This section introduces the formal ontology of Value Management Theory (VMT). The ontology defines the minimal set of entities, relations, and properties required to consistently describe value and anti-value dynamics in socio-economic systems.
O1. Value System (VS)
O1.1. Definition (Essence)
A value system is a formally defined set of actors and directed interactions between them, within which value and anti-value can be meaningfully defined, transmitted, consumed, and transformed.
O1.2. Conditions of Existence
A value system is meaningful as an analytical construct if and only if the following conditions hold:
- there exists a set of actors A, with |A| ≥ 2;
- there exists a set of directed flows F, and the system contains at least two flows ensuring reciprocal interaction between actors (not necessarily symmetric);
- there exists a set of criteria allowing the interpretation of interaction outcomes as value or anti-value within the chosen context.
O1.3. Parameterization
A value system is defined by the tuple:
VS = {A, F, G, R, T}
- A - the set of actors;
- F - the set of flows between actors (internal and external);
- G - criteria or target states defining improvement or degradation;
- R - rules and constraints of interpretation (resource-based, institutional, technological, contractual, etc.);
- T - the temporal horizon of interpretation and analysis.
Note on System Boundaries
System boundaries are implicitly defined by the choice of sets A and F. An actor or flow belongs to a system if and only if it is included in these sets. Therefore, a separate ontological definition of "boundary" is unnecessary and derivable from O1.
O1.4. Value Aggregation Policy
A value system may explicitly or implicitly define a value aggregation policy- a rule that determines how interpreted values and anti-values are aggregated into system-level assessments.
An aggregation policy may define the admissibility or inadmissibility of reducing different types of value to a common scale, the priorities of criteria G, and the rules for trade-offs in cases of value conflicts.
The absence of an explicit aggregation policy implies that any statements about the total value of the system are incomplete and depend on unspecified assumptions.
O2. Actor
An actor is an element of a value system capable of interpreting changes in its state in terms of value and anti-value, forming interests and preferences, and participating in value flows.
An actor is capable of:
- interpreting consumed value and anti-value relative to criteria G;
- consuming value and/or anti-value (i.e., experiencing state changes interpreted within the system);
- producing (sending) planned value and/or anti-value to other actors through flows;
- participating in flows as a sender and/or receiver.
Clarification (Non-obligatory Production)
An actor may be a pure consumer within the analyzed system. Value production by this actor may occur in other systems intentionally excluded from the current analysis.
O3. Value Element
A value element is an abstract object interpreted as value or anti-value that can be transmitted, consumed, and/or transformed within flows of a value system.
A value element may represent:
- a property of a physical object (e.g., material, device);
- a property of an action, event, or service;
- a property of an abstract object (e.g., right, risk, obligation, knowledge, trust).
Element Types
Elements may have types type(E) if distinguishing them is necessary for interpreting flows and actor state changes.
Importantly, element type is a qualitative semantic attribute, not a quantitative one. Quantitative characteristics arise from multiplicity, scale, or intensity of flows.
O4. Value and Its Forms
Value is an interpreted form of actor state change that increases the actor’s ability to reach criteria G within a value system. VMT distinguishes four forms of value interpretation.
O4.1. Potential Value (Vpotential)
Potential value is an interpreted possibility of actor state change that exists before a recipient is defined and before a delivery flow is organized.
It reflects an actor’s capacity to form planned value in the future, without obligation or intent to deliver it to a specific recipient.
O4.2. Planned Value (Vplan)
Planned value is the sender’s interpretation of potential value once a recipient is defined and a decision is made to direct value into a specific flow, as an expected impact on the recipient within the value system.
Planned value exists prior to consumption and characterizes intention and expectation expressed through elements and flows.
O4.3. Realized Value (Vreal)
Realized value is defined exclusively through the interpretation of the receiving actor as the actual ordered change of its state resulting from consumption of a value element.
O4.4. Retrospective Value (Vretro)
Retrospective value is a re-evaluation of previously realized value by the consuming actor, arising from subsequent use of that value to form planned value in new flows and from feedback on its realization.
Formally, V1retro arises when an actor realizes V1real, uses it to form V2plan, observes V2real, and revises the original interpretation of V1real.
Properties:
- retrospective value does not alter the past;
- it is not transferred through flows;
- it influences future interpretations and decisions.
Note on Multiple Value Systems
Apparent “change of value over time” may result either from the emergence of retrospective value within an expanded system or from the transition of an element into a different value system (see O9).
O4.5. Terminal and Instrumental Value
Within a given value system, value elements may be interpreted as terminal or instrumental.
Terminal value is value realized at the point of consumption, after which further use of the element either lies outside the boundaries of the considered value system or forms a new value system.
Instrumental value is value that is significant within the system exclusively as a means for forming, transferring, or amplifying future value at subsequent converters.
The distinction between terminal and instrumental value is contextual and is determined by the boundaries of the value system, the criteria G, and the temporal horizon of consideration.
O5. Anti-Value and Its Forms
Anti-value is an interpreted change of actor state that reduces its ability to reach criteria G within a value system.
Anti-value exists in the following forms:
- AVplan - expected anti-value (sender interpretation);
- AVreal - realized anti-value (receiver interpretation);
- AVretro - retrospective re-evaluation of negative effects.
Anti-value is not "zero value"; it is an independent category of state change.
O6. Value Flow
A value flow is a directed interaction between two actors (sender and receiver) through which one or more value elements and associated expectations are transmitted.
Formally:
F = {as, ar, E, Vplan, AVplan, Vreal, AVreal, t}
- as - sender;
- ar - receiver;
- E - (possibly empty) set of transmitted elements;
- Vplan, AVplan - sender interpretations;
- Vreal, AVreal - receiver interpretations;
- t - temporal reference.
Qualitative and Quantitative Characteristics
Qualitative semantics of a flow are determined by element types and interpretation rules R.
Quantitative characteristics arise from element multiplicity, scale, transmission frequency, and magnitudes of Vplan, Vreal, AVplan, AVreal.
A flow begins when value or anti-value held by the sender is directed toward the receiver. A flow ends when consumption occurs and a definitive realized interpretation Vreal/AVreal is formed.
O7. Value Realization
Value realization is the event (or process) in which the receiving actor consumes flow elements and forms Vreal and/or AVreal as a change of its own state within the value system.
During realization, the actor may:
- change its own state (consumption);
- form planned value for other systems (transfer);
- create new value or anti-value elements (transformation).
O8. Value Transformation and the Transformer Role
O8.1. Transformation
Value transformation is a special case of realization in which, after consuming flow elements and realizing value or anti-value, an actor produces new value or anti-value elements intended for further use or transmission.
O8.2. Transformer as a Role
A transformer is not an entity but a role of an actor in a specific transformation:
role(a) = Transformer if actor a performs transformation per O8.1.
The same role may be realized by multiple actors, enabling redundancy and scaling.
O9. Multiplicity of Value Systems
The same empirical set of interactions may be interpreted as different value systems with different criteria G, rules R, and temporal horizons T. Therefore, value is not a universal quantity.
O10. Observability and Latency
Value and anti-value may be:
- directly observable;
- indirectly observable through indicators;
- latent (unobservable in available data).
Lack of observability does not imply absence of value or anti-value.
Criteria G may not always be fully articulable by an actor; interpretation may be purely qualitative or ordinal.
Sources of Value Interpretation
Sources of changes in value interpretation may differ in their nature.
Epistemic sources of interpretation are based on the observation of the consequences of value realization, feedback, and changes in the state of actors after the use of value elements.
Influential sources of interpretation are based on external interpretative influence (social, informational, institutional) and are not a direct consequence of the realization of value elements.
These sources may lead to different dynamics of changes in planned, realized, and retrospective value.
O11. Participation Condition
An actor’s participation condition in a value system over horizon T is defined by individual threshold levels of interpreted value and anti-value, as well as by the actor’s ability to transform value and direct planned value into flows for which demand exists.
Each actor has a participation threshold θa defining an acceptable balance of participation.
O12. Mutual Participation and Exchange Cycles
A value system exhibits mutual participation over horizon T if, for every actor, there exists at least one cycle of flows connecting:
- production of (at least planned) value for other actors;
- reception of realized value from the system,
such that the participation condition O11 is satisfied.
O13. Flow Resistance
Flow resistance is a property of a flow expressing the cumulative effect of factors leading to:
- divergence between Vplan and Vreal;
- emergence of AVreal.
Resistance may depend on system history: accumulated anti-value, accumulated expectation mismatches, and unaccounted retrospective re-evaluations.
Flow resistance may also include undelivered value - elements directed into a flow but not reaching the receiver due to delays, blockages, or loss of interpretive context.
O14. Inter-System Interaction and Leakage
O14.1. External Flow
A flow is external to a value system if its sender or receiver does not belong to the actor set A of that system.
O14.2. Value Leakage
A system exhibits value leakage over horizon T if the total realized value leaving the system through external flows persistently exceeds the total realized value entering it.
O15. System Types by External Flows
- Donor system - persistent outward leakage;
- Parasitic system - sustainability depends primarily on external inflows without equivalent return;
- Balanced system - external inflows and outflows are symmetric on average;
- Autocatalytic system - a significant portion of realized value remains within the system and reinforces future value production capacity.
O16. Interpretive Dynamics
Actor interpretations of value may change over time under the influence of flows, transformations, and external signals not directly transmitted as value elements.
Interpretive dynamics affect:
- criteria G;
- interpretation rules R;
- correspondence between Vplan and Vreal.
O17. Interpretive Influence
Interpretive influence is an effect by which one actor (or system) alters another actor's interpretation of value.
O18. Value Storage
Value storage is the process of accumulating value by an actor without immediate state change.
Stored value requires maintenance costs and may be used for later transfer or transformation.
Long-term storage of planned value increases the temporal gap between creation and consumption, raising the risk of divergence between Vplan and Vreal. Re-evaluation is required before stored value is directed into a flow.