
39254f1ab1ab4baf3e44446ff22133ee.ppt
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Logics for Data and Knowledge Representation Lightweight Ontologies
Outline q Classifications q Lightweight Ontologies (LO): q Labels q Links q Document Classification q Query-answering on LOs. 2
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Classifications… q q q 4 Classifications hierarchies are easy to use. . . for humans. Classifications hierarchies are pervasive (Google, Yahoo, Amazon, our PC directories, email folders, address book, etc. ). Classifications hierarchies are largely used in industry (Google, Yahoo, e. Bay, Amazon, BBC, CNN, libraries, etc. ).
Classifications. . more q q q 5 Classification hierarchies have been studied for very long (e. g. , Dewey Decimal Classification system -- DCC, Library of Congress Classification system –LCC, etc. ). Classifications hierarchies are lightweight (no roles, trees or simple DAGs, …). Classification hierarchies are a kind of concept hierarchies.
Example q Data Instance of John 6 Instance of Fred Instance of Be. Safe Inc. instances of the concept (class) “Developers” are: John, Fred. q A data instance of “Associations” is: Be. Safe Inc. q We define a class instances as the data instance of a class.
In Classification Hierarchies q q 7 Labels are natural language sentences; useful but hard to deal with in an automated way. Links are of the kind “child-of” (e. g. “economy child-of Europe”), where in an ontology you would have, (instance-of}, or roles, or {is-a} links. Main Problem: No clear semantics for both labels at nodes and links. … we need ontologies for reasoning
Outlines q Classification q Lightweight Ontology (LO): q Labels q Links q Document Classification q Query-answering on LOs. 8
Ontology q Ontologies are explicit specifications of conceptualizations. q The notion of concept is understood as defined in Knowledge Representation, i. e. , as a set of objects or individuals. q There are numerous provers offering services for reasoning about ontologies (Fa. CT++, Pellet, KOAN…). 9
Example of an ontology 10
Ontology as a graph q Ontology: a description of the concepts and relationships in the domain of interest. q They are often thought of as directed graphs whose nodes represent concepts and whose arcs represent relations between concepts. q A mathematical definition comes from ‘graph’, an ontology is an ordered pair O=
L. O, Refinement of Ontology q But there are two observations: 1. Majority of existing ontologies are ‘simple’ taxonomies or classifications, i. e. , categories to classify resources. 2. Ontologies with ‘complex’ relations do exists, but no intuitively reasoning techniques supports such ontologies in general. … so we need ‘lightweight’ ontologies. 12
Example of an Lightweight Ontology Europe 1 Pictures Italy 13 2 3 4 5 Wine and Cheese Austria
Lightweight Ontologies q Ontologies are explicit specifications of conceptualizations. q A (formal) lightweight ontology is a triple O =
From Classifications to Lightweight Ontologies q We know that a lightweight ontology is a formal conceptualization of a domain in terms of concepts and {is-a, instance-of} relationships. q Lightweight ontologies (LOs) add a formal semantics and {instance-of} relationships to classification hierarchies. q In 15 short: LOs make classifications formal!
Lightweight Ontologies and Classification q q q 16 Classification hierarchies are semi-formal, so we need (lightweight) ontologies to automatically reason about classification. A theory of Lightweight Ontology is needed for building the bridge from classifications to simple, i. e. , “lightweight” ontologies. One result: Onto 2 Class, Class 2 Onto operators.
Lightweight Ontologies and Class Logic q The logic of classes (Class. L) provides a formal language (syntax + semantics) to model lightweight ontologies, where: q concepts are modeled by propositions; q {is-a, instance-of} relationships are modeled, respectively, by subsumption (⊑) and class-propositions (i. e. , wffs like P(a)). q An ontology represented by Class. L is a lightweight ontology. 17
Lightweight Ontologies q. A Lightweight Ontology (LO) is a rooted tree, where each node is assigned a label represented by a proposition in Class. L. q. A Lightweight Ontology provides for q formalizing the meaning of labels, and q formalizing the meaning of links q Both 18 formalizations come from Class. L!
Outline q Classification q Lightweight Ontology (LO): q Labels q Links q Document Classification q Query-answering on LOs. 19
Label Semantics q q 20 Natural language words are often ambiguous. E. g. Java (an island, a beverage, an OO programming language) When used with other words in a label, wrong senses can be pruned. E. g. , “Java Language” – only the 3 rd sense of Java is preserved. Level Subjects 0 (1) 1 … Computers and Internet … Programming (5) … … Java Language (7) … Java Beans (8)… … (3) 2 3 4
From NL Labels to Labels in Class Logic q Several approaches to rewrite a natural language label into a Class. L proposition. q Following (Giunchiglia et al. , 2007), we may distinguish four steps: 1. Tokenization (get distinct words); Italian Pictures ‘Italian’, ‘Pictures’ Words stemming (get to a basic form); 2. Pictures picture Rewrite each word into its proposition; 3. picture-noun-1⊓picture-noun-2⊓…⊓picture-verb-2 Prune inconsistent senses. 4. picture-noun-1⊓picture-noun-2⊓…⊓picture-verb-2 picture. N 1 21
Class Logic Label Eamples q E. g. 1: “Java” becomes the proposition Java#1 ⊔ Java#2 ⊔ Java#3 where Java#i is a propositional variable representing the ith-sense of the word “Java” according to a dictionary (e. g. , Word. Net). q E. g. 2: “Java Beans” becomes: (Java#1 ⊔ Java#2 ⊔ Java#3)⊓(Bean#1 ⊔ Bean#2) 22
Advantages of Propositions q NL labels are ambiguous, propositions are NOT! q Extensional semantics of propositions naturally maps nodes to real world objects. q Labels as propositions allow us to deal with the standard problems in classification (e. g. , document classification, query-answering, and matching) by means of Class. L’s reasoning, mainly the SAT problem. 23
Outline q Classification q Lightweight Ontology (LO): q Labels q Links q Document Classification q Query-answering on LOs. 24
Formalizing the Meaning of Links (1) q Child nodes in a classification are always considered in the context of their parent nodes. q Child nodes therefore specialize the meaning of the parent nodes. q Contextuality property of classifications. 25
Formalizing the Meaning of Links (2) q. General intersection relationship(a): can be used to represent facets. The meaning of node 2 is C = A ⊓ B. q. Subsumption relationship (b): child nodes are specific case of the parent nodes. The meaning of node 2 is B. 26 A 1 ? B 2 A C A B B (a) (b)
General Intersection Example l 1 = “Subjects” l 3 = “Computers and Internet” computer hardware programming software networking … 27 l 5 = “Programming” scheduling, planning
Concept at a Node q Parental contextuality is formalized in Class. L by the notion of “concept at a node. ” q. A concept Cr at the root node r is the class proposition (label) used to denote the node. q. A concept Ci at a node ni is the conjunction of a proposition Pi (label of ni) and the concept Cj at node nj parent to ni (if it has any parents). In Class. L: Pi ⊓ Cj. 28
Concept at a Node q. A concept at a node ni can be computed as the conjunction of all the labels from the root of the classification hierarchy to ni. q Concepts at nodes capture the classification semantics by using the meaning of labels (propositions defined by using Word. Net and a linguistic analysis) and the nodes' position. 29
Concept at a Node: Example Europe 1 Pictures 2 3 Wine and Cheese Italy 4 5 Austria In Class. L: C 4 = Ceurope ⊓ Cpictures ⊓ Citaly 30
What have we done? q Calculate the concepts and label and concept at nodes. q In which format? Class. L Java#1 ⊔ Java#2 ⊔ Java#3 Ceurope ⊓ Cpictures ⊓ Citaly … q We 31 have build the Class. L formulas for each node!
Outline q Classification q Lightweight Ontology (LO): q Labels q Links q Document Classification q Query-answering on LOs. 32
Document Classification q q 33 Each document d in a classification is assigned a proposition Cd in Class. L. Cd is called document concept. Cd is build from d in two steps: q keywords are retrieved from d by using standard text mining techniques. q keywords are converted into propositions by using methodology discussed above.
Document Classification “Get specific” Rule q For any given document d and its concept Cd we classify d in each node ni such that: 1. |= Ci ⊒ Cd (i. e. the concept at node ni is more general than Cd); and there is no node nj (j ≠ i), whose concept at node Cj is more specific than Ci and more general than Cd: |= Cj ⊑ Ci and |= Cj ⊒ Cd. 2. 34
Example q q q Suppose we need to classify “Professional Java, JDK-5 th Edition” by W. Clay Richardson et al. The document concept of such document d is: Cd = Java#3⊓ Programming#2. The node 7 is the only node which conforms to the “get specific” rule. 35 Level Subjects 0 (1) 1 Business and Investing (2) … Computers and Internet Small Business and Entrepreneurship (4) … Programming (5) … New Business Enterprises (6) … Java Language (7) … Java Beans (8)… … (3) 2 3 4
Example (cont’) q q q Suppose we need to classify “Visual Basic. Net Programming for Business” by Philip A. Koneman. The document concept of such document d is: Cd = Visual. Basic. Net#1⊓ Programming#2⊓ Business#1 The nodes 2, 5 conform to the “get specific” rule. 36 Level Subjects 0 (1) 1 Business and Investing (2) … Computers and Internet Small Business and Entrepreneurship (4) … Programming (5) … New Business Enterprises (6) … Java Language (7) … Java Beans (8)… … (3) 2 3 4
What have we done by far? q Classify documents. q How? q Get specific algorithm! q But how to implement the algorithm? Class. L! We are reasoning with the ‘Concept Realization’ service of Class. L! (With an empty ABox. ) 37
Outline q Classification q Lightweight Ontology (LO): q Labels q Links q Document Classification q Query-answering on LOs. 38
Classifying q Query-answering on a classification hierarchy of documents based on a query q as a set of keywords is defined in two steps: 1. The proposition Cq 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 SAT problem in Class. L: Aq =df {d∈ document | |= Cd ⊑ Cq}. 39
Query-Answering: A Problem q q q 40 Searching on all the documents may be expensive (millions of documents classified). We define a set of nodes which contain only answers to a query q as follows: Nsq =df {ni node| |= Ci ⊑ Cq} Remark: Each document d in ni in Nsq is an answer to the query q, since |= Cd ⊑ Ci by definition of classification. Thus all the documents d in Nsq ⊆ Aq.
Query-Answering: Classification Set q We extend Nsq (called sound classification answer) by adding a set of nodes (called query classification set) defined as: Clq =df {ni node | d ∈ni and |= Cd ≡ Cq} q i. e. , the nodes which constitute the classification set of a document d, whose concept Cd is equivalent to C q. 41
Query-Answering: Sound Answer Set q The set of answers (retrieval set) to q is finally defined as the following set: Asq =df {d ∈ ni | ni ∈ Nsq} ∪ {d ∈ ni | ni ∈ Clq and |= Cd ⊑ Cq}. q Under this definition, an answer to a query are documents from nodes whose concepts are more specific than the query concept. 42
Example q q q Suppose that a user makes a query q, which is converted into Cq = Java#3⊓Cobol#1, where Cobol#1 is “common business-oriented language. ” It can be shown that Nsq = {7, 8}. Exercise: show it. 43 Level Subjects … 0 (1) Computers and Internet (3) 1 2 Programming (5) … N sq Java Language (7) … N sq Java Beans (8)… 3 4
Example (cont’) q q q Level It can be shown that Nsq = {7, 8}. “Java for COBOL programmers, 2 nd ed. ” is classified in node 2, so it is not an aswer by using only Nsq = {7, 8}. We then consider Clq to compute more answers, among others are the documents in node 5. 44 Subjects … Clq 0 (1) Computers and Internet (3) 1 2 Programming (5) … Java Language (7) … Java Beans (8)… 3 4
Sound Answer Set: Remark q The set Asq is sound (i. e. , contains answers to q), but not complete (i. e. , does not contain all the answers to q). European Union Pictures d q See 45 the next example. (1) (2)
Sound Answer Set Example q Suppose that a user makes a query q like “video or pictures of Italy, ” which is converted into Cq = Italy#1⊓ (Video#2⊔Pictures#1). q Cq is equivalent to: Cq 1 = Video#2⊓Italy#1, Cq 2 = Pictures#1⊓Italy#1. 46 European Union Pictures d (1) (2)
Sound Answer Set Example (cont’) q But not |= C 2 ⊑ C 1 q, hence a document d in 2 about Rome, with Cd = Pictures#1⊓Rome#1 European Union Pictures is not retrieved, since: Nsq = {ni |= Ci ⊑ Cq} = Clq ={1}, so d ∉ Asq. (Asq is not complete) 47 ∅ and d (1) (2)
Final Remarks q The edge structure of a LO is not considered neither for document classification nor for query answering. q The edges information becomes redundant, as it is implicitly encoded in the “concept at a node” notion. q There are more than one way to build a LO from a set of concepts at nodes. 48
What have we done in Query Answering? q Find the set of documents. q How? q Find q But the concept that is subsumed by the query. how to implement it? Class. L! We are reasoning with the ‘Concept subsumption’ service of Class. L! 49
References & Credits q References: F. Giunchiglia, M. Marchese, I. Zaihrayeu. “Encoding Classifications into Lightweight Ontologies. ” J. of Data Semantics VIII, Springer-Verlag LNCS 4380, pp 57 -81, 2007. 50