Students often need some axioms and/or definitions to play with in order to learn formal logic.
What is a definition of a neighbor written in the style of symbolic logic?
By neighbor, we mean a person who lives in a house or an apartment nearby.
For any two people x and y, person x is a neighbor of person y if and only if ... [what are our conditions?]
- What definition, in symbolic logic, might you provide for the string of text nearby?
- What definition, in symbolic logic, might you provide for the string of text house or apartment?
There are two different notions of neighbor that we want to combine:
rural setting. nobody lives within 1 kilometer of your house or apartment, so we consider your neighbors to be the people living in the two closest houses and/or apartment buildings
anybody living in a house or a apartment on the same street that your house or apartment is located on provided that houses are in an urban setting (less than 1/4 mile of open air between a wall in house h1 and a wall in house h2.
A person is said to live in a house or an apartment if the person sleeps in that house or apartment more often than they sleep in other places.
The law might be a good resource for inspiration, but we wish to focus on symbolic logic as much as possible. Ideally, our answer should sound somewhat like a mathematical short paragraph.
| Symbol(s) | English String of Text |
Semantic Notes/Examples |
|---|---|---|
| ∀ | for any |
If I have at least one sister, then every sister of mine is younger than me |
| ∃ | there exists |
I have at least one sister |
| ^ |
conjunction and |
The liquid in vessel v t time t₀ contains water, minced mint leaves, prickly pear fruit juice, edible clay, and the liquid in vessel v at time t₀ contains no other things. |
| v | disjuction and/or |
You may walk and/or hike in this area. |
| ⇒ → ⊃ |
if |
for any x, if x is red iron oxide, then eating x is good for anemia. there exists x such that x is red colored, but eating x is just as good for anemia as a random iron-less edible food item (such as beet root) |
What is a definition, written in symbolic logic, for a person living nearby?
It can never be the empty set, consider the person closest to you in the event that you are at least 10 miles from anybody else in the Universe.
