Can you apply the Monk's Martial Arts feature only to your attack roll but not your damage roll?

Question

The Monk's Martial Arts feature states:

You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons...

Originally I thought this meant you had to either replace use Strength for both rolls or use Dexterity for both rolls. But the section on Finesse weapons states:

When making an attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the attack and damage rolls. You must use the same modifier for both rolls.

Both features have the same "for the attack and damage rolls" bit; however, Martial Arts lacks the requirement that you must use the same modifier for both rolls. Does this mean that you are able to replace only the attack roll's (or only the damage roll's) modifier?

One reason you might want to mix up your modifiers is any time where you want to damage (and thus hit) a creature, but you don't want to deal a lot of damage to it.
In a case like that you would want to use your higher modifier for the attack and your lower modifier for the damage.

Answer 1

No; you apply the same ability modifier to both rolls.

As quoted in your question, the relevant portion of the Martial Arts feature description says (emphasis mine):

You can use Dexterity instead of Strength for the attack and damage rolls of your unarmed strikes and monk weapons.

The feature doesn't give you an option to use Dexterity for your attack roll and Strength for your damage roll, or vice versa. It gives you the option to use Dexterity for both, instead of Strength for both (as would otherwise be the case).

The key word here is "and". If it said "the attack or damage rolls", then you might be able to add your Strength modifier to your attack roll and your Dexterity modifier to your damage roll, or vice versa - but the word "and" here means that the modifier you choose is applied to both rolls.

Thus, the second description of the finesse weapon property is redundant:

When making an attack with a finesse weapon, you use your choice of your Strength or Dexterity modifier for the attack and damage rolls. You must use the same modifier for both rolls.

The second sentence merely clarifies what's already stated in the first sentence - that you can choose either Strength or Dexterity to apply to both your attack and damage rolls. Even without this sentence, the same modifier must be used for both rolls.

This reading relies on a strict reading of the text. "You can use it for attack and damage rolls" could be interpreted to mean "You can use it for attack or damage rolls", but it doesn't seem as natural a reading of the text in this case. Virtually nothing in the game provides for using one modifier for the attack roll and a different modifier for damage rolls.

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This is more explicitly supported by the rules on damage rolls:

When attacking with a weapon, you add your ability modifier — the same modifier used for the attack roll — to the damage.

As you can see, the general rule is that you apply the same ability modifier to both the attack and damage rolls when attacking with weapons (and presumably unarmed strikes as well). The monk's Martial Arts feature lets them use Dexterity instead of Strength for unarmed strikes and monk weapons.

If the intent was to allow you to use different ability modifiers for each one, it would need to explicitly state that this is allowed. In the absence of such an explicit declaration, the same ability modifier must be used for both attack and damage rolls.

Answer 2

Yes, You can use a different modifier for each roll.

Basic English Ambiguity

There are three cases that are hard to describe concisely and unambiguously in English:

1.)

You can use Dexterity instead of strength for attack rolls and damage rolls (you must use the same for both for a single attack).

2.)

You can use Dexterity instead of strength for attack rolls and (as an independent choice) you can use Dexterity instead of strength for damage rolls.

3.)

You can use Dexterity instead of strength for attack rolls or damage rolls (but not both for a single attack).

Without additional context, the phrasing

You can use Dexterity instead of Strength for the attack and damage rolls <...>

could be interpreted as either 1.) or 2.) above.

If it used or instead, it would still be ambiguous, and without additional context

You can use Dexterity instead of Strength for the attack or damage rolls of your unarmed strikes and monk weapons

it could be interpreted as either 2.) or 3.) above, but we couldn't distinguish between the "Inclusive Or" (A or B or both) and the "Exclusive Or" (A or B but not both).

DnD Specific Context

To resolve this question then, we need to look at what DnD 5e typically means when it uses these words in other places where its less ambiguous, and use that information to determine a result here.

And/Or In the Rules

One common way to indicate the inclusive or (one or the other or both) is to use "and/or". This phrase did not appear anywhere in the Basic Rules, so they must be using either "and" or "or" by itself.

This supports the idea that "and" might mean "one or the other or both"

Or Elsewhere in the Rules

To help us resolve the ambiguity, we need to look at how "and" and "or" are used elsewhere in the rules.

From the (basic rules) it's clear that "or" is commonly used as the "exclusive or", that is, to indicate you can do one thing, or the other thing, but not both.

You start with the following equipment, in addition to the equipment granted by your background: <...> (a) a mace or (b) a warhammer (if proficient)

and

When you reach 4th level, and again at 8th, 12th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you can increase two ability scores of your choice by 1.

In both of these cases, it's pretty clear you're not starting with a mace or a warhammer or both, and it's pretty clear you're not improving one ability score by 2 or 2 by 1 or both.

This supports the idea they would have only written the ability as "You can use Dexterity instead of Strength for Attack Rolls or Damage Rolls" if they meant you can use it for one or the other, but not both.

And Elsewhere in The Rules

Again from the Basic Rules:

Forage. The character can keep an eye out for ready sources of food and water

Here and clearly means "The character can keep an eye out for ready sources of food. He can also keep an eye out for ready sources of water." It does not mean he can only spot sources which provide both.

This weakens the argument that "and" by itself is sufficient to mean the ability applies to everything or nothing

Finesse Weapons

As you noted in the question, the very similar text for Finesse Weapons feels the need to specifically add

You must use the same modifier for both rolls.

This weakens the argument that "and" by itself is sufficient to mean the ability applies to everything or nothing

Final Ruling (w/ Caveat)

Note: I skimmed the basic rules for the most common usage of "and" and "or", trying to remain unbiased and inserted what I considered "typical" examples of their usage. An exhaustive or statistically significant comparison might find the actual most common usage is different from what I found.

Considering the way the Basic Rules use "and" and "or", I believe RAW a monk could use Dexterity for the attack roll, and Strength for a Damage Roll

Handy Interpretation Chart For Similar Situations

Inclusive Or

You can use for X and Y.

You can use for X. You can use for Y. You can use for both.

Exclusive Or

You can use for X or Y.

You can use for X. You can use for Y. You cannot use for both.

Both are Linked

You can use for X and Y. If you use for X, you must use it for Y (or similar language)

You can use for X if and only if you use for Y also. Cannot do one or the other.