LING30007 Semantics 2018



project 2: Categorisation and predicate logic


Distributed: Monday 23/04/18

Due: Wednesday 16/05/18

Hand in via Turnitin on LMS by 5 pm NOTE TIME



Question 1: Categorisation [15 points]

Your task in this project is to do some semantic experimentation. It will require you to find 5 (or preferably more) volunteers to engage in a little experiment in human categorisation. [NOTE: you don’t have to do this exercise in English. It can be in any language, as long as you transliterate直译 your examples into roman script, and gloss and translate them appropriately so that we—Cat and Brett—can understand them.]


Task 1. Design and data collection [5 points]

Pick a category (e.g. items of clothing, animals, vehicles, cooking ingredients, tools). What is the internal structure of the category you have chosen? Provide a taxonomy分类学. Can the category be described in terms of one or more prototypes and outliers? What would you predict to be the most quickly or frequently named items in this category?


Now, recruit 5 (or more) participants. Ask your participants to list 30 items of your category in the order in which they come to mind. They shouldn’t think too hard, they should just write them down or tell them to you quickly. Make all your participants do the same category (don’t give them different categories, and don’t let them choose their own).


Task 2. Analysis [5 points]

Now you need to decide what your results can tell you. Do some items occur in more than one list? Where in the list do they occur? Can you rank the items in order of frequency? Are some of the items basic level terms? Which ones?


Task 3. Discussion [5 points]

How does your taxonomy in Task 1 relate to the items in your list, and their relative frequency and place in the list? Discuss any interesting converges and differences from what you predicted, compared to what you discovered.


Question 2 Interpreting model theoretic expressions [10 points]

This is an exercise very much like the one you did in week 7 (GridBlock). Your task is to translate and assign truth values {1, 0} to the following expressions, based on the model presented in the picture below. [Note: you need to be able to see this picture in colour. If you have colour blindness, contact Brett.]


image.png

I am reliably informed (by my 13 year old son, Louie) that the names of these characters, from Mario Bros 2 or thereabouts, are, respectively:

? Block, Coin, Mushroom, Fireflower

Koopa, Lakitu

Fireball, Spike, Goomba

Cheep Cheep, Shelly

End Flag, Empty Block, Wall Block, Brick Block, Cannon


We are going to treat these character names as predicates, in the same way we’ve treated ‘cat’. See below. In addition, we’ll treat ‘red’ and ‘green’ as additional predicates that can further attribute properties to these characters (e.g. Mushrooms and Koopas).


The predicate language will have the following components:

A set of individual variables: {v,w,x,y,z}

A set of predicates:

Red(x), Green(x), Blue(x) , Yellow(x), BackOf(x,y), FrontOf(x,y), LeftOf(x,y), RightOf(x,y), Above(x,y), Below(x,y), Between(x,y,z), QBlock(x), Coin(x), Mushroom(x), Fireflower(x), Koopa(x), Lakitu(x), Fireball(x), Spike(x), Goomba(x), CheepCheep(x), Shelly(x), EndFlag(x), EmptyBlock(x), WallBlock(x), BrickBlock(x), Cannon(x)}

(Note: There are no individual constants: we’re treating all the characters as ‘types/kinds’, like ‘cat’. Also, you should interpret predicates like ‘Above(x,y)’ ‘loosely’ like they typically are in English as meaning ‘x is vertically superior to y’. Interpret predicates like ‘RightOf’ and ‘LeftOf’ from your point of view.).


∀ Universal quantifier ‘for every object’, ‘for all objects’

∃ Existential quantifier ‘there is an object’, ‘for some object’

¬ Negation sign ‘it is not the case that’, ‘not’

& Conjunction sign ‘and’

V Disjunction sign ‘or’

→ Conditional sign ‘if … then …’

↔︎ Biconditional sign ‘if and only if’

= Identity sign ‘is the same thing as’, ‘equals’

≠ Nonidentity sign ‘is not the same thing as’, ‘does not equal’

( ) Parentheses


1. Translate the following propositions into English (5 points)

2. Indicate which of these propositions is true of the world depicted in the image, by writing '1' next to it. Indicate which of these propositions is false by writing '0' next to it. (5 points)


a.

∃xBrickBlock(x)

b.

¬∃xMushroom(x)

c.

∀x(Mushroom(x) → ∃y(Koopa(y) & Below(x,y)))

d.

∃x(Spike(x) & ∃y(Fireball(y) & ∃z(Goomba(z) & Between(x,y,z))))

e.

∀x(Koopa(x) → ∃y(Shelly(y) & Above(x,y)))

f.

∀x(Koopa(x) → Red(x))

g.

¬∀x(Mushroom(x) → Green(x))

h.

∃x(Mushroom(x) & Green(x))

i.

∀x(Spike(x) → ∃y(Koopa(y) & Below(x,y)))

j.

∃x(Koopa(x) & ∃y(Lakitu(y) & RightOf(x,y))))