Formal Grammars vs. Natural Language What LLMs Get Right (and Don’t)

Language. It’s what defines us, how we communicate, think, and build complex societies. But when we talk about “language” in the context of computers, we often find ourselves straddling two very different worlds: the precise, unambiguous realm of formal grammars and the rich, messy, inherently ambiguous domain of natural language. Large Language Models (LLMs) have burst onto the scene, seemingly bridging this chasm with unprecedented fluency. But how deep does that bridge go? What do LLMs truly “get” about language, and what remains elusive?

Let’s dive into this fascinating interplay.

The World of Formal Grammars: Precision and Predictability

Imagine a language where every word has one, and only one, meaning. Every sentence structure is perfectly defined, without exception. There’s no room for metaphor, sarcasm, or cultural nuance. This is, in essence, the world of formal grammars.

What are Formal Grammars?

At their core, formal grammars are sets of rules that define a language’s syntax—how its symbols (words, characters, tokens) can be combined to form valid “sentences” or expressions. They are mathematical constructs, often used in computer science and theoretical linguistics.

Key characteristics include:

• Strict Rules: Defined by a finite set of production rules that specify how symbols can be transformed or combined.
• Unambiguity: For a given input, there is typically only one way to parse it, or if multiple, the grammar explicitly defines how to resolve them.
• Predictability: Given a grammar, you can definitively determine if a string of symbols is “valid” or “grammatical” within that language.
• Deterministic Parsing: Compilers and interpreters rely on formal grammars (like Backus-Naur Form or BNF) to break down code into a structure they can understand and execute.

Examples of Formal Grammars in Action:

• Programming Languages: C++, Python, Java—all are defined by formal grammars. When you write print("Hello, world!") in Python, the Python interpreter uses a formal grammar to understand that print is a function call, "Hello, world!" is a string literal, and the parentheses enclose arguments. A misplaced comma or an unclosed parenthesis results in a precise syntax error.
• Regular Expressions (Regex): A mini-language for pattern matching, regex is a powerful formal grammar used for tasks like searching for specific text patterns or validating email addresses.
• Chomsky Hierarchy: Pioneered by Noam Chomsky, this hierarchy classifies formal grammars based on their expressive power, from the simplest Regular Grammars (like those describing regex) to the most complex Unrestricted Grammars (capable of describing any computable language). Source: Chomsky, N. (1956). Three models for the description of language. IRE Transactions on Information Theory, 2(3), 113-124.

The beauty of formal grammars lies in their precision. They enable computers to perform complex tasks like compilation, parsing, and data validation with absolute certainty, because there is no room for interpretation.

The Labyrinth of Natural Language: Ambiguity and Context

Now, let’s turn to the language we speak, write, and think in every day. Natural language is a vibrant, evolving, and often bewildering system.

What is Natural Language?

Natural languages (English, Spanish, Mandarin, Swahili, etc.) are human languages that have evolved naturally through use and interaction, not through explicit design by rules.

Key characteristics include:

• Ambiguity: Pervasive at every level—lexical (word meaning), syntactic (sentence structure), semantic (overall meaning), and pragmatic (meaning in context). Consider “The pen is in the box.” Does “pen” refer to a writing instrument or an animal enclosure? The context usually clarifies, but a computer needs to be explicitly taught this.
• Context Dependence: The meaning of words and sentences often depends heavily on the surrounding text, the speaker’s intent, the listener’s knowledge, and the shared cultural background.
• Evolution and Fluidity: Languages change over time, new words are coined, old ones fall out of use, and meanings shift. Slang, idioms, and cultural references constantly emerge.
• Pragmatics and Implicature: Beyond the literal meaning, natural language involves understanding implied meanings, sarcasm, irony, metaphors, and indirect speech acts. “It’s a bit chilly in here,” might not be a statement about temperature but a request to close a window.
• Infinite Creativity: Humans can generate and understand an infinite number of novel sentences.

Challenges for Machines:

The inherent ambiguity and context-dependence of natural language have historically made it incredibly difficult for computers to process and truly “understand.” Traditional AI approaches often struggled with parsing complex sentences or disambiguating word meanings without extensive, manually crafted rules and ontologies.

How LLMs Approach Language: Statistical Pattern Matching

Enter Large Language Models. Unlike traditional symbolic AI, which attempted to encode rules and knowledge directly, LLMs operate on a fundamentally different paradigm: statistical pattern recognition at massive scale.

The Underlying Mechanism:

LLMs are essentially neural networks (specifically, transformer architectures) trained on colossal datasets of text and code. Their primary objective during training is to predict the next word (or token) in a sequence, given the preceding words. Source: Vaswani, A., et al. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems, 30.

• Tokens and Embeddings: Text is broken down into “tokens” (words, sub-word units, punctuation). Each token is converted into a numerical vector (an “embedding”) that captures its semantic meaning and relationships to other tokens.
• Attention Mechanisms: The “transformer” architecture’s key innovation is its “attention mechanism,” which allows the model to weigh the importance of different tokens in the input sequence when processing a particular token. This is crucial for understanding long-range dependencies and context.
• Probabilistic Generation: When you prompt an LLM, it doesn’t “think” in terms of grammatical rules or logical deductions. Instead, it generates text by sampling the most probable next tokens based on the patterns it learned during training. It’s a highly sophisticated autocomplete engine.

Through this process, LLMs internalize statistical regularities, semantic relationships, and even some pragmatic patterns from the vast ocean of human-generated text.

What LLMs Get Right (and Why)

The capabilities of modern LLMs are undeniably impressive, often appearing to grasp the nuances of natural language in ways that were unthinkable just a few years ago.

1. Fluency and Coherence: LLMs excel at generating text that flows naturally, is grammatically plausible, and maintains topical coherence over long passages. This is a direct consequence of their training objective: predicting the next most probable word leads to syntactically well-formed and contextually relevant sentences. They have learned the statistical grammar of natural language, not through explicit rules, but through sheer exposure.

2. Contextual Awareness (to a degree): Thanks to attention mechanisms and massive training data, LLMs can often maintain context over hundreds or even thousands of tokens. They can disambiguate words based on surrounding text (e.g., “bank” as a financial institution vs. a river bank) and adjust their output style to match the prompt’s tone.

3. Semantic Nuance: LLMs can capture subtle differences in meaning and relationships between words. They understand that “king” is related to “queen” in the same way “man” is related to “woman” (as demonstrated by vector arithmetic in early word embeddings). This allows them to perform tasks like translation, summarization, and sentiment analysis effectively.

4. Code Generation and Understanding: This is where the bridge between formal and natural language becomes particularly apparent. Programming languages, being formal grammars, have highly predictable and structured patterns. LLMs, having seen billions of lines of code during training, are surprisingly adept at:

   • Generating boilerplate code: They can often write functions, classes, or scripts for common tasks.
   • Debugging and explaining code: They can identify errors or provide natural language explanations of code snippets.
   • Translating between languages: They can sometimes convert code from one programming language to another. Their success here stems from the fact that code, despite its formal nature, also exists within vast natural language corpora (documentation, forums, comments), allowing LLMs to map natural language requests to formal code structures.

5. Handling Some Ambiguity: While ambiguity is a core challenge, LLMs often resolve it by relying on the most probable interpretation given the immediate context, mirroring how humans often intuitively resolve it.

What LLMs Don’t Get Right (and Why)

Despite their incredible feats, LLMs have fundamental limitations, particularly when confronted with tasks that require true understanding, logical reasoning, or strict adherence to formal rules.

1. True Syntactic Parsing and Grammaticality (beyond statistical plausibility): LLMs don’t “parse” sentences in the same way a compiler uses a formal grammar to build a parse tree. They don’t have an explicit, internal model of syntax. They learn correlations and patterns. This means:

   • Grammatical Errors: While generally fluent, they can still make subtle grammatical errors, especially with complex sentence structures, negation, or long-range dependencies that go beyond their learned statistical window.
   • Lack of Proof: They cannot prove the grammatical correctness of a sentence or the validity of a piece of code. They just generate what’s statistically most likely.

2. Logical Consistency and Reasoning: LLMs lack a symbolic reasoning engine. They don’t “understand” cause and effect, logical implications, or contradictions in the human sense.

   • Hallucinations: They can confidently state falsehoods or nonsensical information because their generation process is probabilistic, not grounded in verifiable truth. If a pattern in their training data suggests a connection, they might generate it, even if logically unsound.
   • Difficulty with Multi-Step Reasoning: Tasks requiring complex chains of logic, mathematical proofs, or counterfactual reasoning often expose their limitations. They might generate plausible-looking steps that are fundamentally incorrect.

3. Common Sense and World Knowledge: While trained on vast data, LLMs don’t possess a “common sense” understanding of the world, physics, or human motivations. Their “knowledge” is embedded in statistical relationships of words, not in a grounded model of reality. This is why they struggle with simple spatial reasoning or understanding the physical implications of actions. Source: Marcus, G. (2020). The Next Decade in AI: Four Steps Towards Robust Artificial Intelligence. arXiv preprint arXiv:2002.06177.

4. Ambiguity Resolution (Consistently and Reliably): While they can resolve some ambiguities, they struggle with those requiring deep world knowledge, specific user intent, or subtle pragmatic inferences. Sarcasm or irony, which often rely on a shared understanding of context and human behavior, are particularly challenging.

5. Adherence to Strict Formal Rules (outside of training distribution): If asked to generate output that must conform to a very specific, novel, and complex formal grammar (e.g., a custom data format or a niche query language not heavily represented in training data), LLMs can struggle. They excel when the formal rules are present within their training data, or when the task can be mapped to common programming patterns. They are pattern matchers, not rule enforcers.

6. Explainability and Trustworthiness: Because their operation is based on complex statistical relationships, it’s often difficult to understand why an LLM generated a particular output. This “black box” nature makes them less suitable for applications requiring high certainty, verifiability, or accountability.

Note: While LLMs can “learn” some aspects of formal grammar from code, they do not inherently possess a symbolic parser or a formal understanding of the underlying mathematical logic that defines these grammars. Their “understanding” is an emergent property of statistical correlations.

The Chasm and the Bridge: A Future Perspective

The fundamental difference lies in their approach: formal grammars are symbolic and deterministic, built on explicit rules; natural language is statistical and probabilistic, evolving from usage. LLMs, despite their natural language fluency, operate squarely in the statistical realm.

Can this chasm be fully bridged? The current paradigm of LLMs, based on next-token prediction, seems to have inherent limitations regarding true reasoning and guaranteed adherence to formal logic. This is why we often see discussions about “hybrid AI” systems that combine the statistical power of neural networks with symbolic reasoning engines or knowledge graphs. Such systems could potentially leverage LLMs for their natural language fluency and pattern recognition, while relying on symbolic AI for logical consistency, verifiable facts, and strict adherence to formal rules where necessary.

The journey of AI understanding language is far from over. LLMs have provided an astonishing leap forward in mimicking human language, opening up a world of possibilities. But recognizing their strengths – and crucially, their limitations – is essential for harnessing their power responsibly and intelligently. The future of language AI might not be about one paradigm triumphing over another, but about cleverly combining their complementary strengths.