We propose a new method for semantic parsing of ambiguous and ungrammatical input, such as search queries. We do so by building on an existing semantic parsing framework that uses synchronous context free grammars (SCFG) to jointly model the input sentence and output meaning representation. We generalize this SCFG framework to allow not one, but multiple outputs. Using this formalism, we construct a grammar that takes an ambiguous input string and jointly maps it into both a meaning representation and a natural language paraphrase that is less ambiguous than the original input. This paraphrase can be used to disambiguate the meaning representation via verification using a language model that calculates the probability of each paraphrase.