- Quantifiers: for all, some, none, etc.

These will be covered in later sections on Predicate Logic. (Chapter 6) - Modal termns: possibly, necessarily, never ...

These are terms which are translated in Modal logic (covered in the Philosophy course on Deviant Logic but also used in computer science). - Timing statements: eventually, within 10 minutes,
never (in the sense of time)

These are terms in Temporal Logic - also used in Computer Science to analyse time dependent contral systems etc. - Second Order: for all sequences, for arbitrary finite strings...

These statements which involve infinite collections of our basic objects, belong to higher order logic, which we will not cover. However they are used all the time in Mathematics (and Computer Science). - Space statements: At the workshop on Thinking with Diagrams (which I missed some classes to attend) people described a number of systems (including modified modal systems) which correspond to parts of 'visual reasoning' as it effects, say, design of computer interfaces, or even learning of diagrams for logic!

(a) inclusive

(b) exclusive

A number of confusing translations can also be viewed
as variants of this issue.
In particular, the distinction between inclusive ** or ** and exclusive
** or ** rests on one line of the truth table:

(T,T) | T vs (T,T) | F
If we look at the table of the ** conditional ** A > B,
which is logically equivalent to the inclusive ~A ** or ** B,
this issue rests on the line of the
truth table for (F,T). We have said this is (F,T) ... T.
People who anticipate that this line for conditional
would be (F,T) F, are giving a truth table for the ** biconditional **
A \equiv B
Thus the distinction between ** conditional ** and ** biconditional ** is
has the same roots as the distinction between inclusive and
exclusive ** or **.
We want these two tables to be different and to represent
distinct words in natural language. Perhaps this comparison will clarify
what is happening in some confusing translations.
Consider the confusion in class of translating
A unless B
Logically equivalent translations of this include:
~B > A, A v B and ~A > B.
However if you read the ** or ** of 'unless' as an exclusive OR,
the equivalent forms include:

[A v B] & [~A v ~B] and [~B > A] & [ A > ~B] and ~B <> A .

In all cases, the convention in mathematics is thart ** or ** is
inclusive. If * we * mean exclusive ** or **, * we *will say that.
If * we * mean biconditional rather than conditional, * we * will say that as well.

In general, I find it very useful, when puzzling about a sentence in SL to consider other logically equivalent forms. I recommend building up your repetoire of quick exchanges among logically equivalent forms. The lists inside the from cover of the text are a good place to start.