Prepositions are words that link a noun or pronoun to other words in a sentence, indicating relationships like direction, time, place, or purpose. The correct choice of preposition often depends on the verb and the context. When someone is vaccinated, the primary purpose is to protect them against a specific disease. The preposition "against" correctly conveys this protective action, meaning to prevent or combat the disease.
Therefore, "vaccinated against polio" is the grammatically correct and most logical phrasing. Using "for" would imply vaccination on behalf of polio, which is nonsensical. "By" would typically indicate the agent performing the vaccination (e.g., "vaccinated by the nurse"). "With" might imply the substance used (e.g., "vaccinated with a new serum"), but not the disease itself. Hence, "against" is the most appropriate preposition.