Semantic Spacetime: Theoretical Frameworks

• Semantic Spacetime is a conceptual framework that intertwines space, time, and meaning, modeling local relations, order, and inference.
• It integrates quantum, promise-theoretic, logical, and computational methods to represent narratives, cognitive graphs, and agent interactions.
• The research raises open questions on stability, observer-dependence, and ontological implications, challenging conventional notions in physics and knowledge representation.

Semantic spacetime is a family of formalisms in which space, time, and meaning are treated as mutually implicated rather than separable. In the cited literature, the term denotes, depending on context, a quantum-inspired “theatre of stories” for conceptual entities, a promise-theoretic knowledge space built from autonomous agents and their promises, a non-commutative quantale equipped with a temporal modality, a declarative ontology of space-time histories as first-class logical objects, and an observer-theoretic claim that spacetime structure is fixed only relative to semantics-capable observers (Aerts, 2011, Burgess, 2014, Burgess, 2016, Tabatabai, 2019, Schultz et al., 2018, Stoica, 2024). The literature therefore suggests a shared research program rather than a single canonical theory: semantics is not merely attached to an already given spacetime, but participates in how locality, order, identity, and inference are represented.

1. Genealogy and principal meanings

The 2011 quantum-conceptual formulation identifies semantic spacetime with the “theatre of stories,” where stories play the role that ordinary matter plays in physics, and concepts behave as quantum-like mediators between memory structures (Aerts, 2011). The 2014–2016 promise-theoretic program defines semantic spacetime as a system of autonomous agents whose local promises generate adjacency, time, scale, and semantics; in that program, space is constituted by relationships, time by change in those relationships, and observer interpretation is integral to spacetime itself (Burgess, 2014, Burgess, 2015, Burgess, 2016). A separate algebraic-logical strand defines a non-commutative spacetime as a quantale with an oplax, join-preserving time modality and derives implication as a residuation against temporal delay (Tabatabai, 2019). A knowledge-representation strand treats space-time regions or histories as first-class objects under ASP stable-model semantics (Schultz et al., 2018). A 2024 observer-theoretic paper uses the expression in a different but related sense: sentient observers supply the semantic consistency needed to select a unique spacetime structure from the underdetermined structure of state space (Stoica, 2024).

Formulation	Primary primitives	Characteristic claim
Quantum-conceptual	concepts, stories, semantic place-time	space-time is the “theatre of stories”
Promise-theoretic	agents, promises, adjacency, super-agents	space and time emerge from local promises
Algebraic-logical	quantales, modality $V$, residuation	implication is induced by space and time
Declarative KR	polygons, histories, world-tubes, stable models	space-time histories are first-class logical objects
Observer-theoretic	state space, observables, sentient observers	semantics selects the unique spacetime up to symmetry

A recurrent motif across these lines is the replacement of fixed background structure by local relations. In the promise-theoretic papers this is stated directly: adjacency represents space, clocks measure change, and semantic attachment is carried by promises. In the quantum-conceptual paper the analogous move is from physical space-time to semantic place-time; in the logic paper it is from implication as a primitive connective to implication as a spatio-temporal adjoint; in the ASP framework it is from ad hoc event encodings to explicit world-tubes and interval-scoped relations.

2. Quantum-conceptual semantic spacetime

In the 2011 formulation, quantum particles are interpreted as conceptual entities mediating between pieces of ordinary matter acting as memory structures, and human concepts are taken to mediate between human memory structures in an analogous way. The central identification is: physical field $=$ quantum particles + space-time + ordinary matter, cognitive field $=$ concepts + semantic spacetime + stories. A “story” is defined operationally as a coherent conceptual entity that emerges under type-1 thought to fit stimuli; it is more than a “bag of words,” because ambiguity is reduced by the mind’s tendency to remove disjunctions. On this basis, the equivalent of ordinary matter in the cognitive field is the story, and the equivalent of physical space-time is the “theatre of stories,” i.e. a semantic spacetime in which stories can be situated (Aerts, 2011).

The paper develops this mapping through two comparisons. First, concepts admit states ranging from abstract to concrete. A concept such as Cat can occur in a highly abstract state, while “This Cat Felix” is maximally concrete; the claim is that a concept cannot be both maximally abstract and maximally concrete at the same time, and this mirrors a Heisenberg-like tradeoff between momentum-like and position-like states. In the web environment, each page containing Cat yields a very concrete state of Cat for that environment, while dictionary-like forms correspond to momentum-like states that are nonlocal in “semantic position.” Second, the paper distinguishes the connectives And and Or by locality. For concepts $A$ and $B$, both “$A$ and $B$” and “$A$ or $B$” are concepts, but for objects only conjunction yields an object-like entity, whereas disjunction does not. Conjunction is thus associated with locality and concretization, while disjunction introduces ambiguity and nonlocality.

Semantic locality is operationalized through the World-Wide Web. Web pages are treated as stories; selecting and reading a page elects a semantic place-time parcel, consisting of a semantic place plus a time defined by the moment and sequence of selection. In semantic spaces such as vector space models, LSA, and HAL, documents and terms are vectors, and normalized inner products quantify semantic proximity. Locality therefore means high proximity, coherence, and concreteness; nonlocality means lower proximity and more abstract superpositions. Time is the sequence of interactions and narrative progression, as in the unfolding of a choice such as “coffee or tea.”

The formal backbone is standard quantum formalism. States are represented by unit vectors $|\psi\rangle$ of a complex Hilbert space, measurements by orthogonal projectors $=$0, and probabilities by the Born rule

$=$1

Disjunction is treated schematically as superposition,

$=$2

with the corresponding probability containing an interference term. The paper emphasizes the interpretational contrast more than a full tensor-product treatment of conjunction.

A distinctive empirical device is the “and/or proportion”

$=$3

where $=$4 is the number of webpages containing text $=$5. The paper gives

$=$6

It then reports marked contextual asymmetries. “Dead and alive” versus “dead or alive” yields $=$7; “coffee and tea” versus “coffee or tea” gives $=$8; “want coffee and tea” versus “want coffee or tea” gives $=$9. These examples are used to argue that disjunctive “molecules of meaning” such as “dead or alive” and “coffee or tea” are entrenched nonlocal potentials embedded in stories, while conjunction tends toward localization and concretization. The broader claim is that ambiguity resolution, contextuality, and interference-like behavior in meaning can be modeled as collapse and state update in semantic spacetime.

3. Promise theory, agency, and graph semantics

The promise-theoretic strand begins from the thesis that relationships constitute space and that changes in relationships constitute time. Its atomic unit is the autonomous agent, and its basic formal device is the promise: a voluntary declaration by a promiser to a promisee, typically written as a positive offer or assertion and a complementary negative acceptance or use. In this view, adjacency itself is promised rather than presupposed, boundaries are failures or limits of adjacency, and scalar properties, behaviors, containment, and directed influence are all encoded in promise bodies. A spacetime can therefore be represented as a graph of agents and adjacency promises, but the graph is interpreted semantically rather than purely combinatorially (Burgess, 2014).

This line then scales from individual agents to super-agents. A super-agent is a bounded subspace of sub-agents held together by interior promises; coarse-graining hides interior promises and exposes an aggregate exterior interface. The 2015 paper makes this the basis for a calculus of scaling, occupancy, and tenancy. Hosts promise resources or services of finite valency, tenants accept and use them, and utilization is constrained by capacity. The same paper formalizes boundaries, surfaces, directories, and scale transducers, and argues that semantic and dynamic continuity are maintained by boundary policies, language overlap, and rate constraints. In this framework, topology, adjacency, and “what things are for” emerge from the local exchange of promises rather than from an external coordinator (Burgess, 2015).

The 2016 development crystallizes these ideas into a knowledge-representation framework. A semantic element is defined as

$=$0

and a semantic spacetime is “a collection of semantic elements, in any phase (gas or solid), for which a local change in state, promises or configuration represents a local unit of time.” Knowledge is modeled as iterated sampling and equilibration of promise assessments, with fast context modulating slow knowledge. The paper emphasizes four irreducible association types by which intent propagates: aggregation, causation, cooperation, and similarity. It also insists on discrimination of identities, separation of timescales, and the ability to learn as prerequisites for functional knowledge representation (Burgess, 2016).

Graph-oriented SST work retains the same four-way decomposition but expresses it as typed associations in an explicitly cognitive graph. The 2017 paper defines ST 1 proximity/contiguity, ST 2 gradient/direction, ST 3 aggregate/membership, and ST 4 distinguishability/attribute. Concepts are tokens, relations are directed associative links typed by $=$1, contexts gate activation of edges, and reasoning consists of recursive traversals that aggregate into stories. Context is attached to edges rather than to tokens, and the system separates fast pattern recognition from slower semantic reasoning (Burgess, 2017).

The 2025 graph-theoretic formalization sharpens this into a finite $=$2 representation. It distinguishes three node meta-types—events $=$3, things $=$4, and concepts $=$5—and four link types: Type 0 “near” $=$6, Type 1 “leads-to” $=$7, Type 2 “contains” $=$8, and Type 3 “expresses” $=$9. The paper presents $A$0 as “a closed set of operations that can scale to any degree of semantic complexity,” and gives adjacency, incidence, and path-join matrices to constrain allowed transitions and termination conditions. $A$1-processes terminate on final events or do not terminate, $A$2-processes terminate on atomic things, $A$3-processes on atomic concepts, and $A$4-processes may remain open-ended. This yields a graph process semantics grounded in locality, cooperative causality, and minimal typing rather than in large ontology vocabularies (Burgess, 9 Jun 2025).

A plausible synthesis is that the promise-theoretic tradition treats semantic spacetime as a local theory of knowledge-bearing structure: space is adjacency, time is local change, scale is coarse-graining, and semantics is whatever agents promise, accept, and stabilize under context.

4. Algebraic, logical, and declarative formulations

A different formal line derives semantic spacetime from algebraic semantics. In the 2019 paper, a non-commutative spacetime is a quantale $A$5 equipped with an oplax, join-preserving time modality $A$6, satisfying

$A$7

Here multiplication $A$8 encodes ordered composition of observations and need not be commutative. The central construction is spatio-temporal implication. If $A$9, then

$B$0

equivalently characterized by

$B$1

This is presented as a generalization of Heyting implication, substructural implications, and weak strict implication. In the commutative locale case, one recovers topological Heyting implication; in the non-commutative case, propositions are state-changing relations and time supplies a delayed applicability condition for implication (Tabatabai, 2019).

The same paper develops sequent calculi STL and iSTL, topological semantics, and Kripke semantics, and proves soundness and completeness results model-theoretically. It also proves representation theorems showing that abstract implications can be represented, up to a monotone factor, via spatio-temporal implication on an appropriate non-commutative spacetime. In this strand, “semantic spacetime” is not a metaphor for concepts or agents but an algebraic fabric from which implication and dynamic subjectivity are derived.

A more engineering-oriented formalization appears in ASP Modulo “Space-Time.” There, space-time histories are first-class logical objects with precise declarative semantics. A space-time object $B$2 over interval $B$3 is a function from time to polygons, and its world-tube is

$B$4

Qualitative spatial relations are defined slice-wise and then lifted to histories. For example,

$B$5

while $B$6, $B$7, and $B$8 are defined by analogous time-quantified conditions. The framework also defines native spatio-temporal predicates such as $B$9, $A$0, $A$1, $A$2, $A$3, $A$4, and $A$5, combining qualitative and quantitative constraints under ASP stable-model semantics (Schultz et al., 2018).

Its “modulo” architecture separates a symbolic layer from a geometric solver. The ASP layer encodes ontology, qualitative relations, search, and preferences; the theory layer solves polynomial equalities and inequalities over real-valued polygon vertices, centers, areas, and translations, using integrations of z3 and NLopt/BOBYQA. The system precomputes and encodes 1586 algebraic invariants, including converses, implications, and 3-path inconsistencies, to prune search before numeric checks. The empirical evaluation reports scalability from about $A$6 s to about $A$7 s for one pair over all timesteps when $A$8 to $A$9, robustness from $B$0 to $B$1 under $B$2–$B$3 slice deletions, and practical performance for tens of objects and timesteps. In this setting, semantic spacetime is a declarative KR framework for commonsense reasoning over dynamic regions.

5. Narrative comprehension, invariant concepts, and namespaces

The 2020 narrative-comprehension papers formulate a “Semantic/Quantitative Spacetime Hypothesis” according to which spacetime processes must underpin all aspects of cognition, and meaning can initially be bootstrapped from changes in extent and duration rather than from a pre-given lexicon or grammar. The first paper treats a symbolic stream as an event feature landscape. Sentences are events, words are $B$4, phrases of length $B$5 are $B$6, and fixed-size “legs” of approximately 200 sentences replace paragraphs as a receiver-imposed coarse scale. A finite-memory interferometric process tracks novelty, repetition, and local deviations from homogeneous background distributions. The importance proxy for a fragment is given as

$B$7

with fragments that occur only once excluded from scoring. The paper reports power-law novelty decay for words, weaker repetition for 2-phrases, and a collapse of repetition for longer phrases in single narratives. It also reports meaning-preserving compression judged “related” by human evaluators for non-random narratives, with efficiencies including 148% for History of Bede, 234% for Moby Dick, 129.5% for Origin of Species (6th), and 497.5% for Slogans (Burgess, 2020).

The sequel moves from salience selection to geometry. Input streams are fractionated into $B$8 fragments, events $B$9, and hubs $A$0, and are linked by four fundamental spacetime relations: FOLLOWS, CONTAINS, EXPRESSES, and SIMILAR TO (NEAR). The paper writes, for example,

$A$1

for episodic order, and represents hubs and sentences as containers and expressers of fragment sets. Hub similarity is measured by an overlap score printed as

$A$2

The context ratio is

$A$3

with a reported critical region $A$4–$A$5. Empirical overlap horizons are given as: random $A$6, meaningful $A$7–$A$8, and repetition/self about $A$9. Concepts are persistent local patterns, especially $B$0 and $B$1; themes are regions of hubs linked by NEAR above a similarity horizon; namespaces arise by aggregation of fragments under hubs and are endowed with geometry by NEAR and CONTAINS (Burgess, 2020).

The paper gives concrete results for several corpora. In Darwin’s Origin, 12 regions are obtained from 18 links in 70 hubs, yielding themes such as awe, considered reason/understanding, diversity and inheritance, fossil record, and competition/natural selection. In Bede, 4 regions come from 7 links in 43 hubs. In Moby Dick, 6 regions come from 298 links in 81 hubs, with emotional themes such as apprehension, vengeance, and awe. In Slogans, 2 regions come from 4 links in 90 hubs, and the dominant themes are emotional rather than factual. The framework explicitly warns that if NEAR edges are too permissive, theme separation dissolves into “grey goo” maximum entropy.

These papers therefore operationalize semantic spacetime as a multiscale graph geometry of narratives: statements are trajectories, hubs are contexts, themes are neighborhoods, and concept formation is the stabilization of process invariants under finite-memory observation.

6. Ontological implications, controversies, and open questions

The most radical ontological claim appears in the 2024 observer-theoretic paper. It argues that the same invariance criteria that motivated Galilean relativity, Special Relativity, and gauge symmetry imply that there is no unique set of observables that determines space or spacetime purely from the structure and dynamics of the theory. In its formulation, “space is lost in the state space itself.” Unitary transformations $B$2 that commute with the Hamiltonian preserve dynamical form and relational structure but generate alternative “position” candidates $B$3 that need not represent physical position. The paper then claims that sentient observers, modeled by a semantic evaluation map $B$4, uniquely determine the parameter space on which position observables are defined, up to spacetime symmetries and local gauge transformations. On that basis it argues against Structural Realism and against Physicalism as defined in the paper, because observer-like structures that are structurally isomorphic need not possess reliable semantic access to environmental properties (Stoica, 2024).

Other strands raise different open questions. The 2011 quantum-conceptual paper states that the human cognitive field is “much less organized” than the quantum field, that a complete mathematical theory will be more complex than current quantum formalism, that the Web was too small at the time for longer-sentence statistics, and that the exact topological or metric structure of semantic spacetime remained open (Aerts, 2011). The 2016 promise-theoretic treatment lists further open problems, including the stability of storage and recovery under dynamic states, the compatibility of partial eigenvectors in parallel reasoning, and the roles of pointed graphs and spanning trees in narrative inference (Burgess, 2016). The 2025 graph paper adds a distinct limitation: absorbing states are “ubiquitous in any partial graph,” they leak information, and inverse reconstruction can require “manual injection of remedial information,” which the paper relates to loss of closure and division by zero (Burgess, 9 Jun 2025). The 2020 narrative papers identify parameter sensitivity, concept instability under narrative mixing, and percolation into “grey goo” as practical failure modes (Burgess, 2020).

Several misconceptions are therefore corrected by the literature itself. Semantic spacetime is not only a metaphor for semantic vector spaces, because some formulations are quantum-conceptual, some are promise-theoretic, some are logical-algebraic, and some are computational KR systems. Nor is it simply “semantics on top of spacetime”: in all formulations, semantics enters the constitutive account of locality, identity, implication, or observability. At the same time, the literature does not supply a single agreed metric, topology, or dynamics. The strongest common denominator is narrower and more precise: locality, order, containment, similarity, and attribute are repeatedly treated as primitive semantic-spatiotemporal relations, and cognition or reasoning is repeatedly modeled as movement, collapse, propagation, or path formation within structures built from those relations.