Draft:Evolution of De Morgan's Law from Classical to Hayawic Logic
Evolution of De Morgan’s Law from Classical to Hayawic Logic
[edit]De Morgan’s Law—formulated by Augustus De Morgan in 1847—expresses the relationship between conjunction and disjunction under negation:
- Failed to parse (syntax error): {\displaystyle ¬(A ∧ B) = (¬A) ∨ (¬B)}
- Failed to parse (syntax error): {\displaystyle ¬(A ∨ B) = (¬A) ∧ (¬B)}
Originally developed within the framework of binary logic, these laws became a cornerstone of Boolean algebra and symbolic reasoning. Over time, various thinkers extended and reinterpreted De Morgan’s insight to account for multi-valued and dynamic forms of logic. The following table traces this conceptual development, culminating in its reformulation within the framework of Hayawic Logic (المنطق الحيوي), which generalizes binary opposition into four relational values — affirmation, negation, partiality, and paradox.
| Period | Thinker / Source | Logical Formulation | Philosophical Interpretation | Hayawic Development |
|---|---|---|---|---|
| 1847 | Augustus De Morgan, Formal Logic | ¬(A ∧ B) = (¬A) ∨ (¬B); ¬(A ∨ B) = (¬A) ∧ (¬B) | Two-valued truth: negation inverts conjunction/disjunction. | Foundation of classical binary logic. |
| 1854 | George Boole, Laws of Thought | Algebraic 0/1 representation preserving De Morgan symmetry. | Logic expressed algebraically through symbols. | Basis for Boolean algebra and computation. |
| 1900s–1950s | Łukasiewicz, Tarski, Birkhoff | Multi-valued and lattice logics. | Recognition of intermediate or probabilistic truth values. | Theoretical path toward dynamic logic systems. |
| 1987 | Raiek Alnakari (رائق النقري), Damascus School of Hayawic Logic (مدرسة دمشق للمنطق الحيوي) | Al-Manṭiq al-Ḥayawī (Paris) | Four-valued system { +1, 0, −1, ⊥ }. | Introduction of the Interest Square Unit (وحدة مربع المصالح), defining affirmation, negation, partiality, and paradox. |
| 2000 | David C. Rine & Raiek Alnakari (رائق النقري) | "A Four-Valued Logic B(4) of E(9)" | Maintains De Morgan symmetry within the ISU algebra. | IEEE ISMVL presentation applying Hayawic logic to communication modeling. |
| 2019 | Yasmine Alnakari (ياسمين النقري), Université Paris 8 | L’Unité Carrée des Intérêts (ISU) | Doctoral framework integrating ISU into educational methodology. | Expansion of the Interest Square Unit (وحدة مربع المصالح) as a generative and compensatory learning system within Hayawic Logic. |
Overview
[edit]De Morgan’s binary inversion of logical connectives served as a foundation for formal logic and computation. In contrast, Hayawic Logic (المنطق الحيوي) retains the structural symmetry of De Morgan’s law while extending it beyond binary opposition, representing logical relations as dynamic interactions within a four-valued field. This reinterpretation preserves classical consistency yet introduces paradox as an intrinsic value rather than a contradiction to be eliminated.
References
[edit]- De Morgan, Augustus (1847). Formal Logic: or, The Calculus of Inference, Necessary and Probable. London: Taylor and Walton.
- Boole, George (1854). An Investigation of the Laws of Thought. London: Walton and Maberly.
- Raiek Alnakari (رائق النقري) (1987). Al-Manṭiq al-Ḥayawī. Paris: Dar al-Dirasat al-ʿArabiyya al-Duwaliyya.
- David C. Rine; Raiek Alnakari (رائق النقري) (2000). "A Four-Valued Logic B(4) of E(9) for Modeling Human Communication." IEEE International Symposium on Multiple-Valued Logic (ISMVL).
- Yasmine Alnakari (ياسمين النقري) (2019). L’Unité Carrée des Intérêts (ISU) comme méthode générative et compensatoire en éducation. Doctoral Thesis, Université Paris 8.
See also
[edit]- De Morgan’s Laws
- Boolean algebra
- Multi-valued logic
- Hayawic Logic (المنطق الحيوي)
- Damascus School of Hayawic Logic (مدرسة دمشق للمنطق الحيوي)
- Interest Square Unit (وحدة مربع المصالح)