Introduction to Description Logics Charlie Abela Department of Artificial Intelligence charlie.abela@um.edu.mt

Introduction to Description Logics © Last Lectures Introduced RDF and RDF Schema languages Problems? CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Lecture Outline Knowledge Representation Description Logics: an Overview Reasoning in DL Different Reasoners Suggested Reading list The Semantic Web was not coined in a vacuum. It has its roots in a number of well consolidated areas. Research about how to represent information that can be somehow machine processable has been tackled in the area of knowledge representation. Semantic networks and frames were predecessors of the languages that we are using in the Semantic Web today. We’ll start by taking a look that what knowledge representation is and how it is used in the Semantic Web. In particular we will look at Description logics, which is the underlying logic of a number of Semantic Web languages. I will give a very brief overview of reasoning that is possible with DLs and mention the most popular reasoners in use. CSA 3210 Introduction to Description Logics ©

Knowledge Representation Definitions: It is a part of AI that is concerned with how an agent uses what it knows in deciding what to do [Nardi, Brachman] The study of how to put knowledge into a form that a computer can reason with [Russell, Norvig] It is the study of how knowledge about the world can be represented and what kinds of reasoning can be done with that knowledge [Anonymous] Its all about encoding knowledge in such a way that computers/agents can use and reason with. CSA 3210 Introduction to Description Logics ©

Knowledge Representation Hypothesis Any mechanically embodied intelligent process will be comprised of structural ingredients that a) we as external observers naturally take to represent a propositional account of the knowledge that the overall process exhibits, and b) independent of such external semantical attribution, play a formal but causal and essential role in engendering the behaviour that manifests that knowledge [Smith, 1982]. A successful representation of some knowledge must: be in a form that is understandable by humans must cause the system using the knowledge to behave as if it knows it. To enforce these definitions, Smith states that an intelligent process must use knowledge representation whose form is understandable by humans and which causes the process to behave as if it knows what this knowledge means. CSA 3210 Introduction to Description Logics ©

Knowledge Based Systems printColor(snow):- !, write(“It’s white”). printColor(grass):- !, write(“It’s green”). printColor(sky):- !, write(“It’s yellow”). printColor(X):- write(”Beats me”). printColor(X):- color(X,Y), !, write(!It’s ”),write(Y), write(“.”). printColor(X):- write(“Beats me”). color(snow,white). color(sky,yellow). color(X,Y):- madeOf(X,Z), color(Z,Y). madeOf(grass,vegitation). color(vegetation,green). [from Brachman and Lavesque] Which knowledge base “knows” that for e.g. snow is white or that sky is yellow? CSA 3210 Introduction to Description Logics ©

Knowledge Based-Systems II 2nd program seems to have some desirable features: It is possible to add new tasks and easily make them depend on previous knowledge: e.g. adding a task to enumerate the objects of a given colour: coloredObjects(X,color(X,Y),Out). It is possible to extend the existing behaviour by adding more beliefs: e.g. adding canaries are yellow: color(canaries, yellow) debug faulty behaviour by locating erroneous beliefs of the system: e.g. change clause for the colour of the sky: color(sky, blue) concisely explain and justify the behaviour of the system: e.g. why did the system say that grass is green? grass is a form of vegetation: madeOf(grass,vegitation). vegetation is green: color(vegetation,green). A KB system should therefore, by design, have the ability to be told facts about the world and to adjust its behaviour accordingly CSA 3210 Introduction to Description Logics ©

Knowledge-Based Systems III Within a KB it is possible to differentiate between Intensional knowledge: general knowledge about the problem domain color(X,Y) or printColor(X) Extensional knowledge: knowledge which is specific to a particular scenario color(snow,white) or madeOf(grass, vegetation) CSA 3210 Introduction to Description Logics ©

Overview of Description Logics Description Logics (DLs) is the name given to a set of knowledge representation formalisms DLs represent knowledge of an application domain or world Define the relevant concepts of the domain Use these concepts to specify properties of objects and individuals occurring in the domain One main characteristic of DLs is their capability to provide reasoning Infer implicit knowledge from that explicitly defined in the knowledge base. CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Logical Structures Atomic Concepts (or Concepts): unary predicate symbols Atomic Roles: binary predicates, express relationship between concepts Operators (constructors): Individuals Instances of classes 2. characterizes the concept Parent as the set of individuals having at least one filler of the role hasChild belonging to the concept Person, moreover every filler of the role hasChild must be a person. 3. Union, intersection and complement operators are interpreted as set operations to describe: a Person that is not a Female or An individual that is either a Woman or a Male 4. The number restriction denotes the individuals having at least three children and at most two female relatives. CSA 3210 Introduction to Description Logics ©

Knowledge Representation in DL Intensional knowledge General knowledge about problem domain. A woman is a person and a female. TBox contains intensional knowledge in form of terminology. It is a concept definition: Extensional knowledge Specific knowledge related to a particular problem. Yanika is a female. ABox contains assertions about individuals, called membership assertion: A Knowledge Base (KB) is just a TBox and ABox CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Architecture of a DL KB TBox Description Language Reasoning ABox Knowledge Base Application Programs Rules CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Reasoning The basic inference on concept expressions in Description Logics is subsumption, typically written as Determining subsumption is the problem of checking whether the concept denoted by C (the subsumee) is a subconcept of D (the subsumer) If x is an instance of a class C, and C is a subclass of D, then we can infer that x is an instance of D Another typical inference on concept expressions is concept satisfiability (consistency) problem of checking whether a concept expression does not necessarily denote the empty concept. A special case of subsumption: in which the subsumer is the empty concept, meaning that a concept is not satisfiable. X instance of classes A and B, but A and B are disjoint This is an indication of an error in the ontology CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Uses for Reasoning Reasoning support is important for checking the consistency of the knowledge base and the knowledge itself checking for unintended relationships between classes automatically classifying instances in classes Checks like the preceding ones are valuable for designing large ontologies, where multiple authors are involved integrating and sharing ontologies from various sources CSA 3210 Introduction to Description Logics ©

DL Reasoning Algorithms Earliest algorithms targeted subsumption and where called structural comparisons Transform two input concepts into labelled graphs and test whether one could be embedded into the other The embedded graph corresponds to the more general concept (ie the subsumer) Tableau algorithms are focused on satisfiability other reasoning problems like subsumption, can be solved by first reducing them to satisfiability Concepts are negated and iterative checks for clashes (contradictions) are performed If no clashes are found then concept is satisfiable else it is unsatisfiable CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Different Reasoners FaCT++: a hybrid reasoner, is an optimised version of the original FaCT (Horrocks 1998) Has a very efficient and optimized T-Box reasoning engine distributed under a GPL license Racer: state-of-the art TBox DL reasoner however it is only free for universities and research labs source code not publicly available Pellet based on the tableau algorithms developed for expressive DLs Features: Ontology analysis and repair Entailment: entailment is the key inference Queries are based on Jena’s RDQL CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Suggested Reading D. Nardi, R. J. Brachman. An Introduction to Description Logics, Cambridge University Press, 2002, http://www.inf.unibz.it/~franconi/dl/course/dlhb/dlhb01.pdf (pgs 1-30) CSA 3210 Introduction to Description Logics ©

Introduction to Description Logics © Next Lecture Ontologies Basic components Ontology engineering Examples CSA 3210 Introduction to Description Logics ©