Inconsistent Ontologies Research Articles

Towards counterfactual explanations for ontologies

Debugging and repairing Web Ontology Language (OWL) ontologies has been a key field of research since OWL became a W3C recommendation. One way to understand errors and fix them is through explanations. These explanations are usually extracted from the reasoner and displayed to the ontology authors as is. In the meantime, there has been a recent call in the eXplainable AI (XAI) field to use expert knowledge in the form of knowledge graphs and ontologies. In this paper, a parallel between explanations for machine learning and for ontologies is drawn. This link enables the adaptation of XAI methods to explain ontologies and their entailments. Counterfactual explanations have been identified as a good candidate to solve the explainability problem in machine learning. The CEO (Counterfactual Explanations for Ontologies) method is thus proposed to explain inconsistent ontologies using counterfactual explanations. A preliminary user study is conducted to ensure that using XAI methods for ontologies is relevant and worth pursuing.

An Argumentation-Based Approach for Computing Inconsistency Degree in Possibilistic Lightweight Ontologies

Reasoning with inconsistent ontologies plays an important role in Semantic Web applications. An important feature of argument theory is that it is able to naturally handle inconsistencies in ontologies and allows a user to represent information in the form of an argument. In argumentation, given an inconsistent knowledge base, arguments compete to decide which are the accepted consequences. In this paper, we are interested in using the argumentation for the inconsistency degree of uncertain knowledge bases expressed in possibilistic DL-Lite (the key notion in reasoning from a possibilistic DL-Lite knowledge base) without going through the negative closure. In the present work, the terminological base is assumed to be fully certain and the uncertainty is only considered on the assertion based. We proved that it is coherent and feasible to use Dung’s abstract argumentation theory to compute the inconsistency degree and how argumentation semantics relate to the state of the art of handling inconsistency.

PROSE

The study of paraconsistent reasoning with ontologies is especially important for the Semantic Web since knowledge is not always perfect within it. However, classical OWL reasoners cannot support reasoning with inconsistent ontologies. In this article, the authors present a plugin-based framework called prose to provide rich paraconsistent reasoning services for OWL ontologies, whose architecture contains the three following parts: a classical OWL reasoner, a multi-valued transformer, and an OWL API connecting with them. Within the proposed framework prose, they implement different multi-valued paraconsistent reasoning in the OWL. Moreover, they select three popular classical OWL reasoners and two typical kinds of reasoning services for users. As the authors excepted, prose does exactly enable current classical OWL reasoners to tolerate inconsistency in a simple and convenient way. Finally, they evaluate the three reasoners in a united framework (prose) and, as a result, those results can amend the analysis of the three reasoners on inconsistent ontologies.

A generalized abstract argumentation framework for inconsistency-tolerant ontology reasoning

We propose a new family of abstract argumentation frameworks which we refer to as generalized (identified through the acronym GenAF), due to its ability of adapting to different representation languages. GenAFs are formalized upon an unspecified representation language L but enriched with some inner structure which allows relating formulæ from the underlying knowledge base with primitive elements of arguments. The well-known Dung’s standard semantics are adapted to construct the GenAF’s reasoning machinery. As an application, we reify the GenAF’s abstract language for arguments with the basic ALC flexibility of the presented formalism and a way of applying argumentation for reasoning over inconsistent ontologies. Finally, a detailed study is performed on the matter of argumentation rationality. The GenAF when concretized into a generalized argumentation system (GenAS) is studied under specific conditions which turn it into a standard logic-based argumentation system. This brings the opportunity to verify the scope of widely accepted postulates for logic-based argumentation to control the well behavior of the GenAS and to relate it to other argumentation systems.

Forgetting for distance-based reasoning and repair in DL-Lite

In this paper, we present a forgetting-based approach to handling inconsistency in DL-Lite. Our proposed approach cannot only characterize distance-based reasoning, which is proven to rationally draw meaningful conclusions even from inconsistent DL-Lite knowledge bases but also recovery the consistency of DL-Lite knowledge bases. We first present vectors forgetting for DL-Lite by extending predicates forgetting in DL-Lite and show the predicates to be forgotten which are obtained by computing minimal hitting sets. Moreover, we develop algorithms to compute those predicates by employing Reiter’s HS-tree method and then analyze the computational complexity of those proposed algorithms. Finally, we implement our proposed algorithms and evaluate them on both consistent and inconsistent ontologies. Besides, we discuss some applications of vectors forgetting in privacy protection.

From Classical to Consistent Query Answering under Existential Rules

Querying inconsistent ontologies is an intriguing new problem that gave rise to a flourishing research activity in the description logic (DL) community. The computational complexity of consistent query answering under the main DLs is rather well understood; however, little is known about existential rules. The goal of the current work is to perform an in-depth analysis of the complexity of consistent query answering under the main decidable classes of existential rules enriched with negative constraints. Our investigation focuses on one of the most prominent inconsistency-tolerant semantics, namely, the AR semantics. We establish a generic complexity result, which demonstrates the tight connection between classical and consistent query answering. This result allows us to obtain in a uniform way a relatively complete picture of the complexity of our problem.

Paraconsistent OWL and related logics

The Web Ontology Language OWL is currently the most prominent formalism for representing ontologies in Semantic Web applications. OWL is based on description logics, and automated reasoners are used to infer knowledge implicitly present in OWL ontologies. However, because typical description logics obey the classical principle of explosion, reasoning over inconsistent ontologies is impossible in OWL. This is so despite the fact that inconsistencies are bound to occur in many realistic cases, e.g., when multiple ontologies are merged or when ontologies are created by machine learning or data mining tools.In this paper, we present four-valued paraconsistent description logics which can reason over inconsistencies. We focus on logics corresponding to OWL DL and its profiles. We present the logic $\mathcal {SROIQ}4$, showing that it is both sound relative to classical $\mathcal {SROIQ}$ and that its embedding into $\mathcal {SROIQ}$ is consequence preserving. We also examine paraconsistent varieties of $\mathcal{EL}^{++}$, DL-Lite, and Horn-DLs. The general framework described here has the distinct advantage of allowing classical reasoners to draw sound but nontrivial conclusions from even inconsistent knowledge bases. Truth-value gaps and gluts can also be selectively eliminated from models by inserting additional axioms into knowledge bases. If gaps but not gluts are eliminated, additional classical conclusions can be drawn without affecting paraconsistency.

ONTOarg: A decision support framework for ontology integration based on argumentation

Description Logic Programming (DLP) is a well-known approach to reason with Description Logic (DL) ontologies, translating them into the language of logic programming (LP). Even though DLP offers several advantages in terms of efficiency and reuse of existing logic programming tools (such as Prolog environments), a major hindrance of this approach is its limitation for reasoning in the presence of inconsistent ontologies. Recent research has led to the use of defeasible argumentation to model different DL reasoning capabilities when handling inconsistent ontologies, resulting in so-called δ-ontologies. In this article we present ONTOarg, a decision support framework for performing local-as-view integration of possibly inconsistent and incomplete ontologies in terms of Defeasible Logic Programming (DeLP). We show how to reason on Description Logics (DL) ontologies in an ontology integration system by performing a dialectical analysis in order to determine the membership of individuals to concepts. We present formal definitions of a framework for ontology integration of DL ontologies based on DeLP along with a case study and review some of the properties of the approach.

Paraconsistent query answering over DL-Lite ontologies

Consistent query answering over description logic based ontologies is an important topic in ontology engineering as it can provide meaningful answers to queries posed over inconsistent ontologies. Current approaches for dealing with this problem usually consist of two steps: the first one is to extract some consistent sub-ontologies of an inconsistent ontology, and then the second one is to pose the query over these consistent sub-ontologies. In this paper, we propose an alternative approach to consistent query answering for conjunctive queries over DL-Lite ontologies based on four-valued semantics, where DL-Lite is a family of tractable Description Logics DLs. We give an algorithm to compute answers to a query over an inconsistent DL-Lite ontology and show that it is tractable. In particular, we show that it is in PTime with respect to the size of the TBox, and is LOGSPACE with respect to the size of the ABox.

Reasoning with Inconsistent Ontologies

Reasoning with inconsistent ontologies involves using an inconsistency reasoner to get meaningful answers from inconsistent ontologies. This paper introduces an improved inconsistency reasoner, which selects consistent subsets using minimal inconsistent sets and a resolution method, to improve the run-time performance of the reasoning processing. A minimal inconsistent set contains a minimal explanation for the inconsistency of a given ontology. Thus, it can replace the consistency checking operation, which is executed frequently in existing approaches. When selecting subsets of the inconsistent ontology, formulas which can be directly or indirectly resolved with the negation of the query formula are selected because only those formulas affect the consequences of the reasoner. Therefore, the complexity of the reasoning processing is significantly reduced. Tests show that the run-time performance of the inconsistency reasoner is significantly improved.

REASONING WITH INCONSISTENT ONTOLOGIES THROUGH ARGUMENTATION

Standard approaches to reasoning with description logics (DL) ontologies require them to be consistent. However, as ontologies are complex entities and sometimes built upon other imported ontologies, inconsistencies can arise. In this article, we present δ-ontologies, a framework for reasoning with inconsistent DL ontologies. Our proposal involves expressing DL ontologies as defeasible logic programs (DeLP). Given a query posed w.r.t. an inconsistent ontology, a dialectical analysis will be performed on a DeLP program obtained from such an ontology, where all arguments in favor and against the final answer of the query will be taken into account. We also present an application to ontology integration based on the global-as-view approach.

Tiers of ontology and consistency constraints in geographical information systems

Consistency constraints placed on a database to assure, that values incorporated in the database are consistent, are a well known foundation of Geographical Information Systems. Unfortunately in real situations rules for consistency constraints are not so clear, and inconsistent ontologies are common place, not least in geographical information, covering as it does a much wider realm than many other information systems I have suggested elsewhere 5-tiers of ontology for GIS. Such an ontology can integrate different ontological approaches in a unified system. In this paper the relation of the 5-tier ontology and consistency constraints is explored, and it is shown that different constraints are appropriate to different tiers.