On the Optimality of Kinship Naming: an Information-theoretic Approach

Human languages expand vocabularies by combining existing morphemes rather than inventing arbitrary forms. Communicative efficiency shapes lexical systems at multiple levels (Gibson et al., 2019), yet morphological composition -- combining morphemes through compounding or affixation -- has rarely been modeled as a historically situated speaker choice among competing morpheme sequences, leaving unanswered why a language settles on one morpheme combination over other plausible alternatives. We ask whether a trade-off between listener recoverability and speaker production cost can predict attested compositions over contemporaneously available alternatives. Here we show, within the Rational Speech Act (RSA) framework (Frank & Goodman, 2012; Goodman & Frank, 2016) using a time-indexed lexicon constructed from Corpus of Historical American English (COHA) and Corpus of Contemporary American English (COCA), that across 4323 naturally occurring English compounds and derivations spanning 1820--2019, attested compositions are systematically ranked above unattested alternatives generated from contemporaneously available morphemes. Models integrating semantic informativeness with production cost outperform semantic-only and cost-only baselines on Mean Reciprocal Rank (MRR) and top-k accuracy (Acc@k), with the advantage of the Pragmatic Speaker model ($S_1$) over the semantic-only baseline growing as the candidate set expands, where meaning alone leaves morphological choice underdetermined. These findings suggest that lexicalization reflects a communicative trade-off between expressiveness and efficiency, extending rational accounts of communication from utterance-level choice to the internal structure of words.

Current literature evaluates large language models (LLMs) on multilingual kinship understanding using multiple choice benchmarks, treating it as a recognition problem. We instead prompt five open weight LLMs to generate kinship terms in three non Western languages (Hindi, Tamil, and Korean) across two communicative tasks and pair this with a matched option-supported selection baseline. On identical relation language cells, GPT OSS120B selects the correct term in 90.67% of 75 valid cells but produces an accepted term in 36.00% of the corresponding attempts; Llama 3.370B shows the same pattern (77.92% versus 24.24%). Since the four-option condition displays the candidate terms and does not require script production, the difference is interpreted as an evaluation format gap rather than direct proof that lexical knowledge is intact. On explicitly specified L3 prompts, accuracy varies sharply, from GLM-5.1 at 72.29% to Llama-3.370B at 24.24%. The paternal-lineage advantage is language specific; it is large in Hindi but weak or reversed in Korean, while Tamil shared-term pairs provide a control for measurement variation. These results show that culturally specific kinship generation remains difficult even when the relationship is explicitly stated and motivate generation-based evaluation alongside multiple-choice testing.

We propose a mathematical theory of pragmatic information that connects communication, control, and decision-making. Its central notion is the isoteleia mapping, which formalizes equifinality: distinct semantic paths that lead to the same optimal action are treated as pragmatically equivalent. This mapping yields a three-tier hierarchy of syntactic, semantic, and pragmatic information, in which each successive abstraction removes distinctions that are irrelevant to the task. We then define pragmatic entropy, up/down pragmatic mutual information, channel capacity, and rate-distortion, and prove lossless source coding, channel coding, and rate-distortion theorems that extend Shannon's results. These measures quantify decision uncertainty, reliable transmission, and task-oriented compression at the level of terminal actions. We further introduce pragmatic value of information (VoI) and pragmatic cost of information (CoI) as decision-theoretic duals to rate-distortion and capacity, and develop a Lagrangian dual framework for cross-layer optimization. The resulting pragmatic efficiency bound $\mathcal{E}_p(λ)=\sup_R[Φ_p(R)-λ\mathrm{CoI}_p(R)]$ characterizes the maximum net utility attainable by a resource-constrained intelligent system under a given resource price, yielding a behavioral capacity that extends Shannon's symbol-level capacity to goal-directed action. Extensions to continuous messages provide closed-form expressions for Gaussian channels and sources, while dynamic settings are addressed through a Bellman equation for sequential decision-making. The framework supports task-oriented communication, networked control, autonomous systems, and embodied AI by shifting emphasis from symbol fidelity to the effectiveness of information in guiding actions. In this way, it offers a common language for systems that extract value from information under resource constraints.