Logics for Data and Knowledge Representation

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Logics for Data and KnowledgeRepresentation

• Applications of ClassL Lightweight Ontologies

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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

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Ontologies
ONTOLOGIES LIGHTWEIGHT ONTOLOGIES
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• 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

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Concepts and Relations between them
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• 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.

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Ontology as a graph a mathematical definition
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• An ontology is an ordered pair
• O ltV, Egt
• V is the set of vertices describing the concepts
• E is the set of edges describing relations

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Tree-like Ontologies
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• 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

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ONTOLOGIES LIGHTWEIGHT ONTOLOGIES
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Classification vs. Descriptive Ontologies

• 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.
• 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.

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ONTOLOGIES LIGHTWEIGHT ONTOLOGIES
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Classification vs. Real World semantics

• 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.
• 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.

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ONTOLOGIES LIGHTWEIGHT ONTOLOGIES
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Classification ontologies
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ONTOLOGIES LIGHTWEIGHT ONTOLOGIES
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Descriptive ontologies
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Why Lightweight Ontologies?
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• 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.

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Lightweight Ontologies
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• A (formal) lightweight ontology is a triple
• O ltN,E,Cgt
• where
• N is a finite set of nodes,
• E is a set of edges on N, such that ltN,Egt is a
  rooted tree,
• C is a finite set of concepts expressed in a
  formal language F, such that for any node ni ? N,
  there is one and only one concept ci ? C, and, if
  ni is the parent node for nj, then cj ? ci.
• NOTE lightweight ontologies are in
  classification semantics

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Converting tree-like structures into LOs
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• 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.

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Descriptive and classification ontologies
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• (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.

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Populated (Lightweight) Ontologies
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• 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

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Example of a Populated Ontology
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Animal
?
?
?
?
Head
Body
Bird
Mammal
?
?
?
Predator
Herbivore
Chicken
Instance-of
?
?
?
Chicken Soup
Instance-of
Goat
Tiger
Cat
How to Raise Chicken
Instance-of
Instance-of
Instance-of
Tom and Jerry
www.protectTiger.org

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Lightweight Ontologies in ClassL TBox
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• Subsumption terminologies. Recall
• C is a finite set of concepts expressed in a
  formal language F, such that for any node ni?N,
  there is one and only one concept ci?C, and, if
  ni is the parent node for nj ,then cj ? ci.
• Bird ? Animal
• Mammal ? Animal
• Chicken ? Bird
• Cat ? Predator
• 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.

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Populated LOs in ClassL TBox ABox
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• instance-of links are encoded into concept
  assertions
• Chicken(ChickenSoup)
• Cat(TomAndJerry)
• Instances are the elements of the domain, namely
  the documents classified in the categories.

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Classifications are
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• Easy to use for humans
• Pervasive (Google, Yahoo, Amazon, our PC
  directories, email 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.).

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Classification Example Yahoo! Directory
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Classification Example Email Folders
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Classification Example E-Commerce Category
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Label Semantics
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Level

• 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 3rd 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

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Link semantics
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• 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.

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Concept at node
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In ClassL C4 Ceurope ? Cpictures ? Citaly
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Document Classification
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• Document concept each document d in a
  classification is assigned a proposition Cd in
  ClassL, build from d in two steps
• keywords are retrieved from d by using standard
  text mining techniques.
• 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 Cd we classify d in each node
  ni such that
• ? Cd ? Ci,
• and there is no node nj (j ? i), for which ? Cj ?
  Ci and ? Cd ? Cj.
• In other words we always classify in the node
  with the most specific concept.

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Query-answering
ONTOLOGIES LIGHTWEIGHT ONTOLOGIES
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• Query-answering on a hierarchy of documents based
  on a query q as a set of keywords is defined in
  two steps
• The ClassL proposition Cq is build from q by
  converting qs keywords as said above.
• The set of answers (retrieval set) to q is
  defined as a set of subsumption checking problems
  in ClassL
• Aq d ? document T ? Cd ? Cq

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Semantic Matching Why?
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• 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.

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The Matching Problem
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• 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.

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A Matching Problem
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