# Semantic Operators

### A Certain / A Particular

• If, on a certain day, Q and T enter the building second and third …
• If the fewest possible colors are used and one of the countries is the only one of a certain color …

It seems that “a certain” means “some” which takes widest scope. I.e. in that last example:

• There is some color such that one of the countries is the only one of that color
• and not: one of the countries is the only one such that there is some color that it is of.
• (This second sentence is always false, because for each country, there is some color that it is of).

### Any

There are various ways in which this can be used, and a complex interaction with other operators (negation, modals).
Some Examples from logic puzzles.

### Floating Each

Normal:

• Each of six scientists A, B, C, D, E, and F are to present a paper at a one-day conference.

Floating:

• Six scientists A, B, C, D, E, and F are to present a paper each at a one-day conference.
• Exactly six of seven jugglers — G, H, K, L, N, P, and Q — are each assigned to exactly one of three positions

Some Examples from logic puzzles.

### Except

• No two plays by the same playwright will be scheduled for any of the five weeks, except for week 3, for which two plays by playwright R will be scheduled.

### Only, Alone

• Each office is to be painted only one color according to the following conditions …
• Each office is to be painted one color only according to the following conditions …
• If Trisha is assigned to locker 3 and Marc alone is assigned to locker 1 …
• Some Examples from logic puzzles.

### Respectively

• F and E are the fifth and sixth presenters respectively.
• => F is the fifth presenter.
• => E is the sixth presenter.