Bruijn
Keyword(s):  
Semantic Web ◽  
Logic Programming ◽  
Description Logic ◽  
Description Logics ◽  
Order Logic ◽  
First Order Logic ◽  
Horn Logic ◽  
First Order ◽  
Logical Language ◽  
Rule Languages

This chapter introduces a number of formal logical languages which form the backbone of the Semantic Web. They are used for the representation of both ontologies and rules. The basis for all languages presented in this chapter is the classical first-order logic. Description logics is a family of languages which represent subsets of first-order logic. Expressive description logic languages form the basis for popular ontology languages on the Semantic Web. Logic programming is based on a subset of first-order logic, namely Horn logic, but uses a slightly different semantics and can be extended with non-monotonic negation. Many Semantic Web reasoners are based on logic programming principles and rule languages for the Semantic Web based on logic programming are an ongoing discussion. Frame Logic allows object-oriented style (frame-based) modeling in a logical language. RuleML is an XML-based syntax consisting of different sublanguages for the exchange of specifications in different logical languages over the Web.

Logic-Based Analysis and Verification of Software Product Line Variant Requirement Model

2014 ◽  
Vol 5 (4) ◽  
pp. 52-76
Author(s):  
Shamim H Ripon ◽  
Sk. Jahir Hossain ◽  
Moshiur Mahamud Piash
Keyword(s):  
Semantic Web ◽  
Software Product Line ◽  
Product Line ◽  
Order Logic ◽  
First Order Logic ◽  
Formal Representation ◽  
First Order ◽  
Software Product ◽  
Feature Diagram ◽  
The Common

Software Product Line (SPL) provides the facility to systematically reuse of software improving the efficiency of software development regarding time, cost and quality. The main idea of SPL is to identify the common core functionality that can be implemented once and reused afterwards. A variant model has also to be developed to manage the variants of the SPL. Usually, a domain model consisting of the common and variant requirements is developed during domain engineering phase to alleviate the reuse opportunity. The authors present a product line model comprising of a variant part for the management of variant and a decision table to depict the customization of decision regarding each variant. Feature diagrams are widely used to model SPL variants. Both feature diagram and our variant model, which is based on tabular method, lacks logically sound formal representation and hence, not amenable to formal verification. Formal representation and verification of SPL has gained much interest in recent years. This chapter presents a logical representation of the variant model by using first order logic. With this representation, the table based variant model as well as the graphical feature diagram can now be verified logically. Besides applying first-order-logic to model the features, the authors also present an approach to model and analyze SPL model by using semantic web approach using OWL-DL. The OWL-DL representation also facilitates the search and maintenance of feature models and support knowledge sharing within a reusable engineering context. Reasoning tools are used to verify the consistency of the feature configuration for both logic-based and semantic web-based approaches.

Equivalences between logics and their representing type theories

1995 ◽  
Vol 5 (3) ◽  
pp. 323-349 ◽  
Author(s):  
Philippa Gardner
Keyword(s):  
Natural Deduction ◽  
Order Logic ◽  
First Order Logic ◽  
Logical Framework ◽  
Simple Formulation ◽  
First Order ◽  
Relevant Logics ◽  
First Time ◽  
New Framework

We propose a new framework for representing logics, called LF+, which is based on the Edinburgh Logical Framework. The new framework allows us to give, apparently for the first time, general definitions that capture how well a logic has been represented. These definitions are possible because we are able to distinguish in a generic way that part of the LF+ entailment corresponding to the underlying logic. This distinction does not seem to be possible with other frameworks. Using our definitions, we show that, for example, natural deduction first-order logic can be well-represented in LF+, whereas linear and relevant logics cannot. We also show that our syntactic definitions of representation have a simple formulation as indexed isomorphisms, which both confirms that our approach is a natural one and provides a link between type-theoretic and categorical approaches to frameworks.

Robot Task Planning Using First-Order Logic

2000 ◽  
Author(s):  
Lei Yan ◽  
K. Krishnamurthy
Keyword(s):  
Inference Engine ◽  
Knowledge Bases ◽  
Order Logic ◽  
First Order Logic ◽  
Task Planning ◽  
Inference Method ◽  
First Order ◽  
Simulation Results ◽  
Robot Task ◽  
Domain Information

Abstract Task planning for a robot operating in an unknown environment using first-order logic is considered in this study. The approach is to use one agent to simulate the robot and a second agent to simulate the environment. Both agents employ knowledge bases and an inference engine. The rules for the knowledge bases are developed using first-order logic and the inference method is based on hyper-resolution. A weighting scheme is used by the robot to decide on the action to be taken. After enough domain information is obtained, a task planner, which is also based on rules, is employed. Simulation results validating the methodology are presented for a robot moving inside a warehouse with four rooms. In this example, the environment is initially unknown to the robot. But after mapping the environment, the robot can efficiently plan tasks such as moving an object from one room to another.

Mediating RDF/S Queries to Relational and XML Sources

2009 ◽  
pp. 596-614 ◽  
Author(s):  
I. Koffina ◽  
G. Serfiotis ◽  
V. Christophides ◽  
V. Tannen
Keyword(s):  
Semantic Web ◽  
Relational Databases ◽  
Large Scale ◽  
Order Logic ◽  
Data Sources ◽  
First Order Logic ◽  
Main Design ◽  
First Order ◽  
High Level ◽  
The Web

Semantic Web (SW) technology aims to facilitate the integration of legacy data sources spread worldwide. Despite the plethora of SW languages (e.g., RDF/S, OWL) recently proposed for supporting large-scale information interoperation, the vast majority of legacy sources still rely on relational databases (RDB) published on the Web or corporate intranets as virtual XML. In this article, we advocate a first-order logic framework for mediating high-level queries to relational and/or XML sources using community ontologies expressed in a SW language such as RDF/S. We describe the architecture and reasoning services of our SW integration middleware, termed SWIM, and we present the main design choices and techniques for supporting powerful mappings between different data models, as well as reformulation and optimization of queries expressed against mediator ontologies and views.

scholarly journals On the Expressiveness of Levesque's Normal Form

2008 ◽  
Vol 31 ◽  
pp. 259-272
Author(s):  
Y. Liu ◽  
G. Lakemeyer
Keyword(s):  
Normal Form ◽  
Knowledge Base ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Method ◽  
Closed World Assumption ◽  
First Order ◽  
Closed World ◽  
Polynomial Size

Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closed-world assumption and hence the entailment problem becomes undecidable. Levesque then proposed a limited but efficient inference method V for proper KBs, which is sound and, when the query is in a certain normal form, also logically complete. He conjectured that for every first-order query there is an equivalent one in normal form. In this note, we show that this conjecture is false. In fact, we show that any class of formulas for which V is complete must be strictly less expressive than full first-order logic. Moreover, in the propositional case it is very unlikely that a formula always has a polynomial-size normal form.

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