1. mathematical logic

first order predicate logic、description logic

description logic

  • element

    • individuals: seu, jack, etc.
    • concepts: Person, Course, Student, etc.
    • roles: hasFather, attends, etc

  • constituents

    | Terminological Box | Assertion Box |
    | :————————: | :————————: |
    | ontology,抽象的类 | ground facts，实例 |

  • ALC，the simplest DL

    | ⊤ | ⊥ | ⊓ | ⊔ | ¬ | ∀ | ∃ |
    | :—: | :—: | :—: | :—: | :——: | :—: | :—: |
    | 全集 | 空集 | 与 | 或 | 非(补) | 任意 | 存在 |

    1. ⊤, ⊥ are concepts
    2. for concepts C/D, ¬C, C⊓D, C⊔D are concepts
    3. for a role r and a concept C, ∀r.C and ∃r.C are concepts

    | TBox | ABox |
    | :————————————————————————-: | :—————: |
    | consist of a set of GCIs(general concept inclusion) | C(a)、r(a,b) |

  • Interpretation

    a DL interpretation I consists of a domain△^I and a function·^I .

    image-20230129190730766

    将ALC转化为Interpretation

    1. 定义全集△，要求individual、concept和role在全集中都有对应的实例。
    2. 进行所有元素的实例映射。

    e.g.image-20230129215904011

  • 一些概念

    • satisfiable: a set of axioms has a model
    • inconsistent: does not have a medel,一般是因为模型有误
    • incoherent: 如果一个命名的class必须是空集才满足模型

2. production rules

If A Then B (CF=[0,1]), A→B;

CF: Certainty Factor 置信度

3. semantic network

use human language to label nodes and links.

XML(eXtensible Markup Language )

  • Origins from SGML（标准通用标记语言）⇨ HTML（超文本标记语言）

    HTML注重文本的格式

    e.g. <i>This book</i> has the title <b>KG</b>

    ​ This book has the title KG

  • designed for data exchange

  • XML Syntax

    1. each XML document begin with a declaration containing version number and character encoding (default: Unicode)

      example: <?xml version="1.0" encoding="GB2312"?>

    2. case-sensitive <CITY>≠<City>≠<city>

    3. arbitrarily nested 任意嵌套

    4. empty element can be abbreviated

      example: <year></year>=<year/>

    5. the outermost element is called root element

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      <author>
          <firstName>Jennifer</firstName>
          <lastName>Wu</lastName>
          <email>2050407179@qq.com</email>
          This is some text inside an XML element
      </author>

    6. an attribute is a name-value pair separated by “=”

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      <author email="2050407179@qq.com">
          <firstName>Jennifer</firstName>
          <lastName>Wu</lastName>
          This is some text inside an XML element
      </author>

      ps. 元素不能重复、属性值必须在“ ”中间、根节点存在且唯一

    7. XML Pre-defined Entities

      • HTML 嵌入XML

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        <artical>
            <paragraph>
                <html>
                    <head><title></title></head>
                    <body>
                        <h1>SEU</h1>
                    </body>
                </html>
            </paragraph>
        </artical>

      • 将HTML看为纯文本

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        <artical>
            <paragraph><![CDATA[
                <html>
                    <head><title></title></head>
                    <body>
                        <h1>SEU</h1>
                    </body>
                </html>]]>
            </paragraph>
        </artical>

  • XML Namespaces

    为防止元素名称相同但实际内容不同，添加前缀

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    <table>
        <tr>
            <td>Apples</td>
            <td>Bananas</td>
        </tr>
    </table>
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    <table>
        <name>Coffee Table</name>
        <width>80</width>
        <length>120</length>
    </table>

    添加xmlns

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    <table xmlns="http://www.w3.org/TR/html4/">
        <tr>
            <td>Apples</td>
            <td>Bananas</td>
        </tr>
    </table>
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    <table xmlns="https://www.w3schools.com/furniture">
        <name>Coffee Table</name>
        <width>80</width>
        <length>120</length>
    </table
International Resource Indentifer Uniform Resource Identifier Uniform Resource Locator
IRIs(范围max) URIs URLs
uses Unicode for more languages only uses English characters has a location on the WWW

URI(IRI) format: URI = scheme:[//authority]path[?query] [#fragment]

scheme: type of URI. e.g. http,ftp,file

authority: typically a domain name

path: file system name

query: provides non-hierarchical

  • XML Schema

    一些关于XML的规范。

RDF

a data modle about triples: ( subject, predicate, object)

QName:将长长的URI简化成短的名字

​ e.g. 令foo=http://example.com/ ，那么foo: bar 也就是http://example.com/bar

RDF Triple

subject——predicate——>object

subject: resource/blank node

predicates: resource

object: resource/literal/blank node

一些格式：

"Beantown"^^xsd:string

"France"@en

"France"@fr

"法国"@zh

"001"^^xsd: intenger = "1"^^xsd: intenger

"123.0"^^xsd:decimal="123"^^xsd:intenger

Blank node: unnamed resource e.g. _:x

  • RDF Syntax

  1. Turtle

    • <S><P><O>.(IRIs在<>中，string在””中)
    • 空格被忽略

    e.g.

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    <http://dbpedia.org/resource/Massachusets> <http://example.org/terms/capital> <http://dbpedia.org/resource/Boston>.
    <http://dbpedia.org/resource/Massachusets> <http://example.org/terms/nickname> "The bay station".
    <http://dbpedia.org/resource/Boston> <http://example.org/terms/inState> <http://dbpedia.org/resource/Massachusets>.
    <http://dbpedia.org/resource/Boston> <http://example.org/terms/nickname> "Beantown".
    <http://dbpedia.org/resource/Boston> <http://example.org/terms/population> "642109"^^xsd:integer.

    use Qname

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    @prefix db:<http://dbpedia.org/resource/>
    @prefix dbo:<http://example.org/terms/>

    db:Massachusets dbo:capital db:Boston.
    db:Massachusets dbo:nockname "The bay station".
    db:Boston dbo:inState db:Massachusets.
    db:Boston dbo:nickname "Beantown".
    db:Boston dbo:population "642109"^^xsd:integer.

    use “;” and “,”

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    @prefix db:<http://dbpedia.org/resource/>
    @prefix dbo:<http://example.org/terms/>

    db:Massachusets dbo:capital db:Boston;
                    dbo:nockname "The bay station".
    db:Boston dbo:inState db:Massachusets;
              dbo:nickname "Beantown";
              dbo:population "642109"^^xsd:integer.

  2. RDF/XML

RDFS

ex:book rdf:type rdfs:Class.

性质： transitive、reflective

ex:TextBook rdfs:subClassOf ex:Book.

ex:happilyMarriedWith rdfs:subPropertyOf ex:marriedWith.

ex:isMarriedTo rdfs:domain ex:Person.

ex:isMarriedTo rdfs:range ex:Person.

image-20230128202044499

OWL

RDFS缺陷：不能形容互斥的关系、不能对某一项有数目的限制，比如父亲只能有一个、缺少对相等的定义

exp:Athlete owl:equivalentClass exp:SportsPlayer.

exp:obtain owl:equivalentProperty exp:acquire.

exp:SportsPlayerA owl:sameAS exp:Thomas.

exp:Man owl:disjointWith exp:Woman.

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exp:Mother rdf:type owl:class;
           owl:intersectionOf(exp:Woman exp:Parent).
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exp:Parent rdf:type owl:class;
           owl:unionOf(exp:Mother exp:Father).
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exp:LivePerson rdf:type owl:class;
               owl:complementOf exp:DeadPerson.
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ex:friendOf rdf:type owl:ObjectProperty.
ex:age      rdf:type owl:DataProperty.
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exp:ancestor  rdf:type owl:TransitiveProperty
exp:friendOf  rdf:type owl:SymmetricProperty
exp:hasMother rdf:type owl:FunctionalProperty
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exp:ancestor owl:inverseOf exp:descendant
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exp:Person rdf:type owl:Restriction;
           owl:onProperty exp:hasMother;
           owl:allValuesFrom exp:Woman.
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exp:SemanticWebPapers rdf:type owl:Restriction;
                      owl:onProperty exp:PublishedIn;
                      owl:someValuesFrom exp:AAAIPaper.

Some of the Semantic Web paper were published in AAAI.

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exp:Person rdf:type owl:Restriction;
           owl:onProperty exp:hasParent;
           owl:cardinality "2"^^xsd:integer.