Abductive Logic Grammars

By extending logic grammars with constraint logic, we give them the ability to create knowledge bases that represent the meaning of an input string. Semantic information is thus defined through extra-grammatical means, and a sentence's meaning logically follows as a by-product of string rewriting. We formalize these ideas, and exemplify them both within and outside first-order logic, and for both fixed and dynamic knowledge bases. Within the latter variety, we consider the usual left-to-right derivations that are traditional in logic grammars, but also -- in a significant departure from the norm -- arbitrary (i.e., order-independent) derivations.
We show that rich and accurate knowledge extraction from text can be achieved through the use of this new formalism