WordNet records no synonym and no antonym for loggia. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a roofed arcade or gallery with open sides stretching along the front or side of a building; often at an upper level
Synonyms, antonyms and the broader and narrower relations for loggia come from Princeton University’s WordNet. Full sources and licences.