Interpreting “$X \text{ but } Y$“ as $$X \wedge Y \wedge \diamond(X\wedge\neg Y)$$ is a reasonable starting point. (“X and Y and it would be possible to have X and not Y”.)

This works for the basic examples I found in online dictionaries:

• “He stumbled but did not fall”
• “She fell but wasn’t hurt”
• “He was poor but proud”
• “She’s 83 but she still goes swimming every day”
• “My brother went but I did not”

This correctly identifies that “he is a bachelor but unmarried” is not an appropriate use of “but”.

And this also shows the difference between such examples as:

• “That comment was harsh but fair.” (It was harsh and fair, while some critiques are harsh and unfair.)
• “That comment was fair but harsh.” (It was fair and harsh, while some critiques are fair and compassionate.)

Interpreting “$X \text{ but } Y$“ as $$X \wedge Y \wedge \diamond(X\wedge\neg Y)$$ is a reasonable starting point. (“X and Y and it would be possible to have X and not Y”.)

This works for the basic examples I found in online dictionaries:

• “He was poor but proud”
• “She’s 83 but she still goes swimming every day”
• “My brother went but I did not”
• “He stumbled but did not fall”
• “She fell but wasn’t hurt”

This correctly identifies that “he is a bachelor but unmarried” is not an appropriate use of “but”.

And this also shows the difference between such examples as:

• “That comment was harsh but fair.” (It was harsh and fair, while some comments are harsh and unfair.)
• “That comment was fair but harsh.” (It was fair and harsh, while some comments are fair and compassionate.)