Instance Checking Research Articles

Reasoning on with Defeasibility in ASP

Abstract Reasoning on defeasible knowledge is a topic of interest in the area of description logics, as it is related to the need of representing exceptional instances in knowledge bases. In this direction, in our previous works we presented a framework for representing (contextualized) OWL RL knowledge bases with a notion of justified exceptions on defeasible axioms: reasoning in such framework is realized by a translation into ASP programs. The resulting reasoning process for OWL RL, however, introduces a complex encoding in order to capture reasoning on the negative information needed for reasoning on exceptions. In this paper, we apply the justified exception approach to knowledge bases in , that is, the language underlying OWL QL. We provide a definition for knowledge bases with defeasible axioms and study their semantic and computational properties. In particular, we study the effects of exceptions over unnamed individuals. The limited form of axioms allows us to formulate a simpler ASP encoding, where reasoning on negative information is managed by direct rules. The resulting materialization method gives rise to a complete reasoning procedure for instance checking in with defeasible axioms.1

Reasoning in the Defeasible Description Logic —computing standard inferences under rational and relevant semantics

Defeasible Description Logics (DDLs) extend Description Logics with defeasible concept inclusions. Reasoning in DDLs often employs rational closure according to the (propositional) KLM postulates. A well-known approach to lift this closure to DDLs is by so-called materialisation. Previously investigated algorithms for materialisation-based reasoning employ reductions to classical reasoning using all Boolean connectors. As a first result in this paper, we present a materialisation-based algorithm for the sub-Boolean DDL ▪, using a reduction to reasoning in classical ▪, rendering materialisation-based defeasible reasoning tractable.The main contribution of this article is a kind of canonical model construction, which can be used to decide defeasible subsumption and instance queries in ▪ under rational and the stronger relevant entailment. Our so-called typicality models can reproduce the entailments obtained from materialisation-based rational and relevant closure and, more importantly, obtain stronger versions of rational and relevant entailment. These do not suffer from neglecting defeasible information for concepts appearing nested inside quantifications, which all materialisation-based approaches do. We also show the computational complexity of defeasible subsumption and instance checking in our stronger rational and relevant semantics.

Defeasible Reasoning in 𝒮ℛ𝒪ℰℒ: from Rational Entailment to Rational Closure

In this work we study a rational extension $SROEL^R T$ of the low complexity description logic SROEL, which underlies the OWL EL ontology language. The extension involves a typicality operator T, whose semantics is based on Lehmann and Magidor's ranked models and allows for the definition of defeasible inclusions. We consider both rational entailment and minimal entailment. We show that deciding instance checking under minimal entailment is in general $\Pi^P_2$-hard, while, under rational entailment, instance checking can be computed in polynomial time. We develop a Datalog calculus for instance checking under rational entailment and exploit it, with stratified negation, for computing the rational closure of simple KBs in polynomial time.

Enhancing context knowledge repositories with justifiable exceptions

Dealing with context dependent knowledge is a well-known area of study that roots in John McCarthy's seminal work. More recently, the Contextualized Knowledge Repository (CKR) framework has been conceived as a logic-based approach in which knowledge bases have a two layered structure, modeled by a global context and a set of local contexts. The global context not only contains the meta-knowledge defining the properties of local contexts, but also holds the global (context independent) object knowledge that is shared by all of the local contexts. In many practical cases, however, it is desirable to leave the possibility to “override” the global object knowledge at the local level: in other words, it is interesting to recognize the pieces of knowledge that can admit exceptional instances in the local contexts that do not need to satisfy the general axiom. To address this need, we present in this paper an extension of CKR in which defeasible axioms can be included in the global context. The latter are verified in the local contexts only for the instances for which no exception to overriding exists, where exceptions require a justification in terms of facts that are provable from the knowledge base. We formally define this semantics and study some semantic and computational properties, where we characterize the complexity of the major reasoning tasks, among them satisfiability testing, instance checking, and conjunctive query answering. Furthermore, we present a translation of extended CKRs with knowledge bases in the Description Logic SROIQ-RL under the novel semantics to datalog programs under the stable model (answer set) semantics. We also present an implementation prototype and examine its scalability with respect to the size of the input CKR and the amount (level) of defeasibility in experiments. Finally, we compare our representation approach with some major formalisms for expressing defeasible knowledge in Description Logics and contextual knowledge representation. Our work adds to the body of results on using deductive database technology such as SQL and datalog in these areas, and provides an expressive formalism (in terms of intrinsic complexity) for exception handling by overriding.

Reasoning with Inconsistent Possibilistic Ontologies by Applying Argument Accrual

We present an approach for performing instance checking in possibilistic description logic programming ontologies by accruing arguments that support the membership of individuals to concepts. Ontologies are interpreted as possibilistic logic programs where accruals of arguments as regarded as vertexes in an abstract argumentation framework. A suitable attack relation between accruals is defined. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach that is capable of reasoning under Dung’s grounded semantics.

Uncertain lightweight ontologies in a product-based possibility theory framework

This paper investigates an extension of lightweight ontologies, encoded here in DL-Lite languages, to the product-based possibility theory framework. We first introduce the language (and its associated semantics) used for representing uncertainty in lightweight ontologies. We show that, contrarily to a min-based possibilistic DL-Lite, query answering in a product-based possibility theory is a hard task. We provide equivalent transformations between the problem of computing an inconsistency degree (the key notion in reasoning from a possibilistic DL-Lite knowledge base) and the weighted maximum 2-Horn SAT problem. The last part of the paper provides an encoding of the problem of computing inconsistency degree in product-based possibility DL-Lite as a weighted set cover problem and the use of a greedy algorithm to compute an approximate value of the inconsistency degree. This encoding allows us to provide an approximate algorithm for answering instance checking queries in product-based possibilistic DL-Lite. Experimental studies show the quality of the approximate algorithms for both inconsistency degree computation and instance checking queries.

ASP for minimal entailment in a rational extension of SROEL

AbstractIn this paper we exploit Answer Set Programming (ASP) for reasoning in a rational extensionSROEL(⊓,×)RTof the low complexity description logicSROEL(⊓, ×), which underlies the OWL EL ontology language. In the extended language, a typicality operatorTis allowed to define conceptsT(C) (typicalC's) under a rational semantics. It has been proven that instance checking under rational entailment has a polynomial complexity. To strengthen rational entailment, in this paper we consider a minimal model semantics. We show that, for arbitrarySROEL(⊓,×)RTknowledge bases, instance checking under minimal entailment is ΠP2-complete. Relying on a Small Model result, where models correspond to answer sets of a suitable ASP encoding, we exploit Answer Set Preferences (and, in particular, theasprinframework) for reasoning under minimal entailment.

A Tractable Rule Language in the Modal and Description Logic that Combines CPDL with Regular Grammar Logic

Combining CPDL (Propositional Dynamic Logic with Converse) and regular grammar logic results in an expressive modal logic denoted by CPDLreg. This logic covers TEAMLOG, a logical formalism used to express properties of agents' cooperation in terms of beliefs, goals and intentions. It can also be used as a description logic for expressing terminological knowledge, in which both regular role inclusion axioms and CPDL-like role constructors are allowed. In this paper, we develop an expressive and tractable rule language called Horn-CPDLreg. As a special property, this rule language allows the concept constructor universal restriction to appear on the left hand side of general concept inclusion axioms. We use a special semantics for Horn-CPDLreg that is based on pseudo-interpretations. It is called the constructive semantics and coincides with the traditional semantics when the concept constructor universal restriction is disallowed on the left hand side of concept inclusion axioms or when the language is used as an epistemic formalism and the accessibility relations are serial. We provide an algorithm with PTIME data complexity for checking whether a knowledge base in Horn-CPDLreg has a pseudo-model. This shows that the instance checking problem in Horn-CPDLreg with respect to the constructive semantics has PTIME data complexity.

Integrated Data Repository Toolkit (IDRT). A Suite of Programs to Facilitate Health Analytics on Heterogeneous Medical Data.

In recent years, research data warehouses moved increasingly into the focus of interest of medical research. Nevertheless, there are only a few center-independent infrastructure solutions available. They aim to provide a consolidated view on medical data from various sources such as clinical trials, electronic health records, epidemiological registries or longitudinal cohorts. The i2b2 framework is a well-established solution for such repositories, but it lacks support for importing and integrating clinical data and metadata. The goal of this project was to develop a platform for easy integration and administration of data from heterogeneous sources, to provide capabilities for linking them to medical terminologies and to allow for transforming and mapping of data streams for user-specific views. A suite of three tools has been developed: the i2b2 Wizard for simplifying administration of i2b2, the IDRT Import and Mapping Tool for loading clinical data from various formats like CSV, SQL, CDISC ODM or biobanks and the IDRT i2b2 Web Client Plugin for advanced export options. The Import and Mapping Tool also includes an ontology editor for rearranging and mapping patient data and structures as well as annotating clinical data with medical terminologies, primarily those used in Germany (ICD-10-GM, OPS, ICD-O, etc.). With the three tools functional, new i2b2-based research projects can be created, populated and customized to researcher's needs in a few hours. Amalgamating data and metadata from different databases can be managed easily. With regards to data privacy a pseudonymization service can be plugged in. Using common ontologies and reference terminologies rather than project-specific ones leads to a consistent understanding of the data semantics. i2b2's promise is to enable clinical researchers to devise and test new hypothesis even without a deep knowledge in statistical programing. The approach presented here has been tested in a number of scenarios with millions of observations and tens of thousands of patients. Initially mostly observant, trained researchers were able to construct new analyses on their own. Early feedback indicates that timely and extensive access to their "own" data is appreciated most, but it is also lowering the barrier for other tasks, for instance checking data quality and completeness (missing data, wrong coding).

Tractable Interval Temporal Propositional and Description Logics

We design a tractable Horn fragment of the Halpern-Shoham temporal logic and extend it to interval-based temporal description logics, instance checking in which is P-complete for both combined and data complexity.

Converting Instance Checking to Subsumption: A Rethink for Object Queries over Practical Ontologies.

Efficiently querying Description Logic (DL) ontologies is becoming a vital task in various data-intensive DL applications. Considered as a basic service for answering object queries over DL ontologies, instance checking can be realized by using the most specific concept (MSC) method, which converts instance checking into subsumption problems. This method, however, loses its simplicity and efficiency when applied to large and complex ontologies, as it tends to generate very large MSCs that could lead to intractable reasoning. In this paper, we propose a revision to this MSC method for DL , allowing it to generate much simpler and smaller concepts that are specific enough to answer a given query. With independence between computed MSCs, scalability for query answering can also be achieved by distributing and parallelizing the computations. An empirical evaluation shows the efficacy of our revised MSC method and the significant efficiency achieved when using it for answering object queries.

Converting Instance Checking to Subsumption: A Rethink for Object Queries over Practical Ontologies

Instance checking is considered a central service for data retrieval from description logic (DL) ontologies. In this paper, we propose a revised most specific concept (MSC) method for DL SHI}, which converts instance checking into subsumption problems. This revised method can generate small concepts that are specific-enough to answer a given query, and allow reasoning to explore only a subset of the ABox data to achieve efficiency. Experiments show effectiveness of our proposed method in terms of concept size reduction and the improvement in reasoning efficiency.

Optimizing the Most Specific Concept Method for Efficient Instance Checking.

Instance checking is considered a central tool for data retrieval from description logic (DL) ontologies. In this paper, we propose a revised most specific concept (MSC) method for DL SHI, which converts instance checking into subsumption problems. This revised method can generate small concepts that are specific-enough to answer a given query, and allow reasoning to explore only a subset of the ABox data to achieve efficiency. Experiments show effectiveness of our proposed method in terms of concept size reduction and the improvement in reasoning efficiency.

Absorption for ABoxes

We consider the instance checking problem over S ? I Q ( D ) $\mathcal {SHIQ}(\mathbf{D})$ knowledge bases, that is, the problem of determining if the class membership of a given object is logically implied by a knowledge base expressed in terms of the description logic (DL) dialect S ? I Q ( D ) $\mathcal {SHIQ}(\mathbf{D})$ . Such problems are inevitable in conjunctive query evaluation over such knowledge bases, or indeed for any knowledge bases that rely on an ability to capture disjunction and/or negation in an underlying DL. This includes the problem of evaluating basic graph patterns occurring in SPARQL queries over RDF graphs with the so-called OWL 2 direct semantics entailment regime, that is, where the RDF graph is an OWL 2 ontology. Our main result is a novel method for such problems that derives from an adaptation of binary absorption. We show that the method works particularly well for knowledge bases that have a very large collection of factual assertions about individual objects.

Describing and Recognizing Patterns of Events in Smart Environments With Description Logic

This paper describes a system for context awareness in smart environments, which is based on an ontology expressed in description logic and implemented in OWL 2 EL, which is a subset of the Web Ontology Language that allows for reasoning in polynomial time. The approach is different from all other works in the literature since the proposed system requires only the basic reasoning mechanisms of description logic, i.e., subsumption and instance checking, without any additional external reasoning engine. Experiments performed with data collected in three different scenarios are described, i.e., the CASAS Project at Washington State University, the assisted living facility Villa Basilea in Genoa, and the Merry Porter mobile robot at the Polyclinic of Modena.

Reasoning with inconsistencies in hybrid MKNF knowledge bases

This paper is concerned with the handling of inconsistencies occurring in the combination of description logics and rules, especially in hybrid MKNF knowledge bases. More precisely, we present a paraconsistent semantics for hybrid MKNF knowledge bases (called para-MKNF knowledge bases) based on four-valued logic as proposed by Belnap. We also reduce this paraconsistent semantics to the stable model semantics via a linear transformation operator, which shows the relationship between the two semantics and indicates that the data complexity in our paradigm is not higher than that of classical reasoning. Moreover, we provide fixpoint operators to compute paraconsistent MKNF models, each suitable to different kinds of rules. At last we present the data complexity of instance checking in different paraMKNF knowledge bases.

Towards ABox Modularization of semi-expressive Description Logics

In the last years, the vision of the Semantic Web fostered the interest in reasoning over large and very large sets of assertional statements in knowledge bases. Traditional tableau-based reasoning systems perform bad answering queries over large data sets, because these reasoning systems are based on efficient use of main memory data structures. Increasing expressivity and worst-case complexity further tighten the memory burden. The purpose of our work is to investigate how to release the main memory burden from tableau-based reasoning systems and perform efficient instance checking over SHI-knowledge bases. The key idea is to reduce instance checking for an individual in a knowledge base to smaller subsets of relevant axioms. Modularization techniques are introduced and further refined in order to increase the granularity of modules. For evaluation purposes, experiments on benchmark and real world knowledge bases are carried out. The principal conclusion is that the main memory burden for instance checking can be released from tableau-based reasoning systems for semi-expressive Description Logics, by using modularization techniques.

ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse

Grammar logics were introduced by Farinas del Cerro and Penttonen in 1988 and have been widely studied. In this paper we consider regular grammar logics with converse (REG c logics) and present sound and complete tableau calculi for the general satisfiability problem of REG c logics and the problem of checking consistency of an ABox w.r.t. a TBox in a REG c logic. Using our calculi we develop ExpTime (optimal) tableau decision procedures for the mentioned problems, to which various optimization techniques can be applied. We also prove a new result that the data complexity of the instance checking problem in REG c logics is coNP-complete.

Checking Consistency of an ABox w.r.t. Global Assumptions in PDL

We reformulate Pratt’s tableau decision procedure of checking satisfiability of a set of formulas in PDL. Our formulation is simpler and its implementation is more direct. Extending the method we give the first ExpTime (optimal) tableau decision procedure not based on transformation for checking consistency of an ABox w.r.t. a TBox in PDL (here, PDL is treated as a description logic). We also prove a new result that the data complexity of the instance checking problem in PDL is coNP-complete.

Horn Knowledge Bases in Regular Description Logics with PTIME Data Complexity

Developing a good formalism and an efficient decision procedure for the instance checking problem is desirable for practical application of description logics. The data complexity of the instance checking problem is coNP-complete even for Horn knowledge bases in the basic description logic ALC. In this paper, we present and study weakenings with PTIME data complexity of the instance checking problem for Horn knowledge bases in regular description logics. We also study cases when the weakenings are an exact approximation. In contrast to previous related work of other authors, our approach deals with the case when the constructor ∀ is allowed in premises of program clauses that are used as terminological axioms.