Well, you've got https://en.wikipedia.org/wiki/Lexical_functional_grammar https://en.wikipedia.org/wiki/Lexical_functional_grammar and https://en.wikipedia.org/

Well, you've got https://en.wikipedia.org/wiki/Lexical_functional_grammar https://en.wikipedia.org/wiki/Lexical_functional_grammar and https://en.wikipedia.org/wiki/Head-driven_phrase_structure_grammar https://en.wikipedia.org/wiki/Head-driven_phrase_structure_g... which are both model-theoretic grammars (see http://www.researchgate.net/publication/220718697_On_the_Distinction_between_Model-Theoretic_and_Generative-Enumerative_Syntactic_Frameworks http://www.researchgate.net/publication/220718697_On_the_Dis... ). In short, grammar rules are constraints that have to unify in order to describe a grammatical utterance, instead of phrase-structure rules that generate sentences. And there are newer theories that are much more compatible with a probabilistic / data-oriented outlook, even combining this with the model-theoretic grammar: http://www.nclt.dcu.ie/lfg-dop/ http://www.nclt.dcu.ie/lfg-dop/ People into semantics seem to like https://en.wikipedia.org/wiki/Construction_grammar https://en.wikipedia.org/wiki/Construction_grammar which I never learnt much about. Oh and there's also the Meaning-Text theory, Relational Grammar and various dependency-based frameworks, Optimality Theory applied to syntax, … it goes on and on :)