System-Defining Events

• System-defining events are key occurrences that define system boundaries, order operational behaviors, and alter system logics across various disciplines.
• They are modeled as region-time pairs, synchronization points, or transient disturbances in fields like software engineering, power systems, and international studies.
• Analysis integrates formal approaches—ranging from the Thinging Machine framework to timed transition models—to ensure robust system assembly and resilience.

Searching arXiv for the cited papers to ground the article in current metadata. {"query":"id:(Bhusal et al., 2020) OR id:(Al-Fedaghi, 2020) OR id:(Ma et al., 2018) OR id:(Al-Fedaghi, 2020) OR id:(Cassano et al., 2014) OR id:(Piepers, 2015) OR id:(Al-Fedaghi, 2022) OR id:(Dorninger et al., 30 Jun 2025) OR id:(Al-Fedaghi, 2017) OR id:(Al-Fedaghi, 2021) OR id:(Wang et al., 2015) OR id:(Al-Fedaghi, 2020) OR id:(Mishra et al., 2020)","max_results":10} System-defining events are occurrences whose identification, formalization, or observation determines how a system is delimited, how its admissible behaviors are ordered, how its operating regime is classified, or how its governing logic changes. The available literature suggests that the term has no single domain-independent meaning. In conceptual modeling and software engineering, it denotes time-bound realizations of structured regions in a static model; in concurrent and cyber-physical design, it denotes synchronization points, fair or timed transitions, and interface-visible behaviors; in power systems and nonlinear dynamics, it denotes disruptive hazards, transient disturbances, or rare excursions; in international-systems analysis, it denotes systemic wars; and in algebras of numerical events, it denotes critical observations that alter whether the underlying logic is classical or non-classical (Al-Fedaghi, 2021, Cassano et al., 2014, Bhusal et al., 2020, Mishra et al., 2020, Piepers, 2015, Dorninger et al., 30 Jun 2025).

1. Cross-domain scope

Across the cited literatures, system-defining events serve different but structurally analogous functions. In each case, the event is not merely any occurrence in a system. Rather, it is an occurrence whose formal treatment constrains system semantics, system assembly, risk evaluation, or regime identification.

Domain	Event form	System-defining role
Conceptual and software modeling	Region plus time; compositions of primitive event-processes	Fixes boundaries, interfaces, observable behavior, and chronology
Concurrent and cyber-physical systems	Synchronization points; indexed, fair, spontaneous, or timed transitions	Coordinates components and supports safety, liveness, and real-time validation
Infrastructure, nonlinear dynamics, international order, and numerical-event logic	Hazards, transient disturbances, extreme excursions, systemic wars, or critical numerical events	Classifies regimes, measures resilience, or changes the logic of the system

In the power-resilience literature, the relevant events include “extreme natural events” and “newly emerging man-made attacks,” specifically hurricanes, earthquakes, floods, wind storms, ice storms, typhoons, wildfires, cyber attacks on control and communication networks, and physical attacks such as substation sabotage (Bhusal et al., 2020). In PMU-based situational awareness, six event classes are treated as system-defining: faults, line-tripping, large load change, generation loss, shunt switching, and false data injection (Ma et al., 2018). In dynamical systems, an excursion is an extreme event when its amplitude exceeds a statistically significant threshold such as $x>x_{99}$ or $H_S=\mu+d\sigma$ (Mishra et al., 2020). In the international-system study, a system-defining event is a “systemic war” involving all contemporaneous Great Powers, exceptionally intense, and leaving an enduring imprint on the architecture of international order (Piepers, 2015). In the theory of numerical events, a new event is critical exactly when it changes the classical versus nonclassical character of the logic (Dorninger et al., 30 Jun 2025).

2. Ontological and formal definitions

A major line of work, especially by Al-Fedaghi, develops system-defining events from the Thinging Machine (TM) framework. In TM, every thing is subject to exactly five primitive operations: Create, Process, Receive, Release, and Transfer. A TM event is itself a thimac localized in both a region of a static TM diagram and time. The basic primitive event-processes are written as

$$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$

and complex events are compositions of these primitives, for example

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$

All events can be reduced to these five event processes (Al-Fedaghi, 2020).

A closely related formulation defines an event as a region-time pair. In integrated behavior engineering, an event is

$E=(R,T),$

where $R$ is a connected subdiagram of the static model and $T$ is a time submachine that binds the region into a durative occurrence (Al-Fedaghi, 2021). In the Lupascian extension of TM, the same idea appears as

$E=\langle R,t\rangle ,$

with a negative event given by the same region returned to the static level, written as $\neg E\equiv R$ (Al-Fedaghi, 2022). In the flow-thing-machine formulation, the event is itself an abstract machine,

$E=(S_E,I_E,O_E,\delta_E,TM_E),$

where $H_S=\mu+d\sigma$0, $H_S=\mu+d\sigma$1 is the transition function, and $H_S=\mu+d\sigma$2 carries the time-flow associated with the event (Al-Fedaghi, 2017).

The progression from static structure to behavior is formalized in the three-layer TM scheme

$H_S=\mu+d\sigma$3

where $H_S=\mu+d\sigma$4 is the atemporal static description, $H_S=\mu+d\sigma$5 is the partially ordered set of static changes, and $H_S=\mu+d\sigma$6 is the temporal chronology of events $H_S=\mu+d\sigma$7 (Al-Fedaghi, 2020). The central semantic claim is that FSM states are static, atemporal changes, whereas events are the carriers of behavior once time is injected.

3. Causality, composition, and system assembly

System-defining events do not only denote occurrences; they also impose admissible chronologies. In TM-based causality analysis, two ordering relations are distinguished. Flow-based precedence is expressed as

$H_S=\mu+d\sigma$8

and trigger-based or causal precedence as

$H_S=\mu+d\sigma$9

The static model therefore constrains the set of linearizations that may appear in the dynamic model: any chronology violating either flow or trigger ordering is excluded (Al-Fedaghi, 2020).

This treatment of events is paired with explicit criteria for completeness and consistency. Every flow must have a Create; every Transfer must pair with exactly one Receive at the next machine; Process and Create are distinct; and when sub-machines are collapsed, the relative ordering of primitives must be preserved or the presence of parallelism must be noted (Al-Fedaghi, 2020). These rules make “no phantom data” and “no lost messages” model-theoretic requirements rather than informal desiderata.

In concurrent systems design, Cassano and Maibaum distinguish actions from events by making both explicit in a component signature

$$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$0

Here $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$1, $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$2, and $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$3 are variables, action names, and event names; $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$4 and $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$5 are the prescription and description of action $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$6; and $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$7 is the set of actions observed by event $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$8. An action is a guarded transition with an effect, while an event is a synchronization point that groups actions to fire in lock-step. When components are assembled by colimit in the category $$\mathit{Create}_M(x),\quad \mathit{Process}_M(x),\quad \mathit{Receive}_M(x),\quad \mathit{Release}_M(x),\quad \mathit{Transfer}_{M\to N}(x),$$9, identifying event names forces the union of the observed action-sets to fire atomically without collapsing the underlying action names (Cassano et al., 2014).

Timed Transition Models (TTMs) push this compositional view into verification-oriented cyber-physical modeling. A TTM event may be spontaneous, fair, or timed; indexed events concisely capture actor-specific behavior and fairness; and synchronous events allow simultaneous state updates using primed variables to refer to post-state values. The tool constructs an action-dependency graph for each synchronous set and reports circular-dependency errors when the graph is cyclic (Wang et al., 2015). This makes event structure directly operative in safety, liveness, and real-time reasoning.

4. Infrastructure, resilience, and event classification

In power-system resilience, system-defining events are modeled as hazards propagating in space and time through a hazard field $$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$0. The paper on resilience enhancement reviews propagation models including hurricane arrival via the Poisson law

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$1

empirical wind-field models such as

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$2

the Yang–Meng typhoon momentum equation

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$3

and seismic intensity decay approximated by

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$4

Component impact is then represented by fragility functions

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$5

including earthquake fragility in the form

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$6

followed by system-level metrics such as

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$7

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$8

and

$$E=\bigl\langle \mathit{Create}_M(x), \mathit{Process}_M(x), \mathit{Release}_M(x), \mathit{Transfer}_{M\to N}(x), \mathit{Receive}_N(x) \bigr\rangle .$$9

where $E=(R,T),$0 is the fraction of service restored at time $E=(R,T),$1 (Bhusal et al., 2020).

Event definition in operational monitoring takes a different but complementary form in PMU-based classification. Ma, Basumallik, and Eftekharnejad model PMU time series $E=(R,T),$2 using sliding windows, $E=(R,T),$3-normalization, PAA, SAX symbolic words, and a multivariate Bag-of-Pattern frequency matrix, then reweight rows by a modified TF–DF scheme: $E=(R,T),$4 The resulting voltage- and current-based feature vector is classified by an RBF-SVM or an ensemble of decision trees. On the IEEE 30-bus system, using PMUs at buses $E=(R,T),$5, 2,353 labeled events, and SAX parameters $E=(R,T),$6, $E=(R,T),$7, $E=(R,T),$8, the RBF-SVM achieved overall accuracy $E=(R,T),$9; fault, false data, and shunt switching reached $R$0 detection; generation loss and line tripping reached $R$1; load change reached $R$2; varying PMU coverage from 5 to 7 PMUs produced $R$3–$R$4 accuracy; and with 90 dB white noise the accuracy remained $R$5 (Ma et al., 2018).

These two strands represent different layers of the same infrastructure problem. One treats system-defining events as exogenous hazards and endogenous component failures; the other treats them as transient signatures that must be recognized in real time. A plausible implication is that resilience evaluation and event identification are complementary rather than competing conceptions of the event.

5. Extreme, systemic, and critical events

In nonlinear dynamics, system-defining events appear as rare excursions that exceed a significance threshold. Mishra and collaborators define an extreme event either by a percentile rule $R$6 or by the significant-height criterion

$R$7

They use $R$8 for the forced Liénard system and $R$9 for the coupled-neuron example. Three generic routes generate such events: interior crisis, Pomeau–Manneville intermittency, and breakdown of quasiperiodic motion. After an interior crisis, the mean interval between large excursions scales as

$T$0

whereas type-I intermittency yields laminar-length scaling

$T$1

The inter-event interval distribution is exponential,

$T$2

indicating a Poisson-like, memoryless process of extremes (Mishra et al., 2020).

In historical international-systems analysis, the corresponding regime-changing events are systemic wars. Four such wars are identified between 1495 and 1945: the Thirty Years’ War, the French Revolutionary and Napoleonic Wars, the First World War, and the Second World War. Each is said to introduce an organizational innovation: the sovereignty principle and balance-of-power diplomacy; the Concert of Europe; the League of Nations; and the United Nations together with the Bretton Woods institutions. The timing is described by accelerating cycles with life-span

$T$3

and by a generic log-periodic singularity

$T$4

The study also reports

$T$5

and

$T$6

for systemic wars (Piepers, 2015).

A third notion of system-defining event appears in algebras of numerical events. If $T$7 is a state space, an $T$8-probability is a function

$T$9

A collection $E=\langle R,t\rangle ,$0 containing $E=\langle R,t\rangle ,$1 and $E=\langle R,t\rangle ,$2, ordered pointwise and closed under complementation and finite sums of pairwise orthogonal triples, forms an algebra of $E=\langle R,t\rangle ,$3-probabilities and hence an orthomodular poset. A newly observed numerical event $E=\langle R,t\rangle ,$4 is destructive if $E=\langle R,t\rangle ,$5 cannot be embedded into any algebra of $E=\langle R,t\rangle ,$6-probabilities. It is critical if it changes the classical versus nonclassical character of the logic: either it destroys Boolean embeddability or it forces Boolean embeddability. Reciprocity relations between events provide simple criticality tests, including conditions based on partial reciprocity below or above $E=\langle R,t\rangle ,$7 and the existence of a state $E=\langle R,t\rangle ,$8 with $E=\langle R,t\rangle ,$9 or $\neg E\equiv R$0 (Dorninger et al., 30 Jun 2025).

Taken together, these studies suggest that system-defining events need not be frequent or even operationally observable in the same way. What makes them defining is their capacity to expose or alter the structure of admissible behavior, phase-space accessibility, institutional order, or logical representation.

6. Misconceptions, limitations, and research directions

A recurrent misconception is that an event is simply a label attached to a state transition. Several of the cited works reject that reduction. In TM and related formalisms, the event is a structured region with time, internal primitive operations, and explicit participation of things; in concurrent design, the event is not the same as the action, because the event observes one or more actions that occur together; in extreme-event analysis, not every large excursion qualifies, since the definition is threshold-based and statistical; and in numerical-event logic, “critical” does not mean merely rare, but logic-changing (Al-Fedaghi, 2021, Cassano et al., 2014, Mishra et al., 2020, Dorninger et al., 30 Jun 2025).

The strongest explicit research agenda is developed in the power-resilience review. The identified gaps are that forecast models rely on historical single-event data and neglect measurement and communication noise; existing fragility curves ignore spatiotemporal hazard correlations; interdependencies among critical infrastructures are under-modeled; renewable and mobile resources’ dynamics are often dropped in microgrid resilience studies; short 24 h scheduling horizons can misallocate scarce post-event resources; distribution models commonly assume purely radial topology; lack of demand-side management and islanding standards constrains resource use; and perfect information is unrealistic post-disaster. The proposed directions are correspondingly to leverage big-data analytics and deep learning for multi-event training, integrate scenario-based spatial–temporal simulators with dynamic fragility updates, develop co-simulation frameworks for cascading cross-sector impacts, hybridize Monte Carlo with analytical stochastic models for DERs and BESS uncertainties, employ parallel multi-stage optimization over extended horizons, generalize to weakly meshed configurations using adaptive power-flow formulations, advocate new interconnection policies and compensation schemes, and formulate resilience strategies under partial or imperfect information (Bhusal et al., 2020).

In behavior engineering, the stated direction is toward an integrated event concept capable of subsuming Dromey’s behavior trees, fluents, recurrent events, and Davidsonian action events within a single region-plus-time framework (Al-Fedaghi, 2021). The broader literature suggests that progress on system-defining events depends on preserving two commitments simultaneously: ontological precision about what an event is, and domain-specific rigor about what an event does. Without the first, event models become opaque labels; without the second, they cease to define the system at all.