Logics for Data and Knowledge Representation Applications of ClassL: Lightweight Ontologies

Outline  Ontologies  Descriptive and classification ontologies  Real world and classification semantics  Lightweight Ontologies  Converting classifications into Lightweight Ontologies  Applications on Lightweight Ontologies  Document Classification  Query-answering  Semantic Matching 2

Ontologies  Ontologies are explicit specifications of conceptualizations [Gruber, 1993]  They are often thought of as directed graphs whose nodes represent concepts and whose edges represent relations between concepts 3 Animal BirdHeadMammal PredatorHerbivore GoatTiger Chicken Cat Is-a Eats Is-a Part-of Is-a Eats Body Part-of ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Concepts and Relations between them  CONCEPT: it represents a set of objects or individuals  EXTENSION: the set above is called the concept extension or the concept interpretation  Concepts are often lexically defined, i.e. they have natural language names which are used to describe the concept extensions (e.g. Animal, Lion, Rome), often with an additional description (gloss)  RELATION: a link from the source concept to the target concept  The backbone structure of an ontology graph is a taxonomy in which the relations are ‘is-a’, ‘part-of’ and ‘instance-of’, whereas the remaining structure of the graph supplies auxiliary information about the modeled domain and may include relations like ‘located-in’, ‘eats’, ‘ant’, etc. They are respectively called hierarchical (BT/NT) and associative (RT) relations in Library Science. 4 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Ontology as a graph: a mathematical definition 5  An ontology is an ordered pair O =  V is the set of vertices describing the concepts  E is the set of edges describing relations Animal BirdHeadMammal PredatorHerbivore GoatTiger Chicken Cat Is-a Eats Is-a Part-of Is-a Eats Body Part-of ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Tree-like Ontologies  Take the ontology in the previous slide and remove those auxiliary relations…  … we get a tree-like ontology consisting of its backbone structure with ‘is-a’ and ‘part-of’ relations (*), that is an informal lightweight ontology. (*) Notice that in some cases we can obtain more complex structures like DAGs or even with cycles 6 Animal BirdHeadMammal PredatorHerbivore GoatTiger Chicken Cat Is-a Part-of Is-a Body Part-of ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

o Classification ontologies They are used to classify things, such as books, documents, web pages, etc.; the purpose is to provide domain specific terminology and organize individuals accordingly. Such ontologies usually take the form of classifications with (BT\NT\RT) or without explicit relations. o Descriptive ontologies They are used to describe a piece of world, such as the Gene ontology, Industry ontology, etc.; the purpose is to offer an unambiguous description of the world. Relations are typically explicit (e.g. is-a) and can be of any kind. Classification vs. Descriptive Ontologies ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

o Classification ontologies are in classification semantics In classification ontologies, the extension of each concept (label of a node) is the set of documents about the entities or individual objects described by the label of the concept. For example, the extension of the concept animal is “the set of documents about animals” of any kind. o Descriptive ontologies are in real world semantics In descriptive ontologies, concepts represent real world entities. For example, the extension of the concept animal is the set of real world animals, which can be connected via relations of the proper kind. Classification vs. Real World semantics ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Classification ontologies ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Descriptive ontologies ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Why ‘Lightweight’ Ontologies?  The majority of existing ontologies are ‘simple’ taxonomies or classifications, i.e., hierarchically organized categories used to classify resources.  Ontologies with arbitrary relations do exist, but no intuitive and efficient reasoning techniques support such ontologies in general. … so we need ‘lightweight’ ontologies. 11 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Lightweight Ontologies  A (formal) lightweight ontology is a triple O = where:  N is a finite set of nodes,  E is a set of edges on N, such that is a rooted tree,  C is a finite set of concepts expressed in a formal language F, such that for any node n i ∈ N, there is one and only one concept c i ∈ C, and, if n i is the parent node for n j, then c j ⊑ c i. NOTE: lightweight ontologies are in classification semantics 12 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Converting tree-like structures into LOs  For a descriptive ontology, the backbone taxonomy of ‘is-a’ and ‘instance-of’ is intuitively coincident with the subsumption (‘ ⊑ ’) relation in LOs. NOTE: ‘part-of’ relations correspond to subsumption only if transitive. For instance the following chain cannot be translated: handle part-of door part-of school part-of school system  For a classification ontology, the extension of each node is the set of documents (books, websites, etc.) that should be classified under the node. Therefore, the links has to be interpreted as ‘subset’ relations and can be transformed directly into subsumption in the target LOs. 13 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Descriptive and classification ontologies Animal Vertebrate Mammal A B D Invertebrate C E Bird is-a (a) World Europe France A B D Asia C E Italy part-of F Rome part-of (b)  (a) and (b) are two descriptive ontologies. The corresponding classification ontologies are obtained by substituting all the relations with ‘subset’.  (a) and (b) can be converted into lightweight ontologies by substituting the relations into subsumptions. However, the semantics changes from real world to classification semantics. ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES 14

Populated (Lightweight) Ontologies  In Information Retrieval, the term classification is seen as the process of arranging a set of objects (e.g., documents) into a set of categories or classes.  A classification ontology is said populated if a set of objects has been classified under ‘proper’ nodes.  Thus a populated (lightweight) ontology includes (explicit or implicit) ‘instance-of’ relations 15 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Example of a Populated Ontology 16 ⊑⊑ Head Body Animal BirdMammal PredatorHerbivore GoatTiger Chicken Cat ⊑⊑ ⊑⊑⊑ ⊑ ⊑⊑ ‘Chicken Soup’ ‘How to Raise Chicken’ ‘Tom and Jerry’‘ Instance-of ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Lightweight Ontologies in ClassL: TBox  Subsumption terminologies. Recall: ‘… C is a finite set of concepts expressed in a formal language F, such that for any node n i ∈ N, there is one and only one concept c i ∈ C, and, if n i is the parent node for n j,then c j ⊑ c i.’ 1. Bird ⊑ Animal 2. Mammal ⊑ Animal 3. Chicken ⊑ Bird 4. Cat ⊑ Predator 5. … NOTE: a tree-like ontology can be transformed into a lightweight ontology, but not vice versa. This is because we loose information during the translation. 17 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Populated LOs in ClassL: TBox + ABox  ‘instance-of’ links are encoded into ‘concept assertions’: 1. Chicken(ChickenSoup) 2. Cat(TomAndJerry) 3. …  Instances are the elements of the domain, namely the documents classified in the categories. 18 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Classifications are:  Easy to use for humans  Pervasive (Google, Yahoo, Amazon, our PC directories, folders, address book, etc.).  Largely used in commercial applications (Google, Yahoo, eBay, Amazon, BBC, CNN, libraries, etc.).  Have been studied for very long time (e.g., Dewey Decimal Classification system - DDC, Library of Congress Classification system - LCC, etc.). 19 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Classification Example: Yahoo! Directory 20 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Classification Example: Folders 21 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Classification Example: E-Commerce Category 22 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Label Semantics  Natural language words are often ambiguous E.g. Java (an island, a beverage, a programming language)  When used with other words in a label, improper senses can be pruned E.g., “Java Language” – only the 3 rd sense of Java is preserved  We translate node labels into unambiguous propositions in ClassL in classification semantics  This can be done by using NLP (Natural Language Processing) techniques 23 Level 4 Subjects Computers and Internet … … … … … … … (1) (3) (5) (7) (8) Programming Java Language Java Beans ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Link semantics  Get-specific principle: Child nodes in a classification are always considered in the context of their parent nodes. As a consequence they specialize the meaning of the parent nodes.  Subsumption relation (a): the extension of the child node is a proper subset of the parent node. The meaning of node 2 is B.  General intersection relation (b): the extension of the child node is a subset of the parent node. The meaning of node 2 is C = A ⊓ B.  We generalize to (b). The meaning of the node is what we call the concept at node A B ? A B A B C (b)(a) ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Concept at node Wine and Cheese Italy Europe Austria Pictures In ClassL: C 4 = C europe ⊓ C pictures ⊓ C italy 25 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Document Classification  Document concept: each document d in a classification is assigned a proposition C d in ClassL, build from d in two steps: 1. keywords are retrieved from d by using standard text mining techniques. 2. keywords are converted into propositions by using the methodology discussed above to translate node labels.  Automatic classification: For any given document d and its concept C d we classify d in each node n i such that: 1. ⊨ C d ⊑ C i, 2. and there is no node n j (j ≠ i), for which ⊨ C j ⊑ C i and ⊨ C d ⊑ C j. In other words we always classify in the node with the most specific concept. 26 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Query-answering  Query-answering on a hierarchy of documents based on a query q as a set of keywords is defined in two steps: 1. The ClassL proposition C q is build from q by converting q’s keywords as said above. 2. The set of answers (retrieval set) to q is defined as a set of subsumption checking problems in ClassL: A q = {d ∈ document | T ⊨ C d ⊑ C q } 27 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

Semantic Matching: Why?  Most popular knowledge can be represented as graphs. The heterogeneity between knowledge graphs demands the exposition of relations, such as semantically equivalent.  Some popular situations that can be modeled as a matching problem are:  Concept matching in semantic networks.  Schema matching in distributed databases.  Ontology matching (ontology “alignment”) in the Semantic Web. ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES 28

The Matching Problem  Matching Problem: given two finite graphs, finds all nodes in the two graphs that syntactically or semantically correspond to each other.  Given two graph-like structures (e.g., classifications, XML and database schemas, ontologies), a matching operator produces a mapping between the nodes of the graphs.  Solution: A possible solution [Giunchiglia & Shvaiko, 2003], consists in the conversion of the two graphs in input into lightweight ontologies and then matching them semantically. 29 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES

A Matching Problem ? ? ? 30 ONTOLOGIES :: LIGHTWEIGHT ONTOLOGIES :: CLASSIFICATIONS :: APPLICATIONS ON LIGHTWEIGHT ONTOLOGIES