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I a never-so-mentioned matter, that being how we are able to make sense of grammar in a non-statistical method. Many AI fashions, equivalent to DeepMind’s GEM, and Google’s PARSEVAL don’t rely purely on statistical studying to make sense of grammar. As a substitute, these hybrid fashions reintroduce formal grammars, equivalent to Combinatory Categorial Grammar (CCG), into their structure. This permits these fashions to utilize a long time of Linguistic evaluation in only a few traces of code. Theoretically, permitting them to succeed in the identical stage of competence in much less time and at much less value. However how can we flip grammar into one thing a pc can work with?
To grasp this, we’ll discuss how phrases flip into features, the Algebra behind their mixture, and the way a program returning a TypeError is, in some ways, equal to a sentence with unhealthy grammar.
Pay attention, undefined may convey again some unhealthy reminiscences — phrases crossed out in crimson, ruler to the wrist, or a clean stare within the face of “preposition”.
To a grammarian, that is aided by a set of prescriptive guidelines. Instructions like:
- Thou shalt not use “whom” as a topic.
- Thou shalt have a topic and an object in a sentence.
- Thou shalt not finish sentences with prepositions (at, by, into,…).
As a author, I’ve all the time discovered the commandments a bit restrictive—half ache, half medication. And whereas I can admit this grammar can make clear your writing, it doesn’t assist machines perceive sentence construction. To do that, we might want to focus on Combinatory Categorial Grammar (CCG), if you happen to’re acquainted. Nonetheless, we can not abandon prescriptive grammar. And on this article we’ll use the 2nd Commandment: Each sentence should include a transparent topic and predicate.
From NLP to Proof Nets
Within the early 2000s, statistical CCG parsers had been leaders in offering extensive protection and high-accuracy syntactic parsing by capturing long-distance dependencies and complicated coordination. Whereas not the present sizzling matter in LLMs, it has helped form question-answering, logical inference, and machine translation methods the place structural transparency is desired.
Whereas grammar can now be inferred from sheer information alone, no want for hand-coded guidelines, nonetheless, many state-of-the-art fashions re-inject syntactic alerts as a result of:
- Implicit studying alone can miss corner-case phenomena. A parser might be made to deal with triple-negatives in legalese or enjambment in poetry, however provided that you explicitly encode these patterns.
- Present sooner studying with much less information. Studying grammar from information alone requires billions of data and is computationally expensive.
- Interpretability and management. When analyzing syntactic errors, it’s simpler to take a look at parse-based options than opaque consideration weights.
- Consistency in technology. Purely emergent fashions can drift, flipping verb tenses mid-sentence, mismatching pronouns and antecedents. A syntax-aware parser or grammar module can implement this explicitly.
- Low-resource language constraints. Swahili or Welsh might have much less out there information for typical large-scale coaching. Hand-coded grammar guidelines make up for that.
Proof Nets
Another excuse CCG continues to matter is its deep connection to proof nets (Girard 1987). Proof nets are a graph-based method of representing proofs in linear logic that strip away bureaucratic particulars to disclose the core logical construction. Morrill (1994) and Moot & Retoré (2012) proved that each CCG parse might be translated into considered one of these canonical proof-net graphs, giving a direct, formal bridge between CCG’s syntactic derivations and linear-logic proofs. Lengthy-distance dependencies emerge as specific paths, derivational redundancies are eradicated, and semantic composition follows graph contractions. Once we say linear logic, each components have to be used precisely as soon as in a derivation.
Consider it this manner: as you construct a CCG parse (or its proof web), every syntactic mixture (e.g. a verb phrase combining with its topic) tells you precisely which semantic operation to carry out (perform‐software, perform‐composition, and many others.). That sequence of syntax‐guided steps then composes the meanings of particular person phrases into the which means of the entire sentence in a formally exact method.
The C&C parser and EasyCCG (Lewis & Steedman, 2014) are outstanding instruments within the discipline of CCG parsing. Whereas each are extensively used, EasyCCG is mostly acknowledged for its pace, usually reaching sooner parsing occasions, whereas the C&C parser is often famous for its accuracy, notably on advanced sentences.
The place are we precisely?
Formally Kind-1 on Chomsky Hierarchy, proper under Turing Machines, proper above Pushdown Automata. Kind-1 is Context-Delicate. The deeper the language is within the Chomsky Hierarchy, the upper the generative energy, structural complexity, and computational sources required to parse it.
- Parse: to find out if a string might be constructed given the grammar guidelines.
- Language ( 𝑳) is a finite set of phrases composed by taking parts from an Alphabet (𝚺) set, which accommodates all of the symbols for that language.
With the broader definition, “phrases” don’t need to be phrases. For instance, our “phrases” might be electronic mail addresses, and our alphabet might be numbers, letters, and symbols.
In English, If we need to discuss complete sentences, we are able to let our alphabet Σ be the set of all phrases (our vocabulary). Then a sentence is any finite string in Σ*, and a language L⊆Σ* is simply the set of “well-formed” sentences we care about.
Given this summary definition for language, we are able to discuss esoteric constructions equivalent to languages the place all phrases are issues like (ab, aab, aaabbbb, abb, and many others.) Formally described as follows:
Right here exponentiation seems extra like appending issues to the tip of a string so 3² = 33 ≠ 9
This language is Kind-3 on the hierarchy, a Common Expression . Whereas it is likely to be laborious to seek out sensible makes use of for the above language, probably the most ubiquitous examples of Common Expressions coming to make use of in the actual world is email-address validation on internet types: behind the scenes, the shape makes use of a regex like…
^[A-Za-z0-9._%+-]+@[A-Za-z0-9.-]+.[A-Za-z]{2,}$this@[email protected]@😡grammar.in_the_email_language.ca
Right here the only goal of our grammar is to be sure to enter a sound electronic mail deal with. In CCG our grammar has a extra liguistic goal, it checks if phrases mix gramatically.
Chomsky’s Hierarchy in NLP
As you progress from Kind-3 to Kind-0, you lower the constraints on what you possibly can produce. This will increase the expressive energy at the price of further computation.
Kind-0 (Recursively enumerable grammars): Full semantic parsing or technology in a Turing-complete formalism (e.g. Prolog DCGs with arbitrary further arguments, or neural seq2seq fashions that in precept can simulate any Turing machine).
Kind-1 (Context-sensitive grammars): Swiss-German makes use of cross-serial dependency, the place you want extra details about the encompassing phrases earlier than rewriting. This could require extra computational steps to parse.
Once we cowl the Algrbra of CCG later come again and see how utilizing just one ahead and backward software may encounter a problem with Swiss-German (Trace: it’s important to mix adjoining classes)
Kind-2 (Context-free grammars): A CCG turns into a pure Kind-II (context-free) grammar precisely if you solely permit the 2 software guidelines and no higher-order combinators (kind‐elevating or composition).
Kind-3 (Common grammars): Tokenization, easy sample–primarily based tagging (e.g. recognizing dates, electronic mail addresses, or part-of-speech tags utilizing common expressions or finite‐state transducers)
The Algebra of CCG
Let’s say we now have classes A and B, then ahead software and backward software work as follows:
- A/B says that if we now have a B to the proper of A/B, then the ensuing product is A
- AB says that if we now have a B to the left of AB, then the ensuing product is A.
in apply A and B grow to be components of sheach
The algebra of CCG seems rather a lot just like the multiplication of fractions; discover how “numerators” cancel with “denominators”. Nonetheless, in contrast to multiplication, the order issues. This algebra is not commutative. Don’t bear in mind this as a rule, however a direct consequence of phrase order. This lack of commutativity is critical to distinguish between “We go there.” As a sentence, and “Go we there.” as nonsense.
Combining two atomic classes utilizing or /, (e.g: NP/N) creates a advanced class that classifies a phrase and describes how it may be mixed.
Within the following illustration, “The” combines with “Canine”(Noun (N)) to make the Noun Phrase (NP) “The canine”. Equally, the Noun Phrase “The canine” can mix with “ran”(verb(SNP)) to make the sentence (S) “The canine ran”.
Setting up Full Sentences
Take one thing just like the phrase “a”—clearly not a Noun, Noun Phrase, or Sentence, however we may describe it in these phrases by saying “a” is a phrase that expects a noun on the appropriate to grow to be a noun phrase:
“a” = NP/N
That is how “a ball” (NP/N N → NP) turns into a noun phrase.
Do you see how we are able to cleverly describe articles (a, an, the) by way of NP and N to create a class that describes how they perform, how they work together with the phrases round them? Why name “the” an article once we can name it a perform that expects a noun to grow to be a noun phrase?
We will do the identical factor with verbs. To type a sentence S, we want a topic and a predicate.
- The Topic (RED) does the motion.
- The motion is the verb.
- The Predicate (BLUE) receives the motion.
By splitting the sentence this manner, we are able to see that the verb acts as a fulcrum between two needed components of sentence development, so that you shouldn’t be shocked to see that the verb and adverb take a really particular function in CCG, as they’re classes that include the atomic class S.
We will describe a Verb as one thing that takes a Noun Phrase to the left, and a Noun Phrase to the appropriate to grow to be a sentence. (SNP)/NP. No further atomic classes wanted.
“After debugging for hours” is a subordinate (dependent) adverbial clause. Parsable by C&C or EasyCCG
How This Pertains to Programming
The factor I discover most elegant about CCG is the way it turns the verb “write” right into a perform (SNP)/NP that takes a Noun Phrase to the left and proper as enter to output a sentence. By treating phrases as features, the CCG parser type-checks a sentence the identical method a compiler type-checks a program.
A dreaded TypeError will ensue if you happen to attempt to make a sentence like “run write stroll.” This is not going to compile the identical method sum(“phrase”) wouldn’t compile. Within the first case, you enter a verb the place a Noun Phrase was anticipated, and within the second, you enter a string the place a quantity was anticipated. TypeError
In Lambda calculus, we may write:
λo. λs. write s o -- anticipate an object o, then a topic sIn CCG, each lexical merchandise carries not solely a syntactic class but additionally a small lambda-term encoding its which means — e.g. write is likely to be assigned (S(SNP)/NP with semantics λo. λs.write(s, o) to point it first takes an object (o), then a topic (s). As you apply CCG’s combinatory guidelines (like perform software), you concurrently apply these lambda-terms, composing the meanings of phrases step-by-step into a whole logical type for the entire sentence.
Lambda calculus is a very small formal language that does one factor: It describes methods to construct features and methods to run them. Every thing else — numbers, Booleans, information constructions, even complete applications — might be encoded by way of these features. Consequently, the lambda calculus serves as a exact mathematical mannequin of computation itself.
Conclusion
The facility of CCG lies in its potential to remodel language into an algebraic system, offering a transparent set of compositional directions. That is extremely helpful for revealing the connections between human language and formal computation. Admittedly, the CCG defined right here just isn’t complete sufficient to parse sentences like:
Parsing these sentences requires much more. Once you attempt to construct a complete CCG system to deal with real-world English at scale, you want over 1,200 completely different grammatical classes, revealing how a lot hidden complexity exists in what looks like “extraordinary” language use.
Even the next development is a simplified mannequin:
S
├── S
│ ├── NP CCG
│ └── SNP
│ ├── (SNP)/NP is not
│ └── NP
│ ├── NP/NP simply
│ └── NP
│ ├── NP/N a
│ └── N
│ ├── N/N highly effective
│ └── N
│ ├── N method
│ └── NN
│ ├── (NN)/NP for
│ └── NP
│ ├── NP computer systems
│ └── NPNP
│ ├── (NPNP)/(SNP) to
│ └── SNP
│ ├── (SNP)/NP perceive
│ └── NP
│ ├── N/N sentence
│ └── N construction
├── (SS)/S ; (punctuation)
└── S
├── NP it
└── SNP
├── (SNP)(SNP) additionally
└── SNP
├── (SNP)/(S[TO]NP) seems
└── S[TO]NP
├── (S[TO]NP)/(SNP) to
└── SNP
├── (SNP)/NP mirror
└── NP
├── NP/(SNP) how
└── N
├── N/N our
└── N
├── N brains
└── NN
├── (NN)/NP course of
└── NP languageAt its core, CCG gives a methodical and rigorous strategy to separating sentences, reassembling them, and making certain grammatical consistency. All of the whereas avoiding incomplete sentences like:
References
Wang, S., … et al. (2024). Computational fashions to check language processing within the human mind: A survey. arXiv preprint arXiv:2403.13368. https://arxiv.org/abs/2403.13368
Lewis, M., & Steedman, M. (2014). A* CCG parsing with a supertagger and sensible dynamic programming. In Proceedings of the 2014 Convention on Empirical Strategies in Pure Language Processing (EMNLP) (pp. 1787–1798).
Girard, J.-Y. (1987). Linear logic. Theoretical Laptop Science, 50(1), 1–102.
Morrill, G. (1994). Categorial deduction. Journal of Logic, Language and Data, 3(3), 287–321.
Moot, R., & Retoré, C. (2012). The logic of categorial grammars: A deductive account of pure language syntax and semantics. Springer.
Jurafsky, D., & Martin, J. H. (2023). Speech and language processing (third ed.) [Appendix E: Combinatory Categorial Grammar]. Retrieved Could 29, 2025, from https://internet.stanford.edu/~jurafsky/slp3/E.pdf
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