Ontograph Framework

Tobias Kuhn, 15 October 2010

Table of Contents

Introduction

This document contains resources for the ontograph framework. The ontograph framework is an experiment framework to test the understandability of controlled natural languages and other usability oriented formal languages.

The complete content of this page (including the pictures in the different formats) can be reused freely under the terms of the Creative Commons Attribution License. Click on the icon below for more information. In an experimental setting, the attribution can be dropped.

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The following publications describe the ontograph framework:

[3] Tobias Kuhn. Controlled English for Knowledge Representation. Doctoral thesis, Faculty of Economics, Business Administration and Information Technology of the University of Zurich, 2010.

[2] Tobias Kuhn. An Evaluation Framework for Controlled Natural Languages. In Norbert E. Fuchs, editor, Proceedings of the Workshop on Controlled Natural Language (CNL 2009), Lecture Notes in Computer Science 5972, pages 1-20. Springer, 2010.

[1] Tobias Kuhn. How to Evaluate Controlled Natural Languages. In Pre-Proceedings of the Workshop on Controlled Natural Language (CNL 2009), CEUR Workshop Proceedings, Volume 448, 2009.

Below, a kit is shown that can be used to create ontographs. Furthermore, exemplary ontographs and statements (plus some additional material) are shown that have been used for two experiments.

Kit

The ontograph kit shown below contains the graphical elements out of which ontographs can be created.

Ontograph Kit (png, pdf, odg)
Ontograph Kit

Experiment 1

The four ontographs shown below (1X, 2X, 3X and 4X) have been used for the experiment described in [1]. Each ontograph has two series of statements (a and b) each of which consists of 10 statements in ACE ("Attempto Controlled English"). Only series a has been used for the experiment described in the paper. Some of the statement are true and have a plus sign (+) in the identifier. The others are false and their identifiers have a minus sign (−).

Table 1X

Ontograph (png, pdf, odg) Statements
Ontograph 1X
ID ACE
1a− Mary is a traveler.
1b+ John is a golfer.
2a+ Bill is not a golfer.
2b− Lara is not an officer.
3a+ Mary is an officer or is a woman.
3b− John is a woman or is a traveler.
4a− Sue is an officer and is a traveler.
4b+ Tom is a man and is a golfer.
5a− Every traveler is a man.
5b+ Every officer is a woman.
6a+ No golfer is a woman.
6b− No traveler is a golfer.
7a+ Every woman is an officer and every officer is a woman.
7b− Every golfer is a man and every man is a golfer.
8a− Every traveler who is not a woman is a golfer.
8b+ Every man who is not a golfer is a traveler.
9a+ Every man is a golfer or is a traveler.
9b− Every traveler is a golfer or is an officer.
10a+ Every woman who is a golfer is a traveler.
10b+ Every officer who is a man is a golfer.

Table 2X

Ontograph (png, pdf, odg) Statements
Ontograph 2X
ID ACE
1a+ John sees Tom.
1b− Lara sees Mary.
2a+ Mary does not see Tom.
2b− Tom does not see Lara.
3a− Tom buys a picture.
3b+ John buys a present.
4a− John sees no woman.
4b+ Mary sees no man.
5a+ Tom sees every woman.
5b− Lara sees every man.
6a+ Tom sees nothing but women.
6b− John sees nothing but men.
7a+ Lara buys nothing but presents.
7b+ Lara buys nothing but pictures.
8a− No woman sees herself.
8b+ No man sees himself.
9a+ Every woman buys nothing but pictures.
9b− Every man buys nothing but presents.
10a+ No man who buys a picture is seen by a woman.
10b− No woman who buys a picture is seen by a man.

Table 3X

Ontograph (png, pdf, odg) Statements
Ontograph 3X
ID ACE
1a+ Everything that loves something is a person.
1b− Everything that sees something is an officer.
2a− Everything that is loved by something is a person.
2b+ Everything that is bought by something is a present.
3a+ Everything that sees something is an officer or is a traveler.
3b− Everything that loves something is a traveler or is an officer.
4a− Everything that is bought by something is an aquarium or is an officer.
4b+ Everything that is seen by something is a traveler or is an aquarium.
5a− Everything buys at most 1 thing.
5b+ Everything loves at most 1 thing.
6a+ Everything is bought by at most 1 thing.
6b− Everything is loved by at most 1 thing.
7a− Lara sees at least 2 persons.
7b+ Bill sees at least 2 aquariums.
8a+ Bill is seen by at most 1 traveler.
8b− Sue is loved by at most 1 person.
9a− Every officer is loved by at least 2 persons.
9b+ Every aquarium is seen by at least 2 persons.
10a+ Every officer sees exactly 1 traveler.
10b− Every traveler loves exactly 1 person.

Table 4X

Ontograph (png, pdf, odg) Statements
Ontograph 4X
ID ACE
1a+ If X asks Y then Y asks X.
1b− If X helps Y then Y helps X.
2a+ If X sees Y then Y does not see X.
2b− If X asks Y then Y does not ask X.
3a− Nothing asks itself.
3b+ Nothing sees itself.
4a− If X loves something that loves Y then X loves Y.
4b+ If X sees something that sees Y then X sees Y.
5a+ If X admires Y then X sees Y.
5b− If X sees Y then X admires Y.
6a− If X helps Y then Y admires X.
6b+ If X loves Y then Y sees X.
7a− If X admires Y then X does not see Y.
7b+ If X loves Y then X does not admire Y.
8a+ If X admires Y then Y does not see X.
8b− If X sees Y then Y does not love X.
9a− If X admires Y then X sees Y. If X sees Y then X admires Y.
9b+ If X loves Y then X helps Y. If X helps Y then X loves Y.
10a+ If X sees something that admires Y then X sees Y.
10b− If X asks something that sees Y then X asks Y.

Experiment 2

The examples shown here have been used for a second ontograph experiment. The goal was to compare the controlled natural language ACE ("Attempto Controlled English") to a common formal language, i.e. MLL. MLL stands for "Manchester-like language" and is a language heavily inspired by the Manchester Syntax for OWL. See [2] and [3] for the details.

Below, four series of ontographs (1, 2, 3 and 4) are shown, each consisting of three ontographs (A, B and C). Each ontograph has two series of statements (a and b) each of which consists of 10 statements. These statements are built according to certain patterns, and each statement is expressed in ACE and in MLL. Some of the statement are true and have a plus sign (+) in the identifier. The others are false and their identifiers have a minus sign (–). The ontographs B and C of each series and the respective statements are structurally equivalent in the sense that they can be derived from each other by one-to-one replacements of the names of the individuals, types and relations.

The participants of the experiment received a printed language description sheet for ACE and another one for MLL. Because these description sheets only describe the subset of the language that was used for the given series, each series has its own description sheets. For the sake of neutrality, ACE was called "language A" and MLL was called "language B". German and English versions of the descriptions sheets are available.

At the end, the questionnaire is shown that the participants had to fill out after the experiment.

Series 1

The statements of this series only contain individuals and types, but no relations. These are the used language description sheets:

The following table shows the sentence patterns of Series 1:

ID Name ACE Pattern MLL Pattern
1 individual type [I] is a [T]. [I] HasType [T]
2 negative individual type [I] is not a [T]. [I] HasType not [T]
3 disjunctive individual type [I] is a [T1] or is a [T2]. [I] HasType [T1] or [T2]
4 conjunctive individual type [I] is a [T1] and is a [T2]. [I] HasType [T1] and [T2]
5 subtype Every [T1] is a [T2]. [T1] SubTypeOf [T2]
6 disjoint types No [T1] is a [T2]. [T1] DisjointWith [T2]
7 equivalent types Every [T1] is a [T2] and every [T2] is a [T1]. [T1] EquivalentTo [T2]
8 complex subtype Every [T1] who is not a [T2] is a [T3]. [T1] and (not [T2]) SubTypeOf [T3]
9 complex supertype Every [T1] is a [T2] or is a [T3]. [T1] SubTypeOf [T2] or [T3]
10 complex subtype/supertype Nobody who is a [T1] or who is a [T2] is a [T3] and is a [T4]. [T1] or [T2] SubTypeOf not ([T3] and [T4])

Table 1A

Ontograph (png, pdf, odg) Statements
Ontograph 1A
ID ACE MLL
1a− Mary is a traveler. Mary HasType traveler
1b+ John is a golfer. John HasType golfer
2a+ Bill is not a golfer. Bill HasType not golfer
2b− Lisa is not an officer. Lisa HasType not officer
3a+ Mary is an officer or is a golfer. Mary HasType officer or golfer
3b− John is a woman or is a traveler. John HasType woman or traveler
4a− Sue is an officer and is a traveler. Sue HasType officer and traveler
4b+ Tom is a man and is a golfer. Tom HasType man and golfer
5a− Every man is a golfer. man SubTypeOf golfer
5b+ Every golfer is a man. golfer SubTypeOf man
6a+ No golfer is a woman. golfer DisjointWith woman
6b− No traveler is a golfer. traveler DisjointWith golfer
7a+ Every woman is an officer and every officer is a woman. woman EquivalentTo officer
7b− Every golfer is a man and every man is a golfer. golfer EquivalentTo man
8a− Every traveler who is not a woman is a golfer. traveler and (not woman) SubTypeOf golfer
8b+ Every man who is not a golfer is a traveler. man and (not golfer) SubTypeOf traveler
9a+ Every man is a golfer or is a traveler. man SubTypeOf golfer or traveler
9b− Every traveler is a golfer or is an officer. traveler SubTypeOf golfer or officer
10a+ Nobody who is a man or who is a golfer is an officer and is a traveler. man or golfer SubTypeOf not (officer and traveler)
10b− Nobody who is a traveler or who is an officer is a man and is a golfer. traveler or officer SubTypeOf not (man and golfer)

Table 1B

This ontograph and its statements are structurally equivalent to 1C.

Ontograph (png, pdf, odg) Statements
Ontograph 1B
ID ACE MLL
1a+ John is a traveler. John HasType traveler
1b− Mary is a traveler. Mary HasType traveler
2a− Bill is not an officer. Bill HasType not officer
2b+ Sue is not an officer. Sue HasType not officer
3a− Tom is an officer or is a golfer. Tom HasType officer or golfer
3b+ Paul is a golfer or is a man. Paul HasType golfer or man
4a− Mary is a woman and is a traveler. Mary HasType woman and traveler
4b+ John is a man and is a traveler. John HasType man and traveler
5a− Every man is a traveler. man SubTypeOf traveler
5b+ Every traveler is a man. traveler SubTypeOf man
6a+ No traveler is a golfer. traveler DisjointWith golfer
6b− No officer is a woman. officer DisjointWith woman
7a+ Every woman is a golfer and every golfer is a woman. woman EquivalentTo golfer
7b− Every traveler is a man and every man is a traveler. traveler EquivalentTo man
8a− Every officer who is not a traveler is a golfer. officer and (not traveler) SubTypeOf golfer
8b+ Every man who is not a traveler is an officer. man and (not traveler) SubTypeOf officer
9a+ Every man is a traveler or is an officer. man SubTypeOf traveler or officer
9b− Every officer is a man or is a traveler. officer SubTypeOf man or traveler
10a− Nobody who is a golfer or who is a traveler is a man and is an officer. golfer or traveler SubTypeOf not (man and officer)
10b+ Nobody who is a man or who is a traveler is an officer and is a golfer. man or traveler SubTypeOf not (officer and golfer)

Table 1C

This ontograph and its statements are structurally equivalent to 1B.

Ontograph (png, pdf, odg) Statements
Ontograph 1C
ID ACE MLL
1a+ Lisa is an officer. Lisa HasType officer
1b− Bill is an officer. Bill HasType officer
2a− Sue is not a golfer. Sue HasType not golfer
2b+ Tom is not a golfer. Tom HasType not golfer
3a− Mary is a golfer or is a traveler. Mary HasType golfer or traveler
3b+ Kate is a traveler or is a woman. Kate HasType traveler or woman
4a− Bill is a man and is an officer. Bill HasType man and officer
4b+ Lisa is a woman and is an officer. Lisa HasType woman and officer
5a− Every woman is an officer. woman SubTypeOf officer
5b+ Every officer is a woman. officer SubTypeOf woman
6a+ No officer is a traveler. officer DisjointWith traveler
6b− No golfer is a man. golfer DisjointWith man
7a+ Every man is a traveler and every traveler is a man. man EquivalentTo traveler
7b− Every officer is a woman and every woman is an officer. officer EquivalentTo woman
8a− Every golfer who is not an officer is a traveler. golfer and (not officer) SubTypeOf traveler
8b+ Every woman who is not an officer is a golfer. woman and (not officer) SubTypeOf golfer
9a+ Every woman is an officer or is a golfer. woman SubTypeOf officer or golfer
9b− Every golfer is a woman or is an officer. golfer SubTypeOf woman or officer
10a− Nobody who is a traveler or who is an officer is a woman and is a golfer. traveler or officer SubTypeOf not (woman and golfer)
10b+ Nobody who is a woman or who is an officer is a golfer and is a traveler. woman or officer SubTypeOf not (golfer and traveler)

Series 2

The statements of this series contain relations with different kinds of simple quantifications. These are the used language description sheets:

The following table shows the sentence patterns of Series 2:

ID Name ACE Pattern MLL Pattern
1 relation instance [I1] [R] [I2]. [I1] [R] [I2]
2 negative relation instance [I1] does not [R] [I2]. [I1] not [R] [I2]
3 concrete existential statement [I] [R] a [T]. [I] HasType [R] some [T]
4 concrete negative statement 1 [I] [R] no [T]. [I] HasType not ([R] some [T])
5 concrete negative statement 2 [I] [R] something that is not a [T]. [I] HasType [R] some (not [T])
6 concrete exception statement [I] [R] nothing but [T]. [I] HasType [R] only [T]
7 general existential statement 1 Every [T1] [R] a [T2]. [T1] SubTypeOf [R] some [T2]
8 general existential statement 2 Everything that [R] a [T1] is a [T2]. [R] some [T1] SubTypeOf [T2]
9 general exception statement 1 Every [T1] [R] nothing but [T2]. [T1] SubTypeOf [R] only [T2]
10 general exception statement 2 Everything that [R] nothing but [T1] is a [T2]. [R] only [T1] SubTypeOf [T2]

Table 2A

Ontograph (png, pdf, odg) Statements
Ontograph 2A
ID ACE MLL
1a− Lisa sees Mary. Lisa sees Mary
1b+ John sees Tom. John sees Tom
2a+ Mary does not see Tom. Mary not sees Tom
2b− Tom does not see Lisa. Tom not sees Lisa
3a− Tom buys a picture. Tom HasType buys some picture
3b+ John buys a present. John HasType buys some present
4a+ Mary sees no man. Mary HasType not (sees some man)
4b− John sees no woman. John HasType not (sees some woman)
5a+ John buys something that is not a present. John HasType buys some (not present)
5b− Tom sees something that is not a woman. Tom HasType sees some (not woman)
6a− John sees nothing but men. John HasType sees only man
6b+ Tom sees nothing but women. Tom HasType sees only woman
7a+ Every man buys a present. man SubTypeOf buys some present
7b− Every woman buys a picture. woman SubTypeOf buys some picture
8a+ Everything that buys a present is a man. buys some present SubTypeOf man
8b− Everything that sees a woman is a man. sees some woman SubTypeOf man
9a− Every man buys nothing but presents. man SubTypeOf buys only present
9b+ Every woman buys nothing but pictures. woman SubTypeOf buys only picture
10a+ Everything that buys nothing but pictures is a woman. buys only picture SubTypeOf woman
10b− Everything that sees nothing but women is a man. sees only woman SubTypeOf man

Table 2B

This ontograph and its statements are structurally equivalent to 2C.

Ontograph (png, pdf, odg) Statements
Ontograph 2B
ID ACE MLL
1a− Tom inspects Lisa. Tom inspects Lisa
1b+ Lisa inspects Tom. Lisa inspects Tom
2a+ Lisa does not admire Tom. Lisa not admires Tom
2b− Tom does not admire Lisa. Tom not admires Lisa
3a+ Lisa admires an officer. Lisa HasType admires some officer
3b− Lisa admires a traveler. Lisa HasType admires some traveler
4a+ Paul admires no officer. Paul HasType not (admires some officer)
4b− Lisa inspects no traveler. Lisa HasType not (inspects some traveler)
5a+ Sue admires something that is not a traveler. Sue HasType admires some (not traveler)
5b− Paul admires something that is not an aquarium. Paul HasType admires some (not aquarium)
6a+ Tom inspects nothing but letters. Tom HasType inspects only letter
6b− Lisa inspects nothing but travelers. Lisa HasType inspects only traveler
7a− Every traveler inspects a letter. traveler SubTypeOf inspects some letter
7b+ Every officer inspects an aquarium. officer SubTypeOf inspects some aquarium
8a+ Everything that inspects an aquarium is an officer. inspects some aquarium SubTypeOf officer
8b− Everything that admires a person is an officer. admires some person SubTypeOf officer
9a− Every officer inspects nothing but aquariums. officer SubTypeOf inspects only aquarium
9b+ Every traveler admires nothing but officers. traveler SubTypeOf admires only officer
10a− Everything that admires nothing but persons is an officer. admires only person SubTypeOf officer
10b+ Everything that inspects nothing but letters is a traveler. inspects only letter SubTypeOf traveler

Table 2C

This ontograph and its statements are structurally equivalent to 2B.

Ontograph (png, pdf, odg) Statements
Ontograph 2C
ID ACE MLL
1a− Bill sees Kate. Bill sees Kate
1b+ Kate sees Bill. Kate sees Bill
2a+ Kate does not love Bill. Kate not loves Bill
2b− Bill does not love Kate. Bill not loves Kate
3a+ Kate loves a golfer. Kate HasType loves some golfer
3b− Kate loves an officer. Kate HasType loves some officer
4a+ John loves no golfer. John HasType not (loves some golfer)
4b− Kate sees no officer. Kate HasType not (sees some officer)
5a+ Mary loves something that is not an officer. Mary HasType loves some (not officer)
5b− John loves something that is not a TV. John HasType loves some (not TV)
6a+ Bill sees nothing but aquariums. Bill HasType sees only aquarium
6b− Kate sees nothing but officers. Kate HasType sees only officer
7a− Every officer sees an aquarium. officer SubTypeOf sees some aquarium
7b+ Every golfer sees a TV. golfer SubTypeOf sees some TV
8a+ Everything that sees a TV is a golfer. sees some TV SubTypeOf golfer
8b− Everything that loves a person is a golfer. loves some person SubTypeOf golfer
9a− Every golfer sees nothing but TVs. golfer SubTypeOf sees only TV
9b+ Every officer loves nothing but golfers. officer SubTypeOf loves only golfer
10a− Everything that loves nothing but persons is a golfer. loves only person SubTypeOf golfer
10b+ Everything that sees nothing but aquariums is an officer. sees only aquarium SubTypeOf officer

Series 3

The statements of this series consist of domain, range, and cardinality restrictions. These are the used language description sheets:

The following table shows the sentence patterns of Series 3:

ID Name ACE Pattern MLL Pattern
1 domain Everything that [R] something is a [T]. [R] HasDomain [T]
2 range Everything that is [R] by something is a [T]. [R] HasRange [T]
3 complex domain Everything that [R] something is a [T1] or is a [T2]. [R] HasDomain [T1] or [T2]
4 complex range Everything that is [R] by something is a [T1] or is a [T2]. [R] HasRange [T1] or [T2]
5 minimal cardinality [I] [R] at least 2 [T]. [I] HasType [R] min 2 [T]
6 maximal cardinality [I] [R] at most 1 [T]. [I] HasType [R] max 1 [T]
7 general minimal cardinality 1 Every [T1] [R] at least 2 [T2]. [T1] SubTypeOf [R] min 2 [T2]
8 general minimal cardinality 2 Everything that [R] at least 2 [T1] is a [T2]. [R] min 2 [T1] SubTypeOf [T2]
9 general maximal cardinality Every [T1] [R] at most 1 [T2]. [T1] SubTypeOf [R] max 1 [T2]
10 complex maximal cardinality Everything that is a [T1] or that is a [T2] [R] at most 1 [T3]. [T1] or [T2] SubTypeOf [R] max 1 [T3]

Table 3A

Ontograph (png, pdf, odg) Statements
Ontograph 3A
ID ACE MLL
1a− Everything that sees something is an officer. sees HasDomain officer
1b+ Everything that loves something is a person. loves HasDomain person
2a− Everything that is loved by something is a person. loves HasRange person
2b+ Everything that is bought by something is a present. buys HasRange present
3a− Everything that loves something is a traveler or is an officer. loves HasDomain traveler or officer
3b+ Everything that sees something is an officer or is a traveler. sees HasDomain officer or traveler
4a+ Everything that is seen by something is a traveler or is an aquarium. sees HasRange traveler or aquarium
4b− Everything that is bought by something is an aquarium or is an officer. buys HasRange aquarium or officer
5a+ Tom loves at least 2 officers. Tom HasType loves min 2 officer
5b− Sue sees at least 2 persons. Sue HasType sees min 2 person
6a− Lisa buys at most 1 present. Lisa HasType buys max 1 present
6b+ Bill loves at most 1 person. Bill HasType loves max 1 person
7a+ Every traveler sees at least 2 aquariums. traveler SubTypeOf sees min 2 aquarium
7b− Every officer buys at least 2 presents. officer SubTypeOf buys min 2 present
8a+ Everything that buys at least 2 presents is an officer. buys min 2 present SubTypeOf officer
8b− Everything that loves at least 2 officers is a traveler. love min 2 officer SubTypeOf traveler
9a+ Every officer sees at most 1 aquarium. officer SubTypeOf sees max 1 aquarium
9b− Every person buys at most 1 present. person SubTypeOf buys max 1 present
10a− Everything that is a traveler or that is an officer sees at most 1 aquarium. traveler or officer SubTypeOf sees max 1 aquarium
10b+ Everything that is an officer or that is a traveler loves at most 1 person. officer or traveler SubTypeOf loves max 1 person

Table 3B

This ontograph and its statements are structurally equivalent to 3C.

Ontograph (png, pdf, odg) Statements
Ontograph 3B
ID ACE MLL
1a− Everything that inspects something is an officer. inspects HasDomain officer
1b+ Everything that helps something is an officer. helps HasDomain officer
2a+ Everything that is inspected by something is a letter. inspects HasRange letter
2b− Everything that is seen by something is an officer. sees HasRange officer
3a+ Everything that inspects something is a golfer or is an officer. inspects HasDomain golfer or officer
3b− Everything that sees something is an officer or is a golfer. sees HasDomain officer or golfer
4a+ Everything that is seen by something is an officer or is a picture. sees HasRange officer or picture
4b− Everything that is helped by something is a golfer or is an officer. helps HasRange golfer or officer
5a+ Lisa inspects at least 2 letters. Lisa HasType inspects min 2 letter
5b− Paul sees at least 2 persons. Paul HasType sees min 2 person
6a− Lisa helps at most 1 person. Lisa HasType helps max 1 person
6b+ John sees at most 1 officer. John HasType sees max 1 officer
7a+ Every officer helps at least 2 persons. officer SubTypeOf helps min 2 person
7b− Every officer inspects at least 2 letters. officer SubTypeOf inspects min 2 letter
8a− Everything that sees at least 2 pictures is an officer. sees min 2 picture SubTypeOf officer
8b+ Everything that inspects at least 2 letters is an officer. inspects min 2 letter SubTypeOf officer
9a− Every person inspects at most 1 letter. person SubTypeOf inspects max 1 letter
9b+ Every person helps at most 1 officer. person SubTypeOf helps max 1 officer
10a+ Everything that is an officer or that is a golfer sees at most 1 picture. officer or golfer SubTypeOf sees max 1 picture
10b− Everything that is a golfer or that is an officer inspects at most 1 letter. golfer or officer SubTypeOf inspects max 1 letter

Table 3C

This ontograph and its statements are structurally equivalent to 3B.

Ontograph (png, pdf, odg) Statements
Ontograph 3C
ID ACE MLL
1a− Everything that sees something is a golfer. sees HasDomain golfer
1b+ Everything that helps something is a golfer. helps HasDomain golfer
2a+ Everything that is seen by something is a TV. sees HasRange TV
2b− Everything that is admired by something is a golfer. admires HasRange golfer
3a+ Everything that sees something is a traveler or is a golfer. sees HasDomain traveler or golfer
3b− Everything that admires something is a golfer or is a traveler. admires HasDomain golfer or traveler
4a+ Everything that is admired by something is a golfer or is a present. admires HasRange golfer or present
4b− Everything that is helped by something is a traveler or is a golfer. helps HasRange traveler or golfer
5a+ Kate sees at least 2 TVs. Kate HasType sees min 2 TV
5b− Mary admires at least 2 persons. Mary HasType admires min 2 person
6a− Kate helps at most 1 person. Kate HasType helps max 1 person
6b+ Bill admires at most 1 golfer. Bill HasType admires max 1 golfer
7a+ Every golfer helps at least 2 persons. golfer SubTypeOf helps min 2 person
7b− Every golfer sees at least 2 TVs. golfer SubTypeOf sees min 2 TV
8a− Everything that admires at least 2 presents is a golfer. admires min 2 present SubTypeOf golfer
8b+ Everything that sees at least 2 TVs is a golfer. sees min 2 TV SubTypeOf golfer
9a− Every person sees at most 1 TV. person SubTypeOf sees max 1 TV
9b+ Every person helps at most 1 golfer. person SubTypeOf helps max 1 golfer
10a+ Everything that is a golfer or that is a traveler admires at most 1 present. golfer or traveler SubTypeOf admires max 1 present
10b− Everything that is a traveler or that is a golfer sees at most 1 TV. traveler or golfer SubTypeOf sees max 1 TV

Series 4

The statements of this series are only about relations and not about individuals or types. These are the used language description sheets:

The following table shows the sentence patterns of Series 4:

ID Name ACE Pattern MLL Pattern
1 symmetric relation If X [R] Y then Y [R] X. [R] IsSymmetric
2 asymmetric relation If X [R] Y then Y does not [R] X. [R] IsAsymmetric
3 transitive relation If X [R] somebody who [R] Y then X [R] Y. [R] IsTransitive
4 subrelation 1 If X [R1] Y then X [R2] Y. [R1] SubRelationOf [R2]
5 subrelation 2 If X [R1] Y then X [R2] Y. [R1] SubRelationOf [R2]
6 inverse subrelation If X [R1] Y then Y [R2] X. [R1] SubRelationOf inverse [R2]
7 disjoint relations If X [R1] Y then X does not [R2] Y. [R1] DisjointWith [R2]
8 inverse disjoint relations If X [R1] Y then Y does not [R2] X. [R1] DisjointWith inverse [R2]
9 equivalent relations If X [R1] Y then X [R2] Y. If X [R2] Y then X [R1] Y. [R1] EquivalentTo [R2]
10 inverse equivalent relations If X [R1] Y then Y [R2] X. If Y [R2] X then X [R1] Y. [R1] EquivalentTo inverse [R2]

Table 4A

Ontograph (png, pdf, odg) Statements
Ontograph 4A
ID ACE MLL
1a− If X helps Y then Y helps X. helps IsSymmetric
1b+ If X asks Y then Y asks X. asks IsSymmetric
2a+ If X sees Y then Y does not see X. sees IsAsymmetric
2b− If X asks Y then Y does not ask X. asks IsAsymmetric
3a+ If X sees somebody who sees Y then X sees Y. sees IsTransitive
3b− If X loves somebody who loves Y then X loves Y. loves IsTransitive
4a+ If X admires Y then X sees Y. admires SubRelationOf sees
4b− If X sees Y then X admires Y. sees SubRelationOf admires
5a+ If X inspects Y then X helps Y. inspects SubRelationOf helps
5b− If X helps Y then X inspects Y. helps SubRelationOf inspects
6a− If X helps Y then Y admires X. helps SubRelationOf inverse admires
6b+ If X loves Y then Y sees X. loves SubRelationOf inverse sees
7a+ If X loves Y then X does not admire Y. loves DisjointWith admires
7b− If X admires Y then X does not see Y. admires DisjointWith sees
8a− If X sees Y then Y does not love X. sees DisjointWith inverse love
8b+ If X admires Y then Y does not see X. admires DisjointWith inverse sees
9a− If X admires Y then X sees Y. If X sees Y then X admires Y. admires EquivalentTo sees
9b+ If X loves Y then X helps Y. If X helps Y then X loves Y. loves EquivalentTo helps
10a− If X inspects Y then Y sees X. If Y sees X then X inspects Y. inspects EquivalentTo inverse sees
10b+ If X admires Y then Y inspects X. If Y inspects X then X admires Y. admires EquivalentTo inverse inspects

Table 4B

This ontograph and its statements are structurally equivalent to 4C.

Ontograph (png, pdf, odg) Statements
Ontograph 4B
ID ACE MLL
1a+ If X helps Y then Y helps X. helps IsSymmetric
1b− If X admires Y then Y admires X. admires IsSymmetric
2a+ If X asks Y then Y does not ask X. asks IsAsymmetric
2b− If X helps Y then Y does not help X. helps IsAsymmetric
3a+ If X admires somebody who admires Y then X admires Y. admires IsTransitive
3b− If X sees somebody who sees Y then X sees Y. sees IsTransitive
4a− If X sees Y then X admires Y. sees SubRelationOf admires
4b+ If X inspects Y then X admires Y. inspects SubRelationOf admires
5a+ If X asks Y then X admires Y. asks SubRelationOf admires
5b− If X admires Y then X asks Y. admires SubRelationOf asks
6a− If X loves Y then Y admires X. loves SubRelationOf inverse admires
6b+ If X sees Y then Y admires X. sees SubRelationOf inverse admires
7a− If X admires Y then X does not inspect Y. admires DisjointWith inspects
7b+ If X sees Y then X does not admire Y. sees DisjointWith admires
8a+ If X asks Y then Y does not admire X. asks DisjointWith inverse admires
8b− If X admires Y then Y does not see X. admires DisjointWith inverse sees
9a+ If X loves Y then X inspects Y. If X inspects Y then X loves Y. loves EquivalentTo inspects
9b− If X asks Y then X admires Y. If X admires Y then X asks Y. asks EquivalentTo admires
10a− If X loves Y then Y admires X. If Y admires X then X loves Y. loves EquivalentTo inverse admires
10b+ If X asks Y then Y sees X. If Y sees X then X asks Y. asks EquivalentTo inverse sees

Table 4C

This ontograph and its statements are structurally equivalent to 4B.

Ontograph (png, pdf, odg) Statements
Ontograph 4C
ID ACE MLL
1a+ If X sees Y then Y sees X. sees IsSymmetric
1b− If X loves Y then Y loves X. loves IsSymmetric
2a+ If X helps Y then Y does not help X. helps IsAsymmetric
2b− If X sees Y then Y does not see X. sees IsAsymmetric
3a+ If X loves somebody who loves Y then X loves Y. loves IsTransitive
3b− If X inspects somebody who inspects Y then X inspects Y. inspects IsTransitive
4a− If X inspects Y then X loves Y. inspects SubRelationOf loves
4b+ If X asks Y then X loves Y. asks SubRelationOf loves
5a+ If X helps Y then X loves Y. helps SubRelationOf loves
5b− If X loves Y then X helps Y. loves SubRelationOf helps
6a− If X admires Y then Y loves X. admires SubRelationOf inverse loves
6b+ If X inspects Y then Y loves X. inspects SubRelationOf inverse loves
7a− If X loves Y then X does not ask Y. loves DisjointWith asks
7b+ If X inspects Y then X does not love Y. inspects DisjointWith loves
8a+ If X helps Y then Y does not love X. helps DisjointWith inverse loves
8b− If X loves Y then Y does not inspect X. loves DisjointWith inverse inspects
9a+ If X admires Y then X asks Y. If X asks Y then X admires Y. admires EquivalentTo asks
9b− If X helps Y then X loves Y. If X loves Y then X helps Y. helps EquivalentTo loves
10a− If X admires Y then Y loves X. If Y loves X then X admires Y. admires EquivalentTo inverse loves
10b+ If X helps Y then Y inspects X. If Y inspects X then X helps Y. helps EquivalentTo inverse inspects

Questionnaire

This is the questionnaire that the participants had to fill out after the experiment: