dependent of mortal, via a dependency link mod (for modifier ). Projective dependency grammars are ones with ... Structure Grammar (GPSG), Head -driven Phrase Structure Grammar (HPSG), Lexical-Functional Grammar (LFG), ... sensitivity include Head Grammar , Tree-Adjoining Grammar (TAG), Combinatory Categorial Grammar (CCG), and Linear ... At the same time it should be noted that at least some natural languages have been shown to be mildly context-sensitive (e.g., Dutch and Swiss German exhibit cross-serial dependencies where a series of nominals “NP1 NP2 NP3 …” need to be matched, in the same order, with a subsequent series of verbs, “V1 V2 V3 …”). Grammatical frameworks that seem to allow for approximately the right degree of mild context sensitivity include Head Grammar, Tree-Adjoining Grammar (TAG), Combinatory Categorial Grammar (CCG), and Linear Indexed Grammar (LIG). Head grammars allow insertion of a complement between the head of a phrase (e.g., the initial verb of a VP, the final noun of a NP, or the VP of a sentence) and an already present complement; they were a historical predecessor of Head-Driven Phrase Structure Grammar (HPSG), a type of unification grammar (see below) that has received much attention in computational linguistics. However, unrestricted HPSG can generate the recursively enumerable (in general only semi-decidable) languages. The difference from CFGs is that hierarchical grouping is achieved by directly subordinating words to words (allowing for multiple dependents of a head word ), rather than phrases to phrases. For example, in the sentence of figure 1 we would treat Thetis and mortal as dependents of loves , using dependency links labeled subj and obj respectively, and the determiner a would in turn be a dependent of mortal , via a dependency link mod (for modifier ). Projective dependency grammars are ones with no crossing dependencies (so that the descendants of a node form a continuous text segment), and these generate the same languages as CFGs. Significantly, mildly non-projective dependency grammars, allowing a head word to dominate two separated blocks, provide the same generative capacity as the previously mentioned mildly context-sensitive frameworks that are needed for some languages (Kuhlmann 2013). As noted at the beginning of this section, traditional formal grammars proved too limited in coverage and too rigid in their grammaticality criteria to provide a basis for robust coverage of natural languages as actually used, and this situation persisted until the advent of probabilistic grammars derived from sizable phrase-bracketed corpora (notably the Penn Treebank). Examples of knowledge-based disambiguation would be the disambiguation of ice sculpture to a constitutive relation based on the knowledge that sculptures may be carved or constructed from solid materials, or the disambiguation of a man with a hat to a wearing -relation based on the knowledge that a hat is normally worn on the head. Thus it is important to place some constraints on the initial grammar, e.g., allowing nonterminals to generate either pairs of nonterminals or words, but not both, and also severely limiting the number of allowed nonterminals. A method of preferring small rule sets over large ones, without setting a fixed upper bound, is the use of a Dirichlet process that supplies a probability distribution over the probabilities of an unbounded number of rules. However, computational demonstrations have generally been restricted to very simple, English-like artificial languages, at least when inputs were unannotated word streams. A structure assignment task that can be viewed as a step towards semantic interpretation is semantic role labeling (Palmer et al. 2010). The goal is to assign thematic roles such as agent, theme, recipient, etc. to core phrases or phrasal heads in relation to verbs (and perhaps other complement-taking words). While phrase-based SMT models have been quite successful, they are nonetheless prone to production of syntactically disfluent or semantically odd translations, and much recent research has sought to exploit linguistic structure and patterns of meaning to improve translation quality. Two major approaches to syntactic transfer are hierarchical phrase-based translation and tree-to-string ( TTS ) transduction models. Hierarchical phrase-based approaches use synchronous grammar rules, which simultaneously expand partial derivations of corresponding sentences in two languages. These are automatically induced from an aligned corpus, and the lowest hierarchical layer corresponds to phrase-to-phrase translation rules like those in ordinary phrase-based translation. While quite successful, this approach provides little assurance that “phrases” in the resulting synchronous grammars are semantically coherent units, in the linguistic sense. TTS models obtain better coherency through use of parsers trained on phrase-bracketed text corpora (treebanks). For example, text corpora or newswire might be mined for information about companies, by keying in on known company names and terms such as “Corp.”, “.com”, “headquartered at”, and “annual revenue of”, as well as parts of speech and dependency relations, and matching regular-expression patterns against local text segments containing key phrases or positioned close to them. McCord, M., 1986, “Focalizers, the scoping problem, and semantic interpretation rules in logic grammars,” in M. Van Caneghem and D.H.D. Warren (eds.), Logic Programming and its Applications , Norwood, NJ: Ablex, 223–243. McKeown, K.R., 1985, Text Generation: Using Discourse Strategies and Focus Constraints to Generate Natural Language Text , Cambridge, UK: Cambridge University Press. Minsky, M., 1968, Semantic Information Processing , Cambridge, MA: MIT Press. Moldovan, D.I. and V.