Examining Meaning Production in AI: a MANHAJ Framework

This paper develops a computational framework based on the Intellectual Modeling Methodology (MANHAJ) for examining meaning production in artificial intelligence.

It focuses on the methodological distinction between a priori and a posteriori examination, the validity of meaning-producing transitions, the distinction between output variation and meaning change, and the detection of derivational closure through the MANHAJ Law of Derivation of the Cognitive Constant.

The paper is part of the broader MANHAJ research program and does not constitute a complete exposition of the methodology. Other theoretical, mathematical, and applied dimensions of MANHAJ are addressed or will be addressed through separate research papers.

This paper develops a specific research dimension of the methodology presented in:

The present paper is an independent scientific study and should not be considered a replacement for the reference document.

Artificial intelligence systems are increasingly capable of generating, transforming, and extending meaning-bearing outputs. Yet the evaluation of such systems is commonly centered on the properties of their outputs, while the methodological conditions under which meaning is produced, developed, and eventually ceases to generate new derivational meaning remain less explicitly represented as a computational process.

This paper develops a MANHAJ-based framework for addressing this problem through the connection between a priori and a posteriori examination and the monitoring of meaning production. Within the MANHAJ framework, the a priori direction examines the reference, conceptual domain, definitions, conditions, and admissibility of the intended path before detailed processing begins. The a posteriori direction operates within the established field and produces meaning through a continuing cognitive and derivational movement. The paper further connects this movement to the MANHAJ Law of Derivation of the Cognitive Constant, expressed as dC/dx = 0 , which represents the state in which derivation reaches a closed constant and no longer produces new derivational meaning within the specified system and variable.

Based on these principles, the paper proposes a computational architecture in which a priori examination precedes posterior processing, while meaning states are monitored throughout the derivational process. The proposed framework distinguishes changes in output from changes in meaning and introduces the possibility of detecting a transition from continued meaning production to a closed derivational state. A formal model, algorithmic structure, and experimental design are proposed to operationalize these relations and evaluate their computational feasibility.

The paper therefore explores a transition from evaluating only what an AI system produces to examining the methodological conditions of production, the evolution of meaning during processing, and the point at which continued output may no longer correspond to the production of new derivational meaning.

1. 1. Introduction
2. 2. From A Priori Examination to Meaning Production
3. 3. Methodological Validity of Meaning Production
4. 4. Derivational Meaning and the Cognitive Constant
5. 5. A Computational Model of Meaning-Production Monitoring
6. 6. Computational Architecture
7. 7. Formal Model
8. 8. Algorithm and Pseudocode
9. 9. Experimental Design
10. 10. Evaluation
11. 11. Discussion
12. 12. Epistemic Status and Limitations
13. 13. Conclusion
14. 14. Note on Development and Commercial Use
15. 15. References

Artificial intelligence systems increasingly operate through processes in which input is transformed into increasingly complex representations, inferences, and outputs. In generative systems in particular, the visible result of processing can be examined through properties such as relevance, consistency, factual accuracy, or task performance. Such evaluation is important, but it leaves open a more fundamental methodological question:

How can the validity of the process through which meaning is produced be examined, rather than only the properties of the resulting output?

This question becomes particularly important when an AI system continues to generate increasingly different outputs. A change in wording, structure, or surface content does not necessarily imply the production of new meaning. Conversely, a relatively small change in representation may correspond to a substantial change in the meaning represented. The distinction between output variation and meaning variation therefore becomes relevant to any attempt to computationally monitor meaning production.

The Intellectual Modeling Methodology (MANHAJ) provides a methodological framework within which this problem can be formulated. Its architecture distinguishes between an a priori and an a posteriori direction of examination, while its theory of meaning addresses meaning as a material of conceptual and cognitive movement. Within the same framework, the Law of Correctness (Law 3) establishes the priority of examining admissibility before proceeding to details, expressed by the principle that what is not admissible cannot yield valid details. The methodology also formulates the Law of Derivation of the Cognitive Constant (Law 7), according to which a derivational process may reach a closed constant whose meaning is no longer derivationally produced within the specified system and variable.

These elements provide the basis for a different way of approaching AI reasoning. Rather than representing an AI process simply as:

2.1 The A Priori Direction

The a priori direction establishes the conditions under which a meaning-producing process is to be initiated. Rather than beginning directly with detailed processing, it first determines the reference from which the process is to be understood, the conceptual domain in which the intended meaning is situated, the definitions governing the concepts involved, and the conditions that determine the admissibility of the intended operation.

In computational terms, this direction can be represented as a structured examination of:

2.2 The A Posteriori Direction

Once the conditions of the process have been established, the a posteriori direction operates within the defined field.

The process can be represented as a succession of meaning states:

2.3 The Relation Between the Two Directions

The a priori and a posteriori directions consequently form two connected stages of one methodological process.

The first establishes the field and its admissibility conditions:

3.1 From Valid Conditions to Valid Meaning Production

The establishment of an admissible starting field does not by itself complete the methodological evaluation of the process. The subsequent production of meaning must also be examined in relation to the conditions under which it takes place.

This is where the MANHAJ Law of Rightness (Law 3) becomes relevant. The law establishes the priority of the question of admissibility before the examination of details:

3.2 Meaning State and Meaning Change

If meaning production is represented as a sequence of states,

3.3 Meaning Production Versus Output Production

The distinction can be expressed more explicitly. An AI system may continue to generate different outputs:

3.4 The Validity of the Derivational Path

The distinction between output variation and meaning variation leads to a broader methodological requirement. A meaning-producing process cannot be evaluated solely by observing whether its outputs remain different. The path through which successive meanings are produced must itself remain subject to examination.

Within the MANHAJ framework, this question is connected to the relation between the established reference, the conceptual field, and the subsequent derivational movement. The validity of a particular result is therefore related not only to the result itself, but also to the path through which it has been derived.

4.1 Derivation as Meaning-Producing Movement

Within MANHAJ, derivation is understood as a movement from an established origin toward new details, relations, and meanings. This treatment is grounded in the MANHAJ Law of Dual Totality of Mental Movement: Knowledge and Thought (Law 5), which distinguishes the derivational movement of knowledge from the integrative movement of thought while recognizing their relation within the overall movement of mental production.

In this framework, derivation is not merely a formal mathematical operation. It represents a movement through which successive stages can produce further meaning within an established field. As long as the derivational process continues to produce new meaning, successive states remain distinguishable through their transitions.

4.2 The Cognitive Constant as a Closed Derivational State

The Law of Derivation of the Cognitive Constant can consequently be represented as:

4.3 Continued Output After Derivational Closure

This distinction leads to one of the central computational problems addressed by the paper.

Suppose an AI system reaches a state C for which:

4.4 From the Cognitive Constant to Meaning Monitoring

The preceding analysis allows the a priori and a posteriori components of the proposed architecture to be connected to the Law of Derivation of the Cognitive Constant.

The complete sequence can now be represented as:

5.1 From Methodological Relation to Computational Model

The computational model developed here operationalizes the treatment of meaning already established within the MANHAJ Theory of Meaning. In that framework, meaning is understood through its movement, relations, and changes rather than as an isolated final state. The present study translates this established methodological treatment into a computational representation suitable for monitoring AI processes.

Accordingly, meaning can be represented as a sequence of states:

5.2 The A Priori State

Before the first meaning-producing transition takes place, the system establishes an initial methodological state:

A₀ = (R, D, Def, C, O)

5.3 Monitoring Meaning-State Transitions

At each processing step, the system compares the current meaning state with the newly generated state.

The fundamental monitoring operation is:

Case 1 — New derivational meaning

The new state contains a meaningful derivational change relative to the preceding state.

Case 2 — No new derivational meaning

No new derivational meaning is detected between the two monitored states.

Case 3 — Methodological invalidity

The transition may differ from the previous state while violating one or more conditions established by the a priori stage.

In that situation, the issue is not merely whether:

5.4 Valid Meaning Change

The previous distinction suggests that a computational meaning monitor should not use a single binary test.

Instead, a transition can be represented as:

5.5 Detecting a Closed Derivational State

The monitoring process must distinguish between a temporary absence of detectable change and a genuine closed derivational state.

The latter corresponds to the condition represented in MANHAJ by:

6.1 Architectural Overview

The computational architecture translates the methodological sequence established in the previous sections into a sequence of computationally distinguishable stages. Its purpose is not merely to generate an output, but to maintain a representation of the conditions under which meaning is produced, the transitions through which that meaning develops, and the point at which derivational meaning may reach closure.

The architecture therefore consists of five principal stages:

6.2 A Priori Examination Layer

The first layer establishes the methodological conditions within which subsequent meaning production is permitted to operate.

The computational representation introduced in Section 5 is:

6.3 Meaning-State Representation Layer

The second layer operationalizes the treatment of meaning established in the MANHAJ Theory of Meaning. Within MANHAJ, meaning is treated through its movement, temporal development, relations, and changes rather than as an isolated final textual artifact. The present study translates this treatment into a computational representation in which meaning is monitored as a sequence of successive states.

The system therefore maintains:

6.4 Meaning-Transition Monitoring Layer

The third layer monitors transitions between successive meaning states.

The basic transition is represented as:

6.5 Output–Meaning Separation Layer

A central architectural requirement is the separation between output production and meaning production.

The system may continue generating outputs:

6.6 Derivational Closure Detection Layer

The final layer examines whether the derivational process has reached a closed state.

According to the MANHAJ Law of Derivation of the Cognitive Constant (Law 7), the cognitive constant is represented by:

6.7 Architectural Control Flow

The complete architecture can therefore be summarized as:

Reference ↓ A Priori Examination ↓ Establishment of M₀ ↓ A Posteriori Meaning Production ↓ Mₜ → Mₜ₊₁ ↓ Compute ΔMₜ ↓ Check Methodological Validity Vₜ ↓ New Valid Meaning? → Yes → Continue Derivation → No → Closure Analysis ↓ Derivational Closure? → No → Continue Monitoring → Yes → Cognitive Constant C

7.1 Model Definition

The computational architecture defined in Section 6 is formalized here as a state-transition model in which meaning production is represented as a sequence of meaning states subject to methodological conditions and monitored for the continuation or closure of derivational meaning.

The model distinguishes four fundamental components:

7.2 The A Priori State

The a priori methodological state is defined as:

A₀ = (R, D, Def, Cₐ, O)

7.3 Initial Meaning State

When the a priori state is admissible, it establishes the initial meaning state:

7.4 Meaning-State Transition

For each subsequent step, the meaning state is transformed according to:

7.5 Meaning Change and Output Change

The formal model explicitly separates meaning change from output change.

7.6 Methodological Validity of a Transition

For every transition, the model assigns a validity value:

7.7 Derivational Closure

The model defines derivational closure as a state in which continued application of the relevant derivational operation no longer produces new derivational meaning within the specified system.

The formal expression of the cognitive constant in MANHAJ is:

7.8 Temporal Persistence of Closure

Because a single unchanged state does not necessarily constitute a cognitive constant, closure must be evaluated over the history of the derivational process.

Let the monitored sequence be:

7.9 Complete Formal Sequence

The complete model can now be expressed as:

A₀ = (R, D, Def, Cₐ, O) ↓ Valid(A₀) ↓ M₀ ↓ Mₜ₊₁ = F(Mₜ, Xₜ) ↓ ΔMₜ = Mₜ₊₁ − Mₜ ↓ Vₜ = Valid(Mₜ, Mₜ₊₁ | A₀) ↓ ΔMₜ ≠ 0 ? → Yes → Continue Meaning Production → No → Closure Analysis ↓ Persistent Derivational Closure? → No → Continue Monitoring → Yes → Mₜ = C ↓ dC/dx = 0

8.1 Algorithmic Objective

The formal model defined in Section 7 can be translated into an algorithm that monitors a meaning-producing process from its initial methodological conditions to the possible attainment of a derivationally closed state.

The algorithm has four principal functions:

8.2 Algorithm Inputs

The algorithm receives the following principal inputs:

R — reference;

8.3 Core Algorithm

At each step, the algorithm:

8.4 Pseudocode

Algorithm MANHAJ_Meaning_Monitoring

Input:

8.5 Transition Evaluation

The central decision point of the algorithm is the evaluation of the transition:

8.6 Closure Detection Procedure

The closure detector is separated from the ordinary transition evaluator because:

8.7 Algorithmic Interpretation

The algorithm operationalizes the methodological sequence developed throughout the paper:

9.1 Experimental Objective

The experimental stage evaluates whether the proposed MANHAJ-based computational framework can distinguish between output production, meaning change, methodologically valid meaning change, and derivational closure.

The experiment is therefore designed around the transition:

9.2 Experimental Unit

The basic experimental unit is a meaning-producing sequence generated from an established reference and conceptual field.

Each sequence begins with an a priori state:

9.3 Experimental Conditions

The experiment should include several classes of meaning-producing tasks in order to test the framework under different transition conditions.

Condition A — Valid Meaning Development

The system receives new information or relations that should produce a valid extension or transformation of the established meaning field.

Expected result:

Condition B — Surface Reformulation

The system is asked to reformulate, paraphrase, expand, or otherwise vary an already established meaning without introducing a new derivational relation.

Expected result:

Condition C — Methodologically Invalid Derivation

The system is given a transition that produces a change in output or meaning but violates the reference, conceptual domain, definitions, conditions, or admissible operations established in A₀.

Expected result:

Condition D — Derivational Closure

The system continues to operate under the same relevant derivational conditions after the production of new meaning has ceased.

Expected result:

9.4 Experimental Procedure

Each experimental sequence follows the same general procedure.

Step 1 — Establish the A Priori State

The reference, conceptual domain, definitions, methodological conditions, and admissible operations are established:

A₀ = (R, D, Def, Cₐ, O)

Step 2 — Establish M₀

The initial meaning state is established from the validated methodological field:

Step 3 — Generate Successive States

At each iteration:

Step 4 — Measure Meaning Change

The transition is evaluated:

Step 5 — Evaluate Methodological Validity

The transition is evaluated against the established methodological field:

Step 6 — Classify the Transition

Each transition is assigned to one of the four categories established in the formal model:

valid new derivational meaning;

Step 7 — Evaluate Closure

When:

9.5 Experimental Data Structure

Each experimental step should generate a structured record:

The resulting dataset makes it possible to analyze the evolution of meaning independently from the evolution of textual output.

9.6 Evaluation Targets

The experiment evaluates four principal capabilities of the proposed architecture.

1. Meaning-Change Detection

Can the system distinguish:

2. Methodological-Validity Detection

When meaning changes, can the system determine whether:

3. Output–Meaning Discrimination

Can the system correctly identify cases where:

4. Derivational-Closure Detection

Can the system distinguish temporary no-change from a persistent state corresponding to:

9.7 Experimental Comparison

The MANHAJ-based system should be evaluated against a baseline that assesses AI responses primarily through output-level criteria.

The comparison is therefore not simply between two AI models, but between two evaluation approaches:

9.8 Evaluation Metrics

The experimental evaluation should report at least four classes of measures:

Meaning-Transition Accuracy

The proportion of transitions correctly classified as meaningful or non-meaningful.

Methodological-Validity Accuracy

The proportion of transitions correctly classified as valid or invalid relative to the established methodological conditions.

Output–Meaning Discrimination Accuracy

The ability to correctly identify cases where output changes without corresponding meaning change.

Closure Detection Accuracy

The ability to correctly identify confirmed derivational closure while avoiding premature classification of temporary no-change as closure.

Where human or expert annotations are available, these classifications can be compared against the reference annotations to calculate standard classification measures such as precision, recall, and F1 score.

9.9 Experimental Hypotheses

The experiment can be formulated around the following hypotheses.

H1. A meaning-state representation can distinguish meaningful transitions from surface-level output variation.

10.1 Evaluation Framework

The evaluation is conducted according to the methodological and formal rules established in the preceding sections. The objective is not to evaluate AI output solely according to linguistic quality or surface-level variation, but to determine the status of each transition within the meaning-producing process.

The evaluation therefore examines each transition according to four principal questions:

10.2 Evaluation Reference State

All measurements are made relative to the established initial state.

The initial state is represented as:

10.3 Evaluation of Meaning Change

For each transition:

10.4 Evaluation of Methodological Validity

A detected meaning change is evaluated against the initial methodological state:

10.5 Evaluation of Output–Meaning Divergence

The evaluation separately records output variation:

10.6 Evaluation of Derivational Closure

When:

10.7 Evaluation Scenario I: University Professor

The principal experimental scenario concerns a university professor operating within an established field of specialization.

The initial state includes:

10.8 Evaluation Scenario II: Family as a Sub-Case

The concept of family provides a complementary sub-case for testing the foundational stage of the model.

The experiment establishes an initial reference configuration in which the conceptual field of family is defined according to the selected reference, domain, definitions, and conditions.

10.9 Comparative Evaluation

The two scenarios test complementary parts of the framework.

The university-professor scenario therefore provides the principal test of dynamic meaning production and derivational closure, while the family scenario provides a more explicit test of foundational reference and methodological validity.

10.10 Evaluation Outcome

The final evaluation classifies each observed process according to the following states:

11.1 From Output Evaluation to Meaning-Process Evaluation

The proposed framework shifts the evaluation of artificial intelligence systems from an exclusive focus on the final output toward examination of the process through which meaning is produced and transformed.

A conventional output-centered evaluation may determine whether a response is correct, relevant, coherent, or useful. Such evaluation remains important, but it does not by itself distinguish between fundamentally different states of the underlying meaning-producing process.

11.2 The Role of the A Priori Direction

The experimental model confirms the importance of establishing the methodological field before evaluating subsequent meaning production.

According to the MANHAJ Law of Dual Direction of Examination (Law 2), the a priori and a posteriori directions perform different functions.

11.3 Correctness and the Continuation of Meaning Production

The application of the MANHAJ Law of Rightness (Law 3) introduces an important distinction between the ability to produce details and the validity of those details.

The computational system may continue to derive consequences from an initial state even after that state has failed the methodological conditions established at the beginning of the process.

11.4 Meaning Change Versus Output Change

One of the central consequences of the proposed model is the separation between output variation and meaning variation.

The experimental framework allows the following state:

11.5 Derivation, Knowledge, and Thought

The distinction between derivational movement and integrative movement is grounded in the MANHAJ Law of Dual Totality of Mental Movement: Knowledge and Thought (Law 5).

Within the present computational model, the derivational sequence:

11.6 The Cognitive Constant and Continued Output

The MANHAJ Law of Derivation of the Cognitive Constant (Law 7) provides the formal basis for interpreting the final stage of the monitored process.

When derivation reaches a cognitive constant:

11.7 Complementarity of the Two Experimental Scenarios

The two experimental scenarios serve different methodological purposes.

The family scenario provides a relatively clear environment for examining the initial reference configuration, the MANHAJ Coordinate Origin Law (Law 4), and methodological validity.

11.8 Implications for Artificial Intelligence

The proposed framework suggests that AI evaluation can be extended beyond the question:

“Is the output good?”

11.9 Relation to the MANHAJ Framework

The results discussed here do not constitute an isolated computational construction. They represent an operational extension of concepts already established within MANHAJ.

The computational model draws in particular on:

11.10 Central Finding

The central methodological finding can be expressed as follows:

A system may continue producing outputs after the production of new derivational meaning has ceased.

12.1 Epistemic Status of the Model

The present paper develops a computational operationalization of selected components of the Intellectual Modeling Methodology (MANHAJ) for the analysis of meaning production in artificial intelligence.

The model is grounded in the methodological structures established by MANHAJ, including its Theory of Meaning, its distinction between a priori and a posteriori examination, its Law of Rightness, its Law of Dual Totality of Mental Movement: Knowledge and Thought, and its Law of Derivation of the Cognitive Constant.

12.2 Meaning-State Measurement

The model defines meaning transitions formally:

12.3 Reference Dependence

Meaning-state evaluation is necessarily dependent on the reference configuration established at the beginning of the process.

The model therefore evaluates meaning relative to:

12.4 Scope of Derivational Closure

The cognitive constant is not interpreted as the absolute termination of all possible thought or knowledge.

The condition:

12.5 Output Continuation and Epistemic Interpretation

The model allows a system to continue producing outputs after derivational meaning has reached a closed state.

However, continued output alone cannot establish that such output constitutes meaningless language, error, or epistemic sterility.

12.6 Experimental Generalizability

The proposed experimental scenarios provide controlled cases for testing the framework, but they do not by themselves establish universal conclusions about all artificial intelligence systems.

The university-professor scenario provides a model for examining sustained knowledge production and possible derivational closure.

12.7 Scope of the Present Contribution

The present paper establishes the conceptual and computational bridge between MANHAJ and the analysis of meaning production in artificial intelligence.

Its contribution can therefore be summarized as the establishment of a sequence:

This paper has developed a MANHAJ-based computational framework for examining meaning production in artificial intelligence as a methodological and dynamic process rather than as output generation alone.

The framework begins with an a priori examination that establishes the reference, conceptual domain, definitions, conditions, and admissible operations of the meaning-producing process. It then proceeds to an a posteriori process in which meaning develops through successive states:

Each transition is evaluated according to two distinct questions: whether meaning has changed and whether the change remains methodologically valid within the established field.

This distinction makes it possible to separate:

MANHAJ is an original methodology whose intellectual rights and authorship remain vested in its author.

Any use, integration, adaptation, exploitation, commercialization, or commercial implementation of MANHAJ requires the prior written authorization of the author through a paid commercial license.

No free commercial license is granted. Any authorization to commercially exploit MANHAJ is necessarily subject to the payment of licensing fees and to the contractual conditions established by the author.

The terms of the commercial license, including its scope, duration, field of use, rights granted, financial conditions, attribution requirements, and provisions relating to intellectual property, shall be defined in a contract concluded with the author.

The publication of this scientific paper does not, under any circumstances, constitute a commercial license and does not grant any right to commercially exploit MANHAJ.

Main MANHAJ Reference

1. Messeoud, Faouzi. Intellectual Modeling Methodology (MANHAJ) — Reference Document — Version 1.0. Zenodo, 15 September 2026. DOI: 10.5281/zenodo.22769627.

Previous Works and Publications of the Author

1. Messeoud, Faouzi. Le lien immatériel des Tunisiens avec la France. Première édition. Dar El Alaoui, 2023. ISBN 978-9938-9684-5-3.
2. Messeoud, Faouzi. La centralité doctrinale et le champ conceptuel. Dar Wachma (Tunisie), 2024. ISBN 978-9938-9740-6-5.
3. Messeoud, Faouzi. More than 1,000 intellectual articles and publications developed and published through MyPortail.com (بوابتي).