Strongly Semantic Information Insights

• Strongly semantic information is a framework that defines meaning using criteria like truth, viability, and causal relevance rather than just statistical correlation.
• It unites classical truth-sensitive metrics, observer-based interpretations, and viability as well as causal-leverage approaches to quantify semantic content.
• Applications span deep representation learning, semantic communication systems, and ontology-grounded retrieval, providing actionable insights for theory and engineering.

Searching arXiv for papers on “strongly semantic information” and related semantic information frameworks. Strongly semantic information is a family of concepts in which information is not treated merely as statistical correlation, lexical form, or symbol transmission, but as meaning-bearing structure whose significance is defined by truth, viability, causal efficacy, ontology-grounded interpretation, task relevance, or shared representation across modalities. Across the literature, the term does not denote a single unified theory. Instead, it names a cluster of stronger-than-syntactic views of information: classical truth-sensitive semantic information in the Floridi tradition (Coghill, 1 Aug 2025), viability- and agency-based semantic information in nonequilibrium statistical physics (Kolchinsky et al., 2018, Sowinski et al., 2023), causal-intervention accounts based on future trajectory changes (Bartlett, 2024), and engineering frameworks in which meaning rather than exact symbols is the object of communication, retrieval, or representation (Niu et al., 2024, Qin et al., 2023, Beck et al., 2022). A plausible implication is that “strongly semantic information” functions less as one doctrine than as a recurring criterion: information counts as genuinely semantic only when some stronger condition is met than mere correlation.

1. Classical formulations: truth, contradiction, and semantic content

In the classical semantic-information tradition, the central problem is how to quantify the informativeness of propositions or sentences in a way that reflects meaning rather than only symbol statistics. The survey “Engineering Semantic Communication: A Survey” distinguishes the Carnap–Bar-Hillel line as a “Theory of Weakly Semantic Information” and Floridi’s correction as a “Theory of Strongly Semantic Information,” or TSSI (Wheeler et al., 2022). In the Bar-Hillel–Carnap account, semantic content is inversely related to probability, so a tautology has zero content while a contradiction becomes maximally informative. The 2025 measure-theoretic critique reproduces this as

$CONT(p) = 1 - P(p),$

with $CONT(\perp)=1$ when $P(p)=0$, which is identified as the Bar-Hillel–Carnap paradox (Coghill, 1 Aug 2025).

Floridi’s response is to build truth into the definition of information itself. The 2025 paper summarizes this via the General Definition of Information, under which an infon $\sigma$ is semantic information iff it consists of data, is well formed, meaningful, and truthful; the final clause is the Veridicality Thesis (Coghill, 1 Aug 2025). On this view, “strongly semantic information” is distinguished from weaker accounts precisely because truth is internal to information rather than external to it. The same paper reconstructs Floridi’s metric program through discrepancy measures for falsehood and vacuity, including

$$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$

intended to ensure that contradictions and tautologies both have zero informativeness (Coghill, 1 Aug 2025).

The critique, however, argues that Floridi’s original metric fails on its own terms. It claims that contingent falsehoods can attain the extreme value $-1$, violating the requirement that they lie strictly between the endpoints, and that contradictions do not actually receive maximal inaccuracy, so the Bar-Hillel–Carnap paradox is not removed by the original construction (Coghill, 1 Aug 2025). To address this, the paper proposes a “Measure Theory of Semantic Information” based on a unit-circle or unit-sphere geometry, with orthogonal true and false axes: $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$ and corresponding measure quantities $\Phi_i$, $\Phi_m$, and $\Phi_u$ satisfying

$CONT(\perp)=1$0

In that framework, contradictions and tautologies both have $CONT(\perp)=1$1, while mutually contradictory messages can be equally informative (Coghill, 1 Aug 2025).

The broader survey literature treats these truth-sensitive theories as mathematically ambitious but not complete engineering frameworks. “Engineering Semantic Communication: A Survey” presents TSSI and later truthlikeness measures as foundational efforts to formalize meaning, while also emphasizing paradoxes, brittleness, and scalability limits (Wheeler et al., 2022). This suggests that the classical notion of strongly semantic information is best understood as a formal attempt to make semantic content depend on truth or truthlikeness, rather than on symbol frequency or Shannon uncertainty alone.

2. Observer-dependent and descriptive semantics

A different strand defines semantics not by truth conditions alone but by the relation between data, physical structure, and observer-dependent interpretation. In “Let us first agree on what the term ‘semantics’ means,” Diamant argues that semantics is a special kind of information and sharply distinguishes physical information from semantic information (Diamant, 2012). Physical information is “a description of data structures usually discernable in a data set,” while semantic information is not directly extractable from raw data and instead resides in the observer’s mind, community conventions, and stored knowledge (Diamant, 2012).

This distinction is organized around primary and secondary structures. Primary data structures are formed by physical similarity and ground physical information; secondary structures depend on human convention and ground semantic information (Diamant, 2012). Semantics therefore is not intrinsic to raw data, even though it is still treated as real information. Diamant defines information as “a description, a linguistic text, a piece of a story or a tale,” and places semantic information in a top-down hierarchy resembling narrative structure: title, abstract, paragraph, phrase or sentence, word or object, and then physical attributes at the lowest level (Diamant, 2012).

Within this framework, knowledge is defined explicitly as “Semantic information” brought from the outside and memorized into the information processing system (Diamant, 2012). Meaning arises when extracted physical information is matched against memorized semantic conventions and inserted into this hierarchy. The paper therefore supports a strong conception of semantics as a genuine informational layer, but not as one recoverable from data alone. A plausible implication is that, in this tradition, information is “strongly semantic” when it belongs to a learned and socially stabilized interpretive structure rather than to objective data regularities themselves.

A related but distinct earlier quantitative study of written language does not use the phrase “strongly semantic information” explicitly, yet it identifies semantic content through long-range order in word distributions (0907.1558). There, semantic information is quantified by comparing the real distribution of words across text segments with the distribution produced by random shuffling: $CONT(\perp)=1$2 The paper finds a characteristic informative scale on the order of $CONT(\perp)=1$3 words, often roughly $CONT(\perp)=1$4–$CONT(\perp)=1$5 words, and shows that the words with the largest contributions are closely associated with the main topics of the text (0907.1558). This is not a truth-based theory, but it is stronger than local syntax because it locates meaning-bearing structure in clustered, domain-like word usage rather than in grammatical adjacency alone.

3. Viability-based semantic information, autonomy, and semantic thresholds

The most influential physics-based formulation defines semantic information as the subset of syntactic information that is causally necessary for self-maintenance. In “Semantic information, autonomous agency, and nonequilibrium statistical physics,” semantic information is defined as “the syntactic information that a physical system has about its environment which is causally necessary for the system to maintain its own existence” (Kolchinsky et al., 2018). The system is split into a system $CONT(\perp)=1$6 and environment $CONT(\perp)=1$7, and viability is measured by negative Shannon entropy at time $CONT(\perp)=1$8: $CONT(\perp)=1$9 The semantic content of information is isolated by counterfactual interventions that scramble correlations. For stored semantic information, the full scramble replaces the joint distribution by the product distribution $P(p)=0$0; more selective interventions are defined by coarse-graining the environment (Kolchinsky et al., 2018).

This framework yields a value-of-information quantity defined by the viability difference between the actual and intervened cases. It also defines information/viability curves and “optimal interventions” that preserve the smallest amount of syntactic information compatible with the original viability level (Kolchinsky et al., 2018). The paper further introduces semantic efficiency, thermodynamic multipliers, pointwise semantic content, and an account of agency according to which a system is more autonomous to the extent that it possesses more semantic information (Kolchinsky et al., 2018). The toy food-seeking example illustrates that not all mutual information is semantic: $P(p)=0$1 bits of mutual information can contain only about $P(p)=0$2 bits of semantically relevant content because some distinctions are irrelevant to viability (Kolchinsky et al., 2018).

“Semantic Information in a model of Resource Gathering Agents” specializes this viability-based program to a foraging agent whose viability is expected lifetime: $P(p)=0$3 The agent’s sensor is counterfactually noised to scramble correlations with the environment, producing a viability curve $P(p)=0$4 as a function of the sensor-noise parameter $P(p)=0$5 (Sowinski et al., 2023). The key empirical and theoretical result is a plateau-then-drop structure: viability remains nearly constant while correlations are reduced down to a critical point, but once a critical noise level is crossed, viability falls sharply (Sowinski et al., 2023). The boundary is called the semantic threshold: $P(p)=0$6

Geometrically, the threshold occurs when sensor misalignment becomes large enough that targeted resources can be missed, with

$P(p)=0$7

Below $P(p)=0$8, every targeted resource is still eventually collected; above it, the agent sometimes misses the resource and expected lifetime drops dramatically (Sowinski et al., 2023). The paper therefore interprets the semantic threshold as the boundary between dispensable and indispensable correlations. Above it, removed correlations are semantically irrelevant; below it, “each bit of information affects the agents ability to persist” (Sowinski et al., 2023). The viability-per-bit quantity

$P(p)=0$9

peaks at the threshold and marks the regime where information matters most (Sowinski et al., 2023).

The same paper also makes an explicit agency claim: semantic thresholds may help explain how systems become autonomous agents, contrasting “hurricanes and cells” as driven nonequilibrium systems of which only the latter is typically counted as agentive (Sowinski et al., 2023). This extends the 2018 framework by making the “strong” semantic condition operationally visible as a threshold phenomenon rather than only an optimal-intervention definition.

4. Causal and dynamical generalizations beyond viability

A later generalization removes viability as the privileged criterion and defines semantic information by direct causal influence on future trajectories. “Causal Leverage Density: A General Approach to Semantic Information” treats semantic information as syntactic information that has “intrinsic causal power on the future of a given system” (Bartlett, 2024). Instead of asking whether erasing information lowers viability, it asks whether erasing information changes the distribution of future trajectories through phase space.

The basic intervention is again scrambling or erasure, but the effect is measured by Jensen–Shannon divergence between the original and intervened future distributions: $\sigma$0 This divergence is then normalized by the number of bits scrambled to define causal leverage density: $\sigma$1 When $\sigma$2, the erased information had little causal influence; large $\sigma$3 indicates information with substantial semantic or causal power (Bartlett, 2024).

The paper explicitly presents this as an adaptation of the Kolchinsky–Wolpert intervention logic to nonliving and technological systems for which viability is not the central variable (Bartlett, 2024). It names rocks, hurricanes, cells, neural networks, the teachings of the Buddha, extinct-plant proteins, and origin-of-life scenarios as examples illustrating why future-trajectory influence can be broader than survival-based significance (Bartlett, 2024). This suggests a shift from “strongly semantic” as survival relevance to “strongly semantic” as high normalized causal efficacy.

A plausible implication is that the viability-based and causal-leverage views are not contradictory so much as nested. The former treats maintenance of existence as the privileged future property; the latter treats future-distribution change itself as the primitive criterion. Both preserve the stronger claim that semantics is not exhausted by correlation.

5. Strongly semantic structure in deep representations

Recent representation-learning work uses the phrase in yet another sense: strongly semantic information is the modality-independent or language-independent latent structure encoded in internal representations rather than the survival relevance of correlations. “An approach to identify the most semantically informative deep representations of text and images” studies where in LLMs and vision transformers semantic information is most strongly represented, using Information Imbalance as an asymmetric proxy for relative mutual predictivity (Acevedo et al., 21 May 2025): $\sigma$4 Smaller $\sigma$5 indicates stronger predictivity, while $\sigma$6 means $\sigma$7 is non-informative about $\sigma$8 (Acevedo et al., 21 May 2025).

The paper defines semantic layers as internal layers where representations of semantically related inputs become highly similar. In cross-lingual experiments, it reports that DeepSeek-V3 develops a broad semantic region with English–Spanish minimum Information Imbalance around $\sigma$9, whereas Llama3.1-8B reaches a higher minimum around $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$0 and the minimum is narrower (Acevedo et al., 21 May 2025). It also finds that semantic information is distributed across many tokens rather than concentrated in one position, that deep semantic layers exhibit long-distance token-token correlations, and that causal left-to-right asymmetry strengthens in these layers (Acevedo et al., 21 May 2025).

The same framework is extended to vision transformers, where semantic layers appear in middle layers for image-gpt and near the end for DINOv2, in line with the differing training objectives (Acevedo et al., 21 May 2025). Caption representations in semantic layers of LLMs predict visual representations of corresponding images, and cross-modal information asymmetries depend on the model: with image-gpt, text $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$1 image is stronger, whereas with DINOv2 the asymmetry is reversed or nearly reversed (Acevedo et al., 21 May 2025). Here, “strongly semantic” refers not to veridicality or survival but to distributed, layer-specific, transferable meaning.

A related 2026 study of one-step text reconstruction examines semantic information in learned proto-tokens and concludes that, under standard unconstrained optimization, the $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$2-token tends to capture semantic information more strongly than the $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$3-token (Bondarenko et al., 20 Feb 2026). It distinguishes semantic and syntactic content through lexical versus semantic augmentations, t-SNE clustering, attention visualization, and teacher-based regularization. Anchor loss imposes a sharp trade-off with reconstruction, whereas relational distillation transfers batch-level semantic relations into proto-token space without sacrificing reconstruction quality (Bondarenko et al., 20 Feb 2026). This work is narrower in scope, but it reinforces the representation-learning usage of “strongly semantic” as a property of internal latent geometry rather than of external task performance alone.

6. Engineering uses: communication, retrieval, and ontology-grounded systems

In communication engineering, strongly semantic information is typically contrasted with exact symbol recovery. “A Mathematical Theory of Semantic Communication” formalizes semantic communication around synonymy, represented by a mapping from a semantic alphabet $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$4 to sets of syntactic realizations $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$5 (Niu et al., 2024). Semantic entropy is then the Shannon entropy of synonym classes: $$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$6 with the fundamental bound

$$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$7

The paper defines up and down semantic mutual information, semantic capacity

$$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$8

and semantic rate-distortion

$$-\vartheta(\sigma) = -e(\sigma)/l(\sigma), \qquad \vartheta(\sigma) = n/s^l, \qquad \iota(\sigma) = 1 - \vartheta^2(\sigma),$$9

and proves semantic source coding, channel coding, and rate-distortion coding theorems (Niu et al., 2024). The claimed inequalities

$-1$0

encapsulate the engineering promise: meaning-preserving equivalence classes relax exact syntactic constraints (Niu et al., 2024).

“A Generalized Semantic Communication System: from Sources to Channels” broadens this engineering view by treating both multimodal sources and the wireless environment as carriers of semantics (Qin et al., 2023). For text, speech, and images, semantic communication seeks meaning alignment rather than bit alignment; for the channel, it distinguishes parameter semantics such as AOD, AOA, number of paths, and Doppler shift from environment semantics such as object categories and scene layout (Qin et al., 2023). The paper reports that DeepSC-ST achieves lower WER and significantly better FDSD than two baseline transceivers under Rayleigh channels, and that environment semantics aided mmWave precoding can approach traditional BD performance at SNR $-1$1 dB while reducing training and feedback overhead to essentially zero (Qin et al., 2023).

“Semantic Information Recovery in Wireless Networks” models semantics as a hidden random variable $-1$2 in the Markov chain

$-1$3

and defines semantic communication as data-reduced transmission that preserves $-1$4 rather than reconstructing $-1$5 exactly (Beck et al., 2022). It casts the design as an Information Bottleneck problem,

$-1$6

and implements it through the SINFONY architecture for distributed image classification (Beck et al., 2022). The paper reports an up to 20 dB rate-normalized SNR shift relative to classically designed communication systems (Beck et al., 2022). In this line of work, semantic information is “strongly semantic” because it is explicitly task-relevant and latent.

Knowledge-graph and ontology-based systems express another engineering sense of strong semantics. “Semantic Query Optimisation with Ontology Simulation” contrasts RDF with OWL by describing OWL ontologies as providing “strong semantics,” i.e. machine interpretability beyond lighter RDF structure (Gupta et al., 2010). It represents semantic information as metadata, explicit relations, and ontology-based structure; the ontology of Indian universities contains classes, properties, and instances, and supports ontology-grounded keyword ranking rather than purely syntactic search (Gupta et al., 2010). “Enhancing Information Awareness Through Directed Qualification of Semantic Relevancy Scoring Operations” goes further by requiring semantic content to be traceable to source documents, qualified with provenance, and usable in reasoning and analytics-based ranking through Prov-O plus a relevancy ontology (Bryant et al., 2015). There, semantic information becomes “strongly semantic” when it is not only represented in RDF/OWL but also provenance-aware and analytically qualified (Bryant et al., 2015).

The same pattern appears in semantic retrieval. “Semantic Arabic Information Retrieval Framework” uses a semantic inverted index of the form $-1$7, where $-1$8 is a Reference Concept inferred from ontology reasoning over phrase context (Alshari, 2015). It reports $-1$9 precision for tested Boolean semantic retrieval examples and large precision improvements over traditional VSM baselines, though at substantially higher runtime due to ontology reasoning (Alshari, 2015). “Semantic Information Extraction for Text Data with Probability Graph” defines semantic units as entropy-weighted knowledge-graph quadruples $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$0, then selects the most important ones under compression constraints by minimizing total entropy subject to graph-depth and budget constraints (Zhao et al., 2023). Here again, stronger semantics means that the transmitted or retrieved units are conceptually central and probabilistically reliable rather than merely frequent.

7. Domain-specific operationalizations and persistent controversies

Strongly semantic information also appears as a domain-specific design principle in perception, robotics, and graph-based sensing. In disparity estimation, SegStereo injects semantics both as features and as a loss regularizer. It concatenates transformed left features, correlation features, and left semantic features,

$$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$1

and adds a semantic softmax term to the supervised or unsupervised disparity objectives (Yang et al., 2018). The paper reports unsupervised KITTI gains such as EPE from $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$2 to $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$3 and D1 from $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$4 to $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$5 after adding semantic regularization (Yang et al., 2018). The semantics are “strong” because they alter the learned disparity representation and backpropagate through warping, rather than serving as post hoc refinement.

In LiDAR odometry, SAGE-ICP uses pointwise semantic labels throughout the registration pipeline: semantic voxel downsampling, semantic-assisted correspondence search, adaptive semantic voxel mapping, and dynamic vehicle removal (Cui et al., 2023). Same-class matches are preferred by a semantic Euclidean distance with downweighting factor $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$6, yet geometric gating remains decisive, which is why the method remains robust to label errors (Cui et al., 2023). On KITTI Odometry, the reported averages improve modestly over KISS-ICP, and the registration component runs at about $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$7 Hz, faster than sensor rate (Cui et al., 2023). Here, strongly semantic integration means structural intervention in the algorithm rather than the addition of a semantic side-channel.

In speech emotion recognition, semantic information is separated from paralinguistic information and aligned through cross-modal embedding learning. Speech2Vec embeddings are mapped toward Word2Vec semantics via adversarial alignment and orthogonal refinement, then fused with a paralinguistic 1-D CNN stream through disentangled attention (Tzirakis et al., 2021). On SEWA/AVEC, semantic embeddings are reported to be particularly useful for valence and liking, while the paralinguistic stream is strongest for arousal; the combined model reaches the best reported test results for valence $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$8 and liking $$\iota(\sigma) = \sqrt{1 - (\vartheta_T^2(\sigma) + \vartheta_F^2(\sigma))},$$9 among the compared systems (Tzirakis et al., 2021). The strong-semantic claim here is again operational: word meaning contributes emotion information beyond prosody.

For graph signals, “Reliable Extraction of Semantic Information and Rate of Innovation Estimation for Graph Signals” treats semantics as a hierarchical graph representation of the raw signal, then stabilizes it through time integration, graph-edit-distance innovation detection, and HMM smoothing (Kalfa et al., 2022). The graph-edit distance uses statistical edit costs $\Phi_i$0, and the overall semantic transmission rate is expressed as

$\Phi_i$1

with lower rate under goal filtering (Kalfa et al., 2022). This line of work fits the broader pattern that strongly semantic information is information extracted, regularized, and acted upon at the level of meaningful structure rather than raw samples.

Across these domains, several controversies persist. One is whether semantics must be truth-sensitive, observer-dependent, viability-relevant, or merely task-relevant. Another is whether semantic information is intrinsic to systems or imposed by analysts through task design, ontology construction, or latent-variable supervision. The literature does not resolve these tensions. What it does show is that stronger notions of semantic information consistently reject the identification of meaning with correlation alone. Whether the stronger condition is veridicality (Coghill, 1 Aug 2025), community convention (Diamant, 2012), viability (Kolchinsky et al., 2018), semantic threshold behavior (Sowinski et al., 2023), causal leverage (Bartlett, 2024), modality-transferable latent structure (Acevedo et al., 21 May 2025), or task-preserving communication (Niu et al., 2024, Beck et al., 2022), the common claim is that semantic information is a proper subset or transformation of syntactic information distinguished by necessity, structure, or use.