701 research outputs found
Disjunctive Logic Programs with Inheritance
The paper proposes a new knowledge representation language, called DLP<,
which extends disjunctive logic programming (with strong negation) by
inheritance. The addition of inheritance enhances the knowledge modeling
features of the language providing a natural representation of default
reasoning with exceptions.
A declarative model-theoretic semantics of DLP< is provided, which is shown
to generalize the Answer Set Semantics of disjunctive logic programs.
The knowledge modeling features of the language are illustrated by encoding
classical nonmonotonic problems in DLP<.
The complexity of DLP< is analyzed, proving that inheritance does not cause
any computational overhead, as reasoning in DLP< has exactly the same
complexity as reasoning in disjunctive logic programming. This is confirmed by
the existence of an efficient translation from DLP< to plain disjunctive logic
programming. Using this translation, an advanced KR system supporting the DLP<
language has been implemented on top of the DLV system and has subsequently
been integrated into DLV.Comment: 28 pages; will be published in Theory and Practice of Logic
Programmin
Reasoning about exceptions in ontologies: from the lexicographic closure to the skeptical closure
Reasoning about exceptions in ontologies is nowadays one of the challenges
the description logics community is facing. The paper describes a preferential
approach for dealing with exceptions in Description Logics, based on the
rational closure. The rational closure has the merit of providing a simple and
efficient approach for reasoning with exceptions, but it does not allow
independent handling of the inheritance of different defeasible properties of
concepts. In this work we outline a possible solution to this problem by
introducing a variant of the lexicographical closure, that we call skeptical
closure, which requires to construct a single base. We develop a bi-preference
semantics semantics for defining a characterization of the skeptical closure
Reason Maintenance - State of the Art
This paper describes state of the art in reason maintenance with a focus on its future usage in the KiWi project. To give a bigger picture of the field, it also mentions closely related issues such as non-monotonic logic and paraconsistency. The paper is organized as follows: first, two motivating scenarios referring to semantic wikis are presented which are then used to introduce the different reason maintenance techniques
On principles and problems of defeasible inheritance
We have two aims here: First, to discuss some basic principles underlying different approaches to Defeasible Inheritance; second, to examine problems of these approaches as they already appear in quite simple diagrams. We build upon, but go beyond, the discussion in the joint paper of Touretzky, Horty, and Thomason: A Clash of Intuitions
Translating inheritance nets to default logic
We give a translation of inheritance nets to normal default
theories. To avoid discussions about sceptical and credulous
reasoning we only regard unambiguous nets but allow explicit
exception links restricting the validity of direct links.
Contrary to former translations every link will be translated
to a "hard" fact of the corresponding default theory while the
defaults only repesent the implicit assumptions made when
computing the extension of the net. The translation is sound and
complete if we restrict the deduction mechanism of default logic
appropriately
Revising Description Logic Terminologies to Handle Exceptions: a First Step
Abstract. We propose a methodology to revise a Description Logic knowledge base when detecting exceptions. Our approach relies on the methodology for debugging a Description Logic terminology, addressing the problem of diagnosing incoherent ontologies by identifying a mini-mal subset of axioms responsible for an inconsistency. In the approach we propose, once the source of the inconsistency has been localized, the identified axioms are revised in order to obtain a consistent knowledge base including the detected exception. To this aim, we make use of a non-monotonic extension of the Description Logic ALC based on the com-bination of a typicality operator and the well established nonmonotonic mechanism of rational closure, which allows to deal with prototypical properties and defeasible inheritance.
A Lightweight Defeasible Description Logic in Depth: Quantification in Rational Reasoning and Beyond
Description Logics (DLs) are increasingly successful knowledge representation formalisms, useful for any application requiring implicit derivation of knowledge from explicitly known facts.
A prominent example domain benefiting from these formalisms since the 1990s is the biomedical field.
This area contributes an intangible amount of facts and relations between low- and high-level concepts such as the constitution of cells or interactions between studied illnesses, their symptoms and remedies.
DLs are well-suited for handling large formal knowledge repositories and computing inferable coherences throughout such data, relying on their well-founded first-order semantics.
In particular, DLs of reduced expressivity have proven a tremendous worth for handling large ontologies due to their computational tractability.
In spite of these assets and prevailing influence, classical DLs are not well-suited to adequately model some of the most intuitive forms of reasoning.
The capability for abductive reasoning is imperative for any field subjected to incomplete knowledge and the motivation to complete it with typical expectations.
When such default expectations receive contradicting evidence, an abductive formalism is able to retract previously drawn, conflicting conclusions.
Common examples often include human reasoning or a default characterisation of properties in biology, such as the normal arrangement of organs in the human body.
Treatment of such defeasible knowledge must be aware of exceptional cases - such as a human suffering from the congenital condition situs inversus - and therefore accommodate for the ability to retract defeasible conclusions in a non-monotonic fashion.
Specifically tailored non-monotonic semantics have been continuously investigated for DLs in the past 30 years.
A particularly promising approach, is rooted in the research by Kraus, Lehmann and Magidor for preferential (propositional) logics and Rational Closure (RC).
The biggest advantages of RC are its well-behaviour in terms of formal inference postulates and the efficient computation of defeasible entailments, by relying on a tractable reduction to classical reasoning in the underlying formalism.
A major contribution of this work is a reorganisation of the core of this reasoning method, into an abstract framework formalisation.
This framework is then easily instantiated to provide the reduction method for RC in DLs as well as more advanced closure operators, such as Relevant or Lexicographic Closure.
In spite of their practical aptitude, we discovered that all reduction approaches fail to provide any defeasible conclusions for elements that only occur in the relational neighbourhood of the inspected elements.
More explicitly, a distinguishing advantage of DLs over propositional logic is the capability to model binary relations and describe aspects of a related concept in terms of existential and universal quantification.
Previous approaches to RC (and more advanced closures) are not able to derive typical behaviour for the concepts that occur within such quantification.
The main contribution of this work is to introduce stronger semantics for the lightweight DL EL_bot with the capability to infer the expected entailments, while maintaining a close relation to the reduction method.
We achieve this by introducing a new kind of first-order interpretation that allocates defeasible information on its elements directly.
This allows to compare the level of typicality of such interpretations in terms of defeasible information satisfied at elements in the relational neighbourhood.
A typicality preference relation then provides the means to single out those sets of models with maximal typicality.
Based on this notion, we introduce two types of nested rational semantics, a sceptical and a selective variant, each capable of deriving the missing entailments under RC for arbitrarily nested quantified concepts.
As a proof of versatility for our new semantics, we also show that the stronger Relevant Closure, can be imbued with typical information in the successors of binary relations.
An extensive investigation into the computational complexity of our new semantics shows that the sceptical nested variant comes at considerable additional effort, while the selective semantics reside in the complexity of classical reasoning in the underlying DL, which remains tractable in our case
Semantic networks
AbstractA semantic network is a graph of the structure of meaning. This article introduces semantic network systems and their importance in Artificial Intelligence, followed by I. the early background; II. a summary of the basic ideas and issues including link types, frame systems, case relations, link valence, abstraction, inheritance hierarchies and logic extensions; and III. a survey of ‘world-structuring’ systems including ontologies, causal link models, continuous models, relevance, formal dictionaries, semantic primitives and intersecting inference hierarchies. Speed and practical implementation are briefly discussed. The conclusion argues for a synthesis of relational graph theory, graph-grammar theory and order theory based on semantic primitives and multiple intersecting inference hierarchies
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