Well, if you analyze the statements in terms of prepositional logic, then all the English language conjunctions “and”, “but”, “though”, etc. map to the only type of logical conjunction ∧.
But natural language is richer than (directly mapped) prepositional logic. I interpret the statement “Local roads, though, are still predominantly conventional.” as a clarification of “Intelligent roads are in use, primarily for long-distance travel.”.
Formally, if you just claim: ”Intelligent roads are in use, primarily for long-distance travel.” it is equivalent to: ”Intelligent roads are in use, primarily for long-distance travel.” ∧ ( “Local roads are still predominantly conventional” ∨ ¬”Local roads are still predominantly conventional” ) which is different from ”Intelligent roads are in use, primarily for long-distance travel.” ∧ “Local roads are still predominantly conventional”
However, we can assume that if you claim: ”Intelligent roads are in use, primarily for long-distance travel.” you also wanted to communicate that ”Local roads are still predominantly conventional” not that you are undecided between ”Local roads are still predominantly conventional”, ¬”Local roads are still predominantly conventional” otherwise you would have probably stated that explicitely.
Therefore, the information content of: ”Intelligent roads are in use, primarily for long-distance travel.” and: ”Intelligent roads are in use, primarily for long-distance travel. Local roads, though, are still predominantly conventional.” is rougly the same.
Well, if you analyze the statements in terms of prepositional logic, then all the English language conjunctions “and”, “but”, “though”, etc. map to the only type of logical conjunction ∧.
But natural language is richer than (directly mapped) prepositional logic. I interpret the statement “Local roads, though, are still predominantly conventional.” as a clarification of “Intelligent roads are in use, primarily for long-distance travel.”.
Formally, if you just claim:
”Intelligent roads are in use, primarily for long-distance travel.”
it is equivalent to:
”Intelligent roads are in use, primarily for long-distance travel.” ∧ ( “Local roads are still predominantly conventional” ∨ ¬”Local roads are still predominantly conventional” )
which is different from
”Intelligent roads are in use, primarily for long-distance travel.” ∧ “Local roads are still predominantly conventional”
However, we can assume that if you claim:
”Intelligent roads are in use, primarily for long-distance travel.”
you also wanted to communicate that
”Local roads are still predominantly conventional”
not that you are undecided between
”Local roads are still predominantly conventional”, ¬”Local roads are still predominantly conventional”
otherwise you would have probably stated that explicitely.
Therefore, the information content of:
”Intelligent roads are in use, primarily for long-distance travel.”
and:
”Intelligent roads are in use, primarily for long-distance travel. Local roads, though, are still predominantly conventional.”
is rougly the same.