FoCL, Chapter 22: Database semantics 389

22. Database semantics

22.1 Database metaphor of natural communication

22.1.1 Interaction with a conventional database

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22.1.2 Interaction between speaker and hearer

[figure: .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; .; H; moment of time t2; t1; database; hearer; speaker; S]
\begin{matrix}c \\ ◯ \end{matrix}1999 Roland Hausser

22.1.3 DB interaction and NL communication

• entities involved Database interaction: takes place between two different entities, the user and the database. NL communication: takes place between two similar and equal cognitive agents, the speaker and the hearer.

• Origin of control Database interaction: operations of input and output are controlled by the user. NL communication: there is no user. Instead, the cognitive agents control each other by alternating in the speaker- and the hearer-mode (turn taking).

• Method of control Database interaction: user controls the operations of the database with a programming language the commands of which are executed as electronic procedures. NL communication: speaker controls language production as an autonomous agent, coding the parameters of the utterance situation into the output expressions. The hearer’s interpretation is controlled by the incoming language expression.

• Temporal order Database interaction: output (database as ‘speaker’) occurs necessarily after the input (database as ‘hearer’). NL communication: production (output procedure of the speaker) occurs necessarily before interpretation (input procedure of the hearer).

22.1.4 Sketch of a simple subcontext

[figure: FIDO; is-a; friends; brothers; dog; Felix; Fritz; Zach; Eddie]

22.1.5 Pragmatic interpretation of 22.1.1

[figure: like; agent; .; .; .; .; patient; .; .; .; .; .; .; .; .; .; FIDO; is-a; friends; brothers; dog; Felix; Fritz; Eddie; Zach]

22.2 Descriptive aporia and embarrassment of riches

22.2.1 Model-theoretic definition of a context

Let MS be a model structure (A,I,J,≤,F), where A, I, J are sets, ≤ is a simple ordering on J, and F is a denotation function. A, I, J, and F have the following definition: A = {a_{0}, a_{1}, a_{2}, a_{3}, a_{4}}, I = {i_{1}}, J = {j_{1}} F(fido’)(i_{1}, j_{1}) = a_{0} F(felix’)(i_{1}, j_{1}) = a_{1} F(fritz’)(i_{1}, j_{1}) = a_{2} F(zach’)(i_{1}, j_{1}) = a_{3} F(eddie’)(i_{1}, j_{1}) = a_{4} F(dog’)(i_{1}, j_{1}) = {a_{0}} F(fido-friends’)(i_{1}, j_{1}) = {a_{1}, a_{2}} F(fido-brothers’)(i_{1}, j_{1}) = {a_{3}, a_{4}}

22.2.2 Extending the hearer context to the meaning of a new sentence such as Fido likes Zach

Requires automatic addition of ‘F(like)(i_{1}, j_{1}) = {(a_{0},a_{3})}’ to 22.2.1 22.2.3 Creating a frame

(make-frame
  fido
     (is-a (value dog))
     (friends (value felix fritz))
     (brothers (value zach eddie))
)

22.2.4 Definition of 22.4.2 as a frame

(fido
  (is-a (value dog))
  (friends (value felix fritz))
  (brothers (value zach eddie))
)

22.2.5 Retrieving information

(get-values 'FIDO 'FRIENDS)
(FELIX FRITZ)

22.2.6 Extending the hearer context to Fido likes Zach

Requires deriving

   (fido
     (like (value Zach)
   )

and automatically adding the part

   (like (value Zach)

as a new slot into 22.2.4.

22.3 Propositions as sets of coindexed proplets

22.3.1 Proposition 3.4.2 as a set of proplets (preliminary format)

[\begin{matrix}Type: \\ [ & M-concept: field role: argument & ] \\ Token: \\ [ & I-concept_{loc}: x1 functor: contain prn: 23 id: 7 & ] \end{matrix}] [\begin{matrix}Type: \\ [ & M-concept: contain role: functor & ] \\ Token: \\ [ & I-concept_{loc}: x2 argument 1: field argument 2: triangle prn: 23 epr: 23 and 24 & ] \end{matrix}] [\begin{matrix}Type: \\ [ & M-concept: triangle role: argument & ] \\ Token: \\ [ & I-concept_{loc}: x3 functor: contain prn: 23 id: 8 & ] \end{matrix}]

[\begin{matrix}Type: \\ [ & M-concept: field role: argument & ] \\ Token: \\ [ & I-concept_{loc}: x4 functor: contain prn: 24 id: 7 & ] \end{matrix}] [\begin{matrix}Type: \\ [ & M-concept: contain role: functor & ] \\ Token: \\ [ & I-concept_{loc}: x5 argument 1: field argument 2: square prn: 24 epr: 23 and 24 & ] \end{matrix}] [\begin{matrix}Type: \\ [ & M-concept: square role: argument & ] \\ Token: \\ [ & I-concept_{loc}: x6 functor: contain prn: 24 id: 9 & ] \end{matrix}]

FoCL, Chapter 22: Database semantics 396

22.4 Proplets in a classic database

22.4.1 Types of databases classic: record based non-classic: based on the principle of slot and filler

22.4.2 Types of classic databases

Relational database, hierarchical database, network database 22.4.3 Relations between proplet features

type ↔ token
token ↔ prn
prn ↔ epr
token ↔ id
functor ↔ argument
modifier↔ modified
\begin{matrix}c \\ ◯ \end{matrix}1999 Roland Hausser

22.4.4 Propositions 3.4.2 as a word bank

types simplified proplets

[\begin{matrix}M-concept: contain \\ role: functor \end{matrix}]  [\begin{matrix}I-concept_{loc}: x2 \\ argument 1:field \\ argument 2:triangle \\ prn: 23 \\ epr: 23 and 24 \end{matrix}] [\begin{matrix}I-concept_{loc}: x5 \\ argument 1:field \\ argument 2:square \\ prn: 24 \\ epr: 23 and 24 \end{matrix} ]

[\begin{matrix}M-concept: field \\ role: argument \end{matrix}]  [\begin{matrix}I-concept_{loc}: x1 \\ functor: contain \\ prn: 23 \\ id: 7 \end{matrix}] [\begin{matrix}I-concept_{loc}: x4 \\ functor: contain \\ prn: 24 \\ id:7 \end{matrix}]

[\begin{matrix}M-concept: square \\ role: argument \end{matrix} ]  [\begin{matrix}I-concept_{loc}: x6 \\ functor: contain \\ prn: 24 \\ id: 9 \end{matrix}]

[\begin{matrix}M-concept: triangle \\ role: argument \end{matrix}]  [\begin{matrix}I-concept_{loc}: x3 \\ functor: contain \\ prn: 23 \\ id: 8 \end{matrix}]

22.4.5 Example of a network database

owner records member records Comp.Sci. Riedle Schmidt Stoll ... Mathematics Müller Barth Jacobs ...

Physics  Weber Meier  Miele  ...

22.4.6 Types of continuations

intrapropositional: from argument to functor, functor to argument, from modifier to modified and vice versa

extrapropositional: epr from verb to verb, id from noun to noun

22.5 Example of a word bank

22.5.1 Propositional presentation of subcontext 22.1.4

1. Fido is a dog.

2. Fido has friends.

3. The friends are Zach and Eddie.

4. Fido has brothers.

5. The brothers are Felix and Fritz.

6. Fido likes Zach.

22.5.2 Graphical presentation of the propositions in 22.5.1

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22.5.3 Subcontext 22.1.1 as a word bank

Types Proplets

[M-concept: be_{role: functor}]  [\begin{matrix}I-concept_{loc}: x1 \\ arg1: Fido \\ arg2: dog \\ prn: 1 \\ epr: 1 and 2 \end{matrix}] [\begin{matrix}I-concept_{loc}: x2 \\ arg1: friend \\ arg2: Zach, Eddie \\ prn: 3 \\ epr: 2 and 3 \\ 3 and 4 \end{matrix}] [\begin{matrix}I-concept_{loc}: x3 \\ arg1: brother \\ arg2: Felix, Fritz \\ prn: 5 \\ epr: 4 and 5 \\ 5 and 6 \end{matrix}]

[M-concept: brother_{role: argument}] [\begin{matrix}I-concept_{loc}: x4 \\ functor: have \\ prn: 4 \\ id: \end{matrix}] [\begin{matrix}I-concept_{loc}: x5 \\ functor: be \\ prn: 5 \\ id: \end{matrix}]

[M-concept: dog_{role: argument}]  [\begin{matrix}I-concept_{loc}: x6 \\ functor: be \\ prn: 4 \\ id: \end{matrix}]

[M-concept: Eddie_{role: argument}]  [\begin{matrix}I-concept_{loc}: x7 \\ functor: be \\ prn: 3 \\ id: 3 \end{matrix}]

[M-concept: Felix_{role: argument}]  [\begin{matrix}I-concept_{loc}: x8 \\ functor: be \\ prn: 5 \\ id: 4 \end{matrix}]

[M-concept: Fritz_{role: argument}]  [\begin{matrix}I-concept_{loc}: x9 \\ functor: be \\ prn: 5 \\ id: 5 \end{matrix}]

[M-concept: Fido_{role: argument}]  [\begin{matrix}I-con._{loc}: x10 \\ functor: be \\ prn: 1 \\ id: 1 \end{matrix}] [\begin{matrix}I-con._{loc}: x11 \\ functor: have \\ prn: 2 \\ id: 1 \end{matrix}] [\begin{matrix}I-con._{loc}: x12 \\ functor: have \\ prn: 4 \\ id: 1 \end{matrix}] [\begin{matrix}I-con._{loc}: x13 \\ functor: like \\ prn: 6 \\ id: 1 \end{matrix}]&

[M-concept: friend_{role: argument}]  [\begin{matrix}I-concept_{loc}: x14 \\ functor: have \\ prn: 2 \\ id: \end{matrix}] [\begin{matrix}I-concept_{loc}: x15 \\ functor: be \\ prn: 3 \\ id: \end{matrix}]

[M-concept: have_{role: functor}]  [\begin{matrix}I-concept_{loc}: x16 \\ arg1: Fido \\ arg2: friend \\ prn: 2 \\ epr: 1 and 2 \\ 2 and 3 \end{matrix}] [\begin{matrix}I-concept_{loc}: x17 \\ arg1: Fido \\ arg2: brother \\ prn: 4 \\ epr: 3 and 4 \\ 4 and 5 \end{matrix}]

[M-concept: like_{role: functor}]  [\begin{matrix}I-concept_{loc}: x18 \\ arg1: Fido \\ arg2: Zach \\ prn: 6 \\ epr: 5 and 6 \end{matrix}]&

[M-concept: Zach_{role: argument}]  [\begin{matrix}I-concept_{loc}: x19 \\ functor: be \\ prn: 3 \\ id: 2 \end{matrix}] [\begin{matrix}I-concept_{loc}: x20 \\ functor: like \\ prn: 6 \\ id: 2 \end{matrix}]&

22.5.4 Semantic representation of proposition 6

Types Proplets

[M-concept: Fido_{role: argument}] [\begin{matrix}I-concept_{loc}: x13 \\ functor: like \\ prn: 6 \\ id: ? \end{matrix}]

[M-concept: like_{role: functor}] [\begin{matrix}I-concept_{loc}: x18 \\ arg1: Fido \\ arg2: Zach \\ prn: 6 \\ epr: ? \end{matrix}]

[M-concept: Zach_{role: argument}] [\begin{matrix}I-concept_{loc}: x20 \\ functor: like \\ prn: 6 \\ id: ? \end{matrix}]