If and related words are used in many logical and beyond-logic ways. This writeup is an effort to explore them.

1 If

1.1 If it rains, I’ll get wet

Logical part

R \rightarrow W

Raining?	Wet?	Consistent with phrase?
No	No	Yes
No	Yes	Yes
Yes	No	No
Yes	Yes	Yes

Beyond logic

There’s a temporal connotation (rain starts shortly before wetness) which propositional logic cannot encode.

There’s a causal connotation (rain creates the wetness) which propositional logic cannot encode.

1.2 If you earn 93% or more, you get an A

Logical part

E \leftrightarrow A

Earned 93?	Get A?	Consistent with phrase?
No	No	Yes
No	Yes	No
Yes	No	No
Yes	Yes	Yes

Beyond logic

There’s a temporal connotation (you get the 93% before you get the A) which propositional logic cannot encode.

The \leftarrow part is fuzzy: a 92.8% might get an A, but a 81% won’t. The \rightarrow part is implicitly or more: an A+ would not be a problem. Propositional logic cannot encode this fuzz.

1.3 This program crashes if you type Ctrl+Q

Logical part

C \leftarrow Q

It crashes?	Ctrl+Q?	Consistent with phrase?
No	No	Yes
No	Yes	No
Yes	No	Yes
Yes	Yes	Yes

Beyond logic

There’s a temporal connotation (you type Ctrl+Q before it crashes) which propositional logic cannot encode.

There’s a causal connotation (typing Ctrl+Q triggers the crash) which propositional logic cannot encode.

2 When

2.1 I love it when it rains

Logical part

L \leftarrow R

I love it?	It rains?	Consistent with phrase?
No	No	Yes
No	Yes	No
Yes	No	Yes
Yes	Yes	Yes

Beyond logic

When connotes that the truth of R comes and goes. It also connotes that rain will happen eventually; if in this phrase would have the same logical meaning, but would imply doubt that rain would ever occur.

2.2 I sing when in the shower

Logical part

\top

I sing?	Showering?	Consistent with phrase?
No	No	Yes
No	Yes	Yes
Yes	No	Yes
Yes	Yes	Yes

Beyond logic

This means that there exist some times when I am both in the shower and singing, but does not rule out either singing outside the shower nor that I might have some in-shower time when I’m not singing. We can encode that there exists some time idea with first-order logic (i.e. \exist t \;.\; S(t) \land H(t)) but not with propositional logic.

3 Only

3.1 It only rains at night

Logical part

R \rightarrow N

It rains?	It’s night?	Consistent with phrase?
No	No	Yes
No	Yes	Yes
Yes	No	No
Yes	Yes	Yes

Beyond logic

This one is close to just logic. ☺

3.2 I only love my spouse

Logical part

L \leftrightarrow S

I love it?	It’s my spouse?	Consistent with phrase?
No	No	Yes
No	Yes	No
Yes	No	No
Yes	Yes	Yes

Beyond logic

The use of only implies love means something more specific than it would in a phrase like I love cake and possibly more specific than even I love my spouse.