💬 NLP

Compositionality and the lexicon in evolutionary semantics

This paper introduces an evolutionary framework that integrates formal semantics by modeling the co-evolution of lexical meanings and composition functions, demonstrating how the semantic universal of conservativity emerges as an efficient system-wide abstraction balancing conceptual simplicity and communicative accuracy.

Original authors: Fausto Carcassi

Published 2026-06-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Fausto Carcassi

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine language as a giant, living Lego set. For decades, scientists studying how language works (formal semantics) have focused on the individual bricks: what each specific word means. They've figured out that sentences are built by snapping these bricks together in specific ways.

On the other hand, scientists studying how language evolved (evolutionary semantics) have mostly looked at the finished structures or treated the bricks as unshaped blobs of clay. They've asked, "Why do humans have these specific shapes?" but they often ignored how the bricks are snapped together.

This paper, by Fausto Carcassi, tries to build a bridge between these two groups. It argues that you can't understand why language looks the way it does unless you look at the bricks (words) and the snapping mechanism (grammar rules) evolving together.

Here is the story of the paper, broken down into simple concepts:

1. The Mystery of "Conservativity"

The paper focuses on a famous rule in language called conservativity.

The Rule: In almost every language, words like "all," "some," "no," and "most" work in a very specific, restricted way. They only care about the group they are talking about right now.
The Analogy: Imagine you are looking at a bowl of fruit. If you say, "All the apples are red," you are only looking at the apples in the bowl. You aren't worrying about the bananas in the bowl or the oranges in the kitchen.
The Puzzle: Humans are smart. We could easily invent a word that breaks this rule. For example, a word that means "The number of apples is greater than the number of bananas." This would require looking at both groups at once. But, amazingly, we don't seem to have these "non-conservative" words for our main counting words (determiners). We have them for verbs (like "outnumber"), but not for words like "all" or "some." Why?

2. The Old Explanations vs. The New Idea

Previous scientists tried to explain this in two ways:

The "Brick" Theory: Maybe our brains just can't conceive of the "non-conservative" shapes. (The paper says this is weak because we can understand complex verbs).
The "Glue" Theory: Maybe the way we snap words together forces us to be conservative.

Carcassi's paper suggests the answer is a mix of both, but with a twist: It's about efficiency.

3. The "Factory" Analogy

Imagine a factory that makes sentences.

The Bricks: The words (like "all," "some").
The Assembly Line: The rules that put the words together.

In the past, researchers thought the factory just made every single word from scratch. If you wanted a new word, you had to design a whole new machine for it. This is inefficient.

Carcassi's model suggests that the most efficient factories design a specialized Assembly Line that does the heavy lifting for all the words at once.

The Innovation: Instead of making every word handle its own logic, the factory builds a "Conservativity Module" into the Assembly Line itself.
How it works: The Assembly Line is programmed to say, "Hey, whenever we use a counting word, we automatically ignore everything outside the main group."
The Benefit: Now, the individual words (the bricks) can be very simple. They don't need to carry the heavy instruction "Ignore the rest of the universe." The Assembly Line handles that for everyone.

4. The Experiment: Simulating Language Evolution

The author built a computer simulation (a digital lab) to test this.

The Setup: He created digital "agents" (robots) that need to communicate about a world of objects. They have to describe which objects are "targets" and which are "distractors."
The Pressure: The robots face two competing pressures:
1. Be Accurate: They need to communicate clearly so the other robot knows exactly what they mean.
2. Be Simple: They need to keep their language system small and easy to learn (low "complexity").

The simulation let the robots evolve their own languages over thousands of generations, trying to find the perfect balance between being simple and being accurate.

5. The Results: Why "Conservativity" Wins

The simulation showed that the most successful languages (the ones that communicated best with the least effort) naturally evolved the "Conservativity Module" in their Assembly Line.

The Trade-off: If the robots tried to make every word handle its own complex logic, the system became too heavy and hard to learn.
The Sweet Spot: By putting the "conservative" rule into the Assembly Line (the composition function) rather than in every single word, the system became incredibly efficient. It allowed the robots to create complex meanings without making the language too complicated.
The "Pragmatic" Factor: This only worked when the robots were "pragmatic"—meaning they used context and implied meaning (like humans do). If they were just literal robots, the rule didn't matter as much.

6. Why This Matters

The paper solves a long-standing puzzle: Why do we have "conservative" words for counting, but not for other things?

The Answer: Because the "Assembly Line" for counting words (determiners) evolved to be super-efficient by sharing a rule.
The Contrast: Verbs (like "outnumber") don't have this same shared Assembly Line. They are more open-ended, so they don't need to compress their rules in the same way. This explains why we can have complex, non-conservative verbs but not complex, non-conservative counting words.

The Bottom Line

This paper argues that to understand why human language is the way it is, we can't just look at the dictionary. We have to look at the grammar factory that builds sentences.

It turns out that the most efficient way to build a language is to have a "smart factory floor" that automatically handles the boring, repetitive rules (like conservativity) for all the words at once. This makes the individual words simpler, the whole system easier to learn, and communication more accurate. It's a perfect example of how evolution favors systems that are both clever and simple.

Technical Summary: Compositionality and the Lexicon in Evolutionary Semantics

Problem Statement
Formal semantics has established that sentence meanings arise through the recursive composition of lexical meanings. However, the field of evolutionary semantics, which seeks to explain semantic universals through pressures for simplicity and communicative accuracy, has largely modeled lexicons as collections of unstructured signals or holistic compositions lacking interpretable lexical parts. This methodological gap makes it difficult to use formal semantic characterizations of universals to generate evolutionary explanations.

The paper focuses on conservativity, arguably the most well-known semantic universal (Barwise & Cooper, 1981; Keenan & Stavi, 1986), which states that simple determiners express quantifiers conservative on a specific argument (typically the second). Previous evolutionary accounts struggle to reconcile several empirical tensions:

Learnability: Non-conservative quantifiers are difficult for English speakers to acquire (Claim 4), yet non-conservative relations in the verbal domain (e.g., "outnumber") are learnable (Claim 5).
Complexity: While some models suggest conservative quantifiers are conceptually simpler (Claim 3), this does not explain why the constraint applies specifically to determiners and not verbs.
Explanation: Existing explanations (lexical restriction, interface filtering, ordered predication) either redescribe the phenomenon, rely on unproven psycholinguistic mechanisms, or fail to provide an evolutionary account for why determiners specialize in restricted quantification.

Methodology
The authors introduce a computational framework that integrates formal semantic insights into evolutionary modeling. The core innovation is a model where lexical meanings and a composition function co-evolve under pressures for conceptual simplicity and communicative accuracy.

Communication Model: The framework uses a signaling game involving a sender ( $S$ ) and a receiver ( $R$ ) in a context of five objects with integer features. $S$ constructs a signal to restrict the common ground, and $R$ updates beliefs. Success is measured by the reduction of possible contexts.
Language Structure: The language consists of a lexicon and an interpretation function. Crucially, the model allows for semi-categorematic analyses. Unlike traditional formal semantics which places all content in lexical entries (categorematic) or composition rules (syncategorematic), this framework distributes semantic content between the two.
Variable Components: The study leaves unspecified:
1. The meanings of three quantifiers ( $Q_1, Q_2, Q_3$ ).
2. The specific composition function ( $C^c_Q$ ) that combines a quantifier with its arguments ( $L$ and $R$ ).
Optimization: The system explores a space of possible languages defined by probabilistic context-free grammars (PCFGs). It evaluates these languages on a Pareto frontier balancing:
- Communicative Accuracy: The expected utility of the communication game, incorporating Gricean pragmatic enrichment (implicatures).
- Conceptual Complexity: The descriptive complexity of the global interpretation function, allowing abstractions in the composition function to reduce the complexity of individual lexical entries.
Processing Assumption: The model assumes "gradualness," where arguments are processed progressively as they are assigned values. This restricts the right argument from using the left argument's value until the left is processed, but does not inherently force conservativity.

Key Contributions

Framework Integration: The paper proposes a template for studying universals that involve global compression within a grammatical category and the co-evolution of lexical and compositional meaning. It bridges the gap between formal semantics (which models structure) and evolutionary semantics (which models optimization).
Novel Account of Conservativity: The authors argue that conservativity is not merely a feature of individual quantifier meanings but a system-level abstraction in the composition function. By defining conservativity once in the composition function (e.g., restricting the second argument to the intersection of the first), languages can achieve high communicative accuracy with minimal global complexity.
Resolution of Empirical Tensions: The model demonstrates that the sensitivity to syntactic structure (determiners vs. verbs) arises because the composition function can evolve specific constraints for specific grammatical categories. This explains why non-conservative meanings are learnable in verbs (where the composition function remains unconstrained) but not in determiners (where the system-level abstraction makes non-conservative additions costly or impossible).

Results
The simulation results, analyzed via the Pareto frontier, reveal three distinct groups of languages:

Simple, Low-Accuracy Systems: Languages with degenerate quantifiers and no system-level abstractions. These are simple but communicatively ineffective.
Optimal Systems (The Pareto Frontier): Languages that strike the best balance between complexity and accuracy. These systems consistently evolve a conservative composition function.
- Pragmatic Necessity: Conservativity emerges as a successful strategy only when agents are pragmatic. Literal agents do not systematically select conservative systems. The abstraction allows for complex entailment patterns (e.g., "all" entails "some") that pragmatic agents exploit to increase accuracy.
- Global Compression: The composition function encodes the restriction (e.g., $Q(L)(R)$ becomes $Q(L)(L \cap R)$ ), allowing individual quantifiers to be defined simply (e.g., just comparing set sizes) while the system as a whole remains conservative.
Complex, Diminishing Returns Systems: Languages with exotic quantifiers and high complexity that offer negligible gains in accuracy.

The results show that conservative languages are relatively rare in the prior space (~23%) but dominate the high-accuracy, low-complexity frontier when pragmatic enrichment is active. Furthermore, the ability to form abstractions in the composition function is a prerequisite for the emergence of conservativity; without it, the frontier is dominated by non-conservative systems.

Significance and Claims
The paper claims that the picture of sentential meaning developed in formal semantics can be productively combined with evolutionary modeling. Specifically:

Reframing Universals: Semantic universals like conservativity should be characterized as interactions between lexical meanings and composition, rather than properties of lexical entries alone.
Explanatory Power: The model provides a better account of the data than previous models by explaining the grammatical sensitivity of conservativity (why it applies to determiners but not verbs) and the learnability constraints observed in psycholinguistic experiments.
Methodological Shift: The authors argue that evolutionary models must move beyond unstructured signals to include explicit composition functions and syntactic types to accurately model the evolution of linguistic universals.
Modesty: The authors acknowledge limitations, including the computational feasibility of evolving only three quantifiers at once and the reliance on specific choices for the lexicon and conceptual primitives. They suggest that while the specific results depend on these choices, the explanation for the emergence of conservativity via system-level compression is robust.

In conclusion, the paper demonstrates that conservativity emerges as an efficient system-wide abstraction that minimizes global complexity while maximizing communicative accuracy in a pragmatic setting, offering a novel evolutionary explanation for a foundational semantic universal.