Terminological Knowledge Representation Research Articles

An Occurrence Description Logic


 
 
 Description Logics (DLs) are a family of well-known terminological knowledge representation formalisms in modern semantics-based systems. This research focuses on analysing how our developed Occurrence Logic (OccL) can conceptually and logically support the development of a description logic. OccL is integrated into the alternative theory of natural language syntax in Deviational Syntactic Structures under the label ‘EFA(X)3’ (or the third version of Epi-Formal Analysis in Syntax, EFA(X), which is a radical linguistic theory). From the logical point of view, OccL is a formal logic that mainly deals with the occurrences of symbols as well as with their priorities within linguistic descriptions, i.e. natural language syntax, semantics and phonology. In this article—based on our OccL-based definitions of the concepts of strong implication and occurrence value as well as of the logical concept Identical Occurrence Constructor (IDOC) that is the most fundamental logical concept in our formalism—we will model Occurrence Description Logic (ODL). Accordingly, we will formally-logically analyse ‘occurrence(s) of symbol(s)’ within descriptions of the world in ODL. In addition, we will analyse and assess the logical concepts of occurrence and occurrence priority in ODL. This research can make a strong logical background for our future research in the development of a Modal Occurrence Description Logic.
 
 

On Logical Characterisation of Human Concept Learning based on Terminological Systems

The central focus of this article is the epistemological assumption that knowledge could be generated based on human beings’ experiences and over their conceptions of the world. Logical characterisation of human inductive learning over their produced conceptions within terminological systems and providing a logical background for theorising over the Human Concept Learning Problem (HCLP) in terminological systems are the main contributions of this research. In order to make a linkage between ‘Logic’ and ‘Cognition’, Description Logics (DLs) will be employed to provide a logical description and analysis of actual human inductive reasoning (and learning). This research connects with the topics ‘logic & learning’, ‘cognitive modelling’, and ‘terminological knowledge representation’.

Crimes against children: an apparently terminological knowledge representation of entities in FunGramKB

This article describes an example of the difficulties involved in the construction of a term-based satellite (or domain-specific) ontology integrated in FunGramKB –a lexico-conceptual knowledge base for the computational processing of natural language (Periñán-Pascual & Arcas-Túnez 2004, 2007, 2010a; Periñán-Pascual & Mairal-Usón 2009, 2010). The main hypothesis is that the multilevel model of FunGramKB Core Ontology can be connected to terminological satellite ontologies in order to minimize redundancy and maximize information (Periñán-Pascual & Arcas-Túnez 2010b). To this end we follow the four-phase COHERENT methodology (Periñán-Pascual & Mairal-Usón 2011): COnceptualization, HiErarchization, REmodelling and refinemeNT. In doing so, the paper furnishes substantial evidence on the structuring of a set of concepts borrowed from criminal law, an apparently terminological domain (cf. Breuker, Valente & Winkels 2005; Valente 2005; Breuker, Casanovas & Klein 2008). The <em>Globalcrimeterm</em> corpus has been used as an empirical foundation (Felices-Lago & Ureña-Gómez Moreno 2012, 2014). To illustrate this process, we have selected the superordinate basic concept +CRIME_00 (Alameda-Hernández & Felices-Lago 2016) and its basic and terminal subordinate concepts in the domains of organized crime and terrorism (all of them under the metaconcept #ENTITY), particularly those crimes referring predominantly to children or involving children with other vulnerable groups. The creation of specific definitions for the target concepts in this paper uses COREL (a conceptual representation language (Periñán-Pascual & Mairal-Usón 2010)) and the following upper-level conceptual path: #ENTITY> #PHYSICAL> #PROCESS> +OCCURRENCE_00> +CRIME_00. Consequently, the modelling, subsumption and hierarchisation of concepts such as $ABDUCTION_00, $CHILD_ABUSE_00, $CHILD_PORNOGRAPHY_00, $COERCE_D_00, $CHILD_TRAFFICKING_00, $MOLEST_D_00, $FORCED_LABOUR, among others, are presented.

Legal modeling and automated reasoning with ON-LINE

In this paper we present a modeling approach to legal knowledge systems and its computational realization in the ON-LINE architecture. ON-LINE has modules for modeling legal sources, for storing and retrieving legal information and for reasoning with legal knowledge. The approach takes two perspectives: domain and task. In the domain perspective, a core ontology divides legal knowledge into five major categories: normative, world, responsibility, reactive and creative. For the normative knowledge, which is most typical of legal domains, we developed a new representation and inference formalisms which are an alternative to deontic logic. For the world knowledge, we argue for using a terminological knowledge representation language. The structure of the ontology is not a taxonomy, but a network of dependencies between the categories. These dependencies reflect the global structure of arguments in legal reasoning. In the task perspective, we followed a top-down approach using the CommonKADS modeling library. Design, planning and assessment were identified as typical tasks in the legal domain. For assessment, a model was specified and implemented.

A refined architecture for terminological systems: Terminology = Schema + Views

Traditionally, the core of a Terminological Knowledge Representation System (TKRS) consists of a TBox or terminology, where concepts are introduced, and an ABox or world description, where facts about individuals are stated in terms of concept memberships. This design has a drawback because in most applications the TBox has to meet two functions at a time: On the one hand—similarly to a database schema—frame-like structures with type information are introduced through primitive concepts and primitive roles; on the other hand, views on the objects in the knowledge base are provided through defined concepts. We propose to account for this conceptual separation by partitioning the TBox into two components for primitive and defined concepts, which we call the schema and the view part. We envision the two parts to differ with respect to the language for concepts, the statements allowed, and the semantics. We argue that this separation achieves more conceptual clarity about the role of primitive and defined concepts and the semantics of terminological cycles. Two case studies show the computational benefits to be gained from the refined architecture.

The Complexity of Concept Languages

A basic feature of Terminological Knowledge Representation Systems is to represent knowledge by means of taxonomies, here called terminologies, and to provide a specialized reasoning engine to do inferences on these structures. The taxonomy is built through a representation language called aconcept language(ordescription logic), which is given a well-defined set-theoretic semantics. The efficiency of reasoning has often been advocated as a primary motivation for the use of such systems. The main contributions of the paper are: (1) a complexity analysis of concept satisfiability and subsumption for a wide class of concept languages; (2) algorithms for these inferences that comply with the worst-case complexity of the reasoning task they perform.

Logical considerations on default semantics

We consider a reinterpretation of the rules of default logic. We make Reiter’s default rules into a constructive method of building models, not theories. To allow reasoning in firstdorder systems, we equip standard firstdorder logic with a (new) Kleene 3dvalued partial model semantics. Then, using our methodology, we add defaults to this semantic system. The result is that our logic is an ordinary monotonic one, but its semantics is now nonmonotonic. Reiter’s extensions now appear in the semantics, not in the syntax. As an application, we show that this semantics gives a partial solution to the conceptual problems with open defaults pointed out by Lifschitz lV. Lifschitz, On open defaults, in: Proceedings of the Symposium on Computational Logics (1990)r, and Baader and Hollunder lF. Baader and B. Hollunder, Embedding defaults into terminological knowledge representation formalisms, in: Proceedings of Third Annual Conference on Knowledge Representation (MorgandKaufmann, 1992)r. The solution is not complete, chiefly because in making the defaults modeldtheoretic, we can only add conjunctive information to our models. This is in contrast to default theories, where extensions can contain disjunctive formulas, and therefore disjunctive information. Our proposal to treat the problem of open defaults uses a semantic notion of nonmonotonic entailment for our logic, related to the idea of “only knowing”. Our notion is “only having information” given by a formula. We discuss the differences between this and “minimaldknowledge” ideas. Finally, we consider the Kraus–Lehmann–Magidor lS. Kraus, D. Lehmann and M. Magidor, Nonmonotonic reasoning, preferential models, and cumulative logics, Artificial Intelligence 44 (1990) 167–207r axioms for preferential consequence relations. We find that our consequence relation satisfies the most basic of the laws, and the Or law, but it does not satisfy the law of Cut, nor the law of Cautious Monotony. We give intuitive examples using our system, on the other hand, which on the surface seem to violate these two laws. We make some comparisons, using our examples, to probabilistic interpretations for which these laws are true, and we compare our models to the cumulative models of Kraus, Lehmann, and Magidor. We also show sufficient conditions for the laws to hold. These involve limiting the use of disjunction in our formulas in one way or another. We show how to make use of the theory of complete partially ordered sets, or domain theory. We can augment any Scott domain with a default set. We state a version of Reiter’s extension operator on arbitrary domains as well. This version makes clear the basic orderdtheoretic nature of Reiter’s definitions. A threedvariable function is involved. Finding extensions corresponds to taking fixed points twice, with respect to two of these variables. In the special case of preconditiondfree defaults, a general relation on Scott domains induced from the set of defaults is shown to characterize extensions. We show how a general notion of domain theory, the logic induced from the Scott topology on a domain, guides us to a correct notion of “affirmable sentence” in a specific case such as our firstdorder systems. We also prove our consequence laws in such a way that they hold not only in firstdorder systems, but in any logic derived from the Scott topology on an arbitrary domain.

Using automata theory for characterizing the semantics of terminological cycles

In most of the implemented terminological knowledge representation systems it is not possible to state recursive concept definitions, so-called terminological cycles. One reason is that it is not clear what kind of semantics to use for such cycles. In addition, the inference algorithms used in such systems may go astray in the presence of terminological cycles. In this paper we consider terminological cycles in a very small terminological representation language. For this language, the effect of the three types of semantics introduced by B. Nebel can completely be described with the help of finite automata. These descriptions provide for a rather intuitive understanding of terminologies with recursive definitions, and they give an insight into the essential features of the respective semantics. In addition, one obtains algorithms and complexity results for the subsumption problem and for related inference tasks. The results of this paper may help to decide what kind of semantics is most appropriate for cyclic definitions, depending on the representation task.

A formal definition for the expressive power to terminological knowledge representation languages

A formal definition for the expressive power to terminological knowledge representation languages

A Formal Definition for the Expressive Power of Terminological Knowledge Representation Languages

A Formal Definition for the Expressive Power of Terminological Knowledge Representation Languages

Embedding defaults into terminological knowledge representation formalisms

Embedding defaults into terminological knowledge representation formalisms

A multi-dimensional terminological knowledge representation language

ABSTRACT An extension of the concept description language ALC used in KL-ONE-like terminological reasoning is presented. The extension includes multi-modal operators that either stand for the usual role quantifications or for modalities such as belief, time, etc. The modal operators can be used at all levels of the concept terms, and they can be used to modify both concepts and roles. This is an instance of a new kind of combination of modal logics where the modal operators of one logic may operate directly on the operators of the other logic. Different versions of this logic are investigated and various results about decidability and undecidability are presented. The main problem, however, decidability of the basic version of the logic, remains open.

Embedding defaults into terminological knowledge representation formalisms

We consider the problem of integrating Reiter's default logic into terminological representation systems. It turns out that such an integration is less straightforward than we expected, considering the fact that the terminological language is a decidable sublanguage of first-order logic. Semantically, one has the unpleasant effect that the consequences of a terminological default theory may be rather unintuitive, and may even vary with the syntactic structure of equivalent concept expressions. This is due to the unsatisfactory treatment of open defaults via Skolemization in Reiter's semantics. On the algorithmic side, we show that this treatment may lead to an undecidable default consequence relation, even though our base language is decidable, and we have only finitely many (open) defaults. Because of these problems, we then consider a restricted semantics for open defaults in our terminological default theories: default rules are applied only to individuals that are explicitly present in the knowledge base. In this semantics it is possible to compute all extensions of a finite terminological default theory, which means that this type of default reasoning is decidable. We describe an algorithm for computing extensions and show how the inference procedures of terminological systems can be modified to give optimal support to this algorithm.

BUILDING A FEDERATED RELATIONAL DATABASE SYSTEM: AN APPROACH USING A KNOWLEDGE-BASED SYSTEM

Due to the emerging interest in integrating different application environments, there have been many recent proposals for federated systems. In this paper, a federated system that permits the integration of heterogeneous relational databases using a terminological knowledge representation system is presented. In particular, two of the system's components: the translator and the integrator are explained in depth. The translator permits one to obtain a terminology from a relational schema, either semiautomatically, by expressing database properties, or manually, by using a set of predefined operations. In turn, the integrator generates a federated terminology by integrating several terminologies using the semantics expressed as correspondences between the data elements of different terminologies. Unlike many other approaches, the use of a terminological system permits us to obtain a semantically richer federated terminology and, at the same time, define a wider and more consistent integration process.

Decidable Reasoning in Terminological Knowledge Representation Systems

Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRSs. The new features studied, often required in practical applications, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability, subsumption and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.

Decidable reasoning in terminological knowledge representation systems

Terminological knowledge representation systems (TKRSs) are tools for designing and using knowledge bases that make use of terminological languages (or concept languages). We analyze from a theoretical point of view a TKRS whose capabilities go beyond the ones of presently available TKRSs. The new features studied, often required in practical applications, can be summarized in three main points. First, we consider a highly expressive terminological language, called ALCNR, including general complements of concepts, number restrictions and role conjunction. Second, we allow to express inclusion statements between general concepts, and terminological cycles as a particular case. Third, we prove the decidability of a number of desirable TKRS-deduction services (like satisfiability, subsumption and instance checking) through a sound, complete and terminating calculus for reasoning in ALCNR-knowledge bases. Our calculus extends the general technique of constraint systems. As a byproduct of the proof, we get also the result that inclusion statements in ALCNR can be simulated by terminological cycles, if descriptive semantics is adopted.

Attributive concept descriptions with complements

We investigate the consequences of adding unions and complements to attributive concept descriptions employed in terminological knowledge representation languages. It is shown that deciding coherence and subsumption of such descriptions are PSPACE-complete problems that can be decided with linear space.

Terminological reasoning is inherently intractable

Computational tractability has been a major concern in the area of terminological knowledge representation and reasoning. However, all analyses of the computational complexity of terminological reasoning are based on the hidden assumption that subsumption in terminologies reduces to subsumption of concept descriptions without a significant increase in computational complexity. In this paper it will be shown that this assumption, which seems to work in the “normal case,” is nevertheless wrong. Subsumption in terminologies turns out to be co-NP-complete for a minimal terminological representation language that is a subset of every useful terminological language.