Qualia Abstraction Language (QAL)

• Qualia Abstraction Language (QAL) is a compositional formalism that models quantum phenomena as streams of introspective microstates rather than state vectors.
• It defines grammatical primitives—modality, shape, and functional effect—to capture the dynamic transformations of conscious experience.
• QAL reconstructs quantum mechanical concepts such as superposition, collapse, and entanglement through non-commutative semantic transformations in a first-person framework.

Searching arXiv for papers on Qualia Abstraction Language and related formalizations of qualia. Qualia Abstraction Language (QAL) is a formalism proposed for reconstructing quantum mechanics in terms of structured dynamics of subjective experience rather than state vectors in Hilbert space. In this framework, physical systems are modeled as evolving streams of introspective units, and canonical quantum notions such as superposition, collapse, measurement, entanglement, and decoherence are reinterpreted as transformations internal to first-person structure (Sienicki et al., 3 Aug 2025). Within the surrounding literature on qualia, QAL is distinctive because it is presented as an explicit compositional formalism with grammatical primitives; earlier work typically offered ontological constraints, topological models, algebraic structures, or toy mathematical surrogates for qualia without introducing a dedicated abstraction language (Brownstein, 11 Feb 2025).

1. Definition and theoretical scope

QAL is defined as a compositional formalism and morphodynamic language whose basic units encode introspective transformation rather than physical state in Hilbert space (Sienicki et al., 3 Aug 2025). Its central ontological move is to treat a system not as an external mathematical object described by amplitudes over basis states, but as a temporally ordered stream of phenomenally typed microstates. On this view, the observer is not external to the formalism; the observer is embedded within the system as the site of semantic evolution.

The paper introducing QAL states that the observer paradox in quantum mechanics reflects a linguistic absence rather than an ontological absence: conventional formalism lacks a vocabulary for modeling first-person structure (Sienicki et al., 3 Aug 2025). QAL is intended to supply that vocabulary. Its philosophical alignment is explicitly with nominalism, anti-Platonism, phenomenology, constructivism, and endophysics, while also engaging relational and internalist views of observation. The resulting program is therefore not merely a reinterpretation of measurement; it is a proposal to rebuild physical description as a grammar of awareness.

A plausible implication is that QAL occupies two roles at once. First, it is a representational system for introspective structure. Second, it is a replacement-level ontology for quantum-theoretic description. That dual role distinguishes it from earlier qualia formalisms that remained local models of phenomenal organization rather than comprehensive reconstructions of physics.

2. Grammatical primitives and atomic units

The basic representational atom of QAL is the qualia triplet

$$q_i \in \mathcal{Q} = \mathcal{M} \times \mathcal{S} \times \mathcal{F},$$

where $\mathcal{M}$ is modality, $\mathcal{S}$ is shape, and $\mathcal{F}$ is functional effect (Sienicki et al., 3 Aug 2025). The atomic notation is also written as

$$q = [m\!-\!s\!-\!f], \quad \text{where } m \in \mathcal{M},\ s \in \mathcal{S},\ f \in \mathcal{F}.$$

The grammar is given in BNF-like form:

$\mathcal{F}$0

The three components have distinct roles. Modality specifies the experiential domain, with examples including visual, kinesthetic, and metacognitive. Shape specifies phenomenological morphology or intensity profile, with examples including diffuse, sharp, and oscillatory. Functional effect specifies what a qualia unit does within the stream, with examples including constriction, expansion, and resonance (Sienicki et al., 3 Aug 2025). A token such as me-lo-ka is glossed in the paper as a metacognitive expansion and gentle outward reflection.

The explicit separation of modality, shape, and functional effect is important because QAL is designed to encode not simply what is sensed, but how sensing transforms awareness. This differentiates QAL from models that treat qualia as static labels, scalar values, or unstructured points.

3. Streams, coherence, and morphodynamic rules

A QAL-described system is represented as a stream

$Q = q_1 . q_2 . q_3 . \dots . q_n,$

or equivalently as an ordered tuple $(q_1, q_2, \ldots, q_n)$ with each $q_i \in \mathcal{Q}$ (Sienicki et al., 3 Aug 2025). The stream is governed by local continuity constraints. The paper specifies modal continuity, according to which successive modalities must match or be semantically adjacent; shape compatibility, minimizing discontinuity through a shape distance metric; and effect resonance, according to which later effects should reinforce or resolve earlier ones. These conditions define a phenomenologically coherent stream.

Composition is explicitly non-commutative: $$em\text{-}xa\text{-}dr . vi\text{-}lo\text{-}br \neq vi\text{-}lo\text{-}br . em\text{-}xa\text{-}dr.$$ Order therefore has constitutive significance, much as operator order matters in standard quantum mechanics (Sienicki et al., 3 Aug 2025).

QAL introduces a semantic distance

$$\delta(q_i, q_j) = \lambda_m d_\mathcal{M}(m_i, m_j) + \lambda_s d_\mathcal{S}(s_i, s_j) + \lambda_f d_\mathcal{F}(f_i, f_j),$$

with

$\mathcal{M}$0

and a stream coherence functional

$\mathcal{M}$1

Higher coherence corresponds to smoother experiential unfolding (Sienicki et al., 3 Aug 2025).

Evolution is described by an operator

$\mathcal{M}$2

and, at unit level, by a variational rule of the form

$\mathcal{M}$3

where $\mathcal{M}$4 encodes contextual modulation such as attention, memory, resonance, and emotional valence (Sienicki et al., 3 Aug 2025). Stability is characterized by approximate constancy of coherence and sufficiently small inter-unit semantic distance.

The same framework defines collapse and fragmentation conditions. If

$\mathcal{M}$5

the stream undergoes collapse or fragmentation. Fragmentation is represented as

$\mathcal{M}$6

and the paper also gives attractor-style convergence and metastability conditions for long-run stream behavior. At the extreme limit, qualic termination is defined by

$\mathcal{M}$7

which the paper interprets as the end of the introspective stream (Sienicki et al., 3 Aug 2025).

4. Reconstruction of quantum-mechanical concepts

QAL maps standard quantum concepts into phenomenological-morphodynamic counterparts rather than treating them as merely analogous. Standard superposition,

$\mathcal{M}$8

is reinterpreted as structured ambiguity: a stream phase in which multiple semantic continuations remain unresolved (Sienicki et al., 3 Aug 2025). A criterion is given by

$\mathcal{M}$9

under which competing continuations are nearly equally distant in semantic space. The system is then said to be in superpositional ambiguity.

Standard collapse,

$\mathcal{S}$0

is replaced by introspective contraction or semantic contraction: $\mathcal{S}$1 A contraction rule is stated as choosing the next qualic state by minimizing semantic distance while preserving coherence above threshold $\mathcal{S}$2 (Sienicki et al., 3 Aug 2025). Collapse is therefore construed as internal resolution rather than external projection.

Measurement is treated as an internal phase-shift,

$\mathcal{S}$3

The measurement event is thus not a boundary between system and observer, but a semantic reorganization of awareness (Sienicki et al., 3 Aug 2025).

Entanglement is recast as qualic resonance or resonant identity coupling rather than tensor-factor nonseparability. Two streams $\mathcal{S}$4 and $\mathcal{S}$5 are resonantly linked if there exists a shared morphodynamic attractor connecting them. Decoherence, correspondingly, becomes fragmentation of the qualia stream: breakdown of continuity, dissociation, loss of resonant integration, and splitting into partially coherent branches (Sienicki et al., 3 Aug 2025).

This reconstruction is philosophically strong. It does not claim merely that introspective language can describe observer-side phenomena in quantum theory; it claims that quantum theory itself should be reformulated in that language.

5. Relation to earlier formalizations of qualia

Prior work on qualia provides several mathematical precursors to QAL, but most of it stops short of a fully specified abstraction language. In "On the distinction between beables and qualia" (Brownstein, 11 Feb 2025), qualia and de Broglie-Bohm beables are treated as distinct but mutually necessary. Qualia require a substrate with continuity of identity across time and consistency with Born-rule probabilities across time, while beables require qualia to avoid ontological redundancy. That paper explicitly does not propose a language for encoding qualia; it offers a substrate-selection principle and ontological constraints.

"Nelson Goodman’s qualia and the Discrete Cat Mapping" (Amunategui, 2013) presents a mathematically explicit toy model in which qualia are represented by discrete, position-indexed surrogates evolving under the discrete Arnold cat map. Its equivalence table links quale, qualia with pixel, pixels, two-dimensional concretum with configuration on the screen, and map with Arnold discrete map. The model preserves finitude, positionality, order, recurrence, and temporal reidentification, but the paper stresses that these are analogies rather than a full calculus.

"A Mathematical Framework for Consciousness in Neural Networks" (Lima, 2017) proposes that qualia correspond to singularities in the mathematical representations of neural network topology, with singularities serving as coordinate-invariant markers of irreducibility. The framework provides a singularity set,

$\mathcal{S}$6

and a bound singularity set for modeling binding, but it explicitly does not define syntax, semantics, or a formal qualia language.

"Qualia as physical measurements: a mathematical model of qualia and pure concepts" (Resende, 2022) defines a space of qualia as a sober topological space $\mathcal{S}$7, with points as qualia and open sets as pure concepts. It adds sequential composition, disjunction, and involution, yielding an involutive quantale and a measurement-space interpretation. The paper’s strong conjecture is that qualia and physical measurements are of the same nature, but again the result is a topological-algebraic theory rather than a grammar of tokenized qualia streams.

"An algebraic theory to discriminate qualia in the brain" (Ohmura et al., 2023) moves closer to a language-like abstraction by treating qualia types as multiple metric spaces connected by algebraic independence of transformations. It introduces commuting transformation modules, vector-valued transformation parameters, and a latent decomposition into distinct qualia-specific spaces, together with empirical results on synthetic image data. That structure is highly relevant to QAL because it supplies a semantics for qualia categories and transformations, but the primary formal objects remain transformations and invariant spaces rather than explicit grammatical streams.

Taken together, these works suggest that QAL consolidates several previously separate themes: ontological carrier conditions, discrete symbolic surrogates, topological irreducibility, measurement-space structure, and algebraic decomposition into qualia-specific spaces. What is new in QAL is the attempt to combine explicit grammar, stream syntax, and reconstruction of physical theory within a single formalism.

6. Limitations, controversies, and terminological ambiguity

The current QAL literature is programmatic rather than settled. The paper introducing QAL states several open problems: no fully rigorous mathematical topology for qualia space is provided; the semantic metric $\mathcal{S}$8 and coherence function $\mathcal{S}$9 are only sketched; many formulas are suggestive rather than formally complete; and it remains unclear how QAL could be empirically tested against standard quantum mechanics (Sienicki et al., 3 Aug 2025). Open questions include metric completeness, the algebraic structure of qualic composition, recovery of standard quantum mechanics as a limit, a QAL analogue of Schrödinger dynamics, AI implementation, and formalization of inter-stream resonance.

A common misconception would be to treat QAL as simply another reductive encoding of qualia into physical variables. The related literature repeatedly resists that move. The beables paper argues that qualia are non-material, experiential, and not directly reducible to physical description, even when they require an appropriate substrate (Brownstein, 11 Feb 2025). The singularity framework likewise insists that qualia are not identical with singularities, but that singularities mark points where quantitative description reaches an in-principle limit (Lima, 2017). QAL inherits that anti-reductive pressure while still attempting formalization.

There is also a terminological ambiguity. An unrelated paper introduces "Quala", a true full-stack quantum programming language for hardware-level control, calibration, and branching logic (Frey et al., 2021). That language integrates gate-level programming, a timing layer, low-level FPGA instructions, symbolic calibration, and adaptive execution, but it concerns quantum hardware programming rather than phenomenal representation. The lexical resemblance can obscure the distinction between a programming language for quantum devices and a proposed formal language of awareness.

The status of QAL is therefore best described as exploratory but explicit. It is more formal than earlier qualia models that lacked grammar, yet less complete than mature physical calculi. Its significance lies in making first-person structure the primary medium of formal description and in testing whether a grammar of qualia can be made to bear the explanatory load normally assigned to wavefunctions, measurements, and observers.