A property is like a claim with a hole in it. Here are some examples of properties:
- ▯ is blue.
- ▯ is a student.
- ▯ walks to the store.
- Some people speak ▯ fluently.
- I don't know whether ▯ likes conlangs.
If you've looked at the Toaq dictionary, this notation may be familiar. Toaq verbs are defined as relations, which are claims with any number of holes in them. In other words, a property is a unary (one hole) relation.
You can think of the hole as "abstracting away" who the claim is about. In English, rather than leaving literal holes in our claims, we say things like: "blueness, studenthood, walking to the store."
"Satisfying" a property
Let's consider the property "some people speak ▯ fluently" and call it P.
If filling the hole with say, Esperanto, makes a true claim, "some people speak Esperanto fluently", then we say that Esperanto satisfies P.
In logical notation, we write P(Esperanto) to mean the filled-in claim "some people speak Esperanto fluently."
Using properties
Example: "try to"
There are many Toaq verbs with slots that expect a property:
leo = ▯ tries to satisfy property ▯.
Toaq has grammar to describe a property: you use a 
content clause with the word ja in it.
This word, ja, corresponds to the hole in the property.
For example:
gêanua ja ke tỏqfua
▯ lifts up the table.
Lẻo jí gêanua ja ke tỏqfua.
I try to satisfy "▯ lifts up the table."
In English, we just say "I try to lift up the table." There's no word that corresponds to ja. Properties in Toaq often correspond to English infinitives and gerunds.
Example: comparatives
Here is another example:
huaq = ▯ is more than ▯ in property ▯.
This word says that one thing satisfies some property to a greater degree/extent than another.
shêaqsao ja
▯ is tall.
Hủaq jí súq shêaqsao ja.
I am more than you in "▯ is tall."
I am taller than you.
This example somewhat demonstrates the usefulness of properties. We can say shêaqsao ja to refer to "tallness" or "being tall" in the abstract, and then use huaq to compare two concrete "fillings" of that property.
If we only had complete clauses, we'd have to repeat ourselves and say something like "shêaqsao jí is more true than shêaqsao súq".
ja is a determiner
The "property hole marker" ja is a determiner, just like sa or tushı. This means it can be followed by a verb in 
to give a name and domain to the hole it creates.
mîu ja dẻo môıjoe déo = ▯ (déo), a child, opines that déo is smart.
= "for children to find themselves smart."
Nested clause gotcha
One may approach expressing a property like I don't know whether ▯ likes conlangs like this:
*bû dủa jí mâ hẻ chỏ ja baq fỉeqzu
Sadly this is incorrect! The ja associates with the nested clause marked in red instead. In situations like these, one is forced to instead say
lâ ja pỏq bı bủ dủa jí mâ hẻ chỏ póq baq fỉeqzu.
Note tha this approach is never wrong – it’s never incorrect to move a ja into a topic phrase, and doing so reduces cognitive load on both speaker and listener.
Serial verbs
The rules of serial verbs are designed to work well with property slots.
They essentially let words with property slots, like leo and huaq, act as auxiliary verbs:
leo geanua = ▯ tries to lift up ▯.
huaq sheaqsao = ▯ is taller than ▯.
This works so well that you don't see Toaq speakers say ja anywhere near as often as they use verbs like leo and huaq. Once you're used to the rules of serial verbs, they're easier and shorter. But now you know how it works under the hood!
See the article on serial verbs for more info.