There are different types of approaches to solve P vs NP, some of them are logical approaches. The lecturer's PhD thesis [11] is based on one of these logical approaches 2002 [2], [6]. Till 2011, he and some other logicians made an unsuccessful aƩempt to shed light on this problem in this way. In 2010‐2011, he started to introduce another logical approach based on paradoxes, more specifically ?Unexpected Hanging Paradox?. The goal is to use paradoxes similar to applying paradoxes (Liar Paradoxes) in the Godel?s Incompleteness Theorem [14], [15], [16]. In [5], [16] (2017), he showed by defining a new version of this paradox, we face a contradiction, not a paradox. To cope with this situation, in 2019 Fuzzy Time [4], [17] (or as some of the speaker?s colleagues used it later on, Temporal Continuum (2023) or Continuity in Time (2024)) came into the centre of the subject and discussion. Nevertheless, we have concepts similar to the fuzziness of Time and space in the history of science, Mathematics, Philosophy and Physics [7], [12], [13]. Based on that, the speaker claimed a new interpretation of Quantum Mechanics, the ?Fuzzy time‐particle? interpretation of Quantum Mechanics [1], [3], [4]. ?Theory of Fuzzy Time Computation?, is introduced in [8], [9], [10], monthly seminars of the Iranian Association of Logic [18], and The 10th annual conference of the Iranian Association for Logic (IAL) (2023) [19]. In 2023, this Theory was introduced in a paper in HAL [9] and now it is in development. In this lecture, after defining this Theory, we explain a part of it in details, and as the main conclusion, we prove TC+CON(TC^* )ͰP≠NP.
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References.
1. Computing Fuzzy Time Function, F.Didehvar, Philpapers, SSRN 2022
2. B.Poizat, Les petit cailloux. Une approach modele-theorique de l?Algorithmie , Nur al-Mantiq wal-Ma?rifah, no.3.Ale?as, Lyon 1995, 2 pp.
3. Does accepting Fuzzy Time-Particle interpretation of Quantum Mechanics, refutes the other interpretations? (Is fuzziness of time checkable experimentally?), F.Didehvar, Philpapers, SSRN, 2021
4.Fuzzy time a solution for unexpected hanging Paradox ( a Fuzzy interpretation Of Quntum Mechanics)), Philpapers 2019-4-13
5. Is Classical Mathematics appropriate for Theory of Computation? F.Didehvar, Philpapers(Manuscript), 2017,2018,2019, Handbook of the 6th World Congress and School on Universal Logic, Vichy France, 2018
6. L. Blum, M.Shub, S. Smale, ?On a Theory of Computation and Complexity over the real numbers: NP-Comleness, Recursive Functions and Universal Machines, Bull.Amer.Mth.Soc.(N.S.) 21 (1): 1-46 (July 1989).
7. , M. Van Aten, On BrouwerWadsworth Philosopher?s Series, 2004 (PersianTranslation by M. Ardeshir)
8. TC+CON(TC*) deduce P is not equal to NP, F.Didehvar, Philpapers(Manuscript), 2020
9.-Theory of Fuzzy Time Computation (TC^* vs TC &TQC), hal-04330281
10. P ≠ NP, by Accepting to Make a Shift in the Theory (Time as a Fuzzy Concept), F.Didehvar, Philpapers, SSRN, 2021
11. Some Concepts and Problems in Theory of Complexity in Structures, published as ?Generalization of Some Concepts Theory in Structures?, Ph.D Thesis, 2002
12. C.Wetterich, Probabilistic Time, Foundation of Physics, 2012
13. Zeno Paradox, Unexpected Hanging Paradox (Modeling of Reality & Physical Reality, A Historical-Philosophical view), F.Didehvar, Philpapers, (Manuscript)2022 Conferences
14. When proof doesn?t show the Truth, Philosophy Day in Iran (Logic and Philosophical Logic, Tradition and Modern), 2010/11/19, Tehran, Iran.
15. A Semantic Situation without Syntax (Non-axiomatizibility of Theories), Universal Logic 2015, (5th World Congress and school, 2015/6/28, Istanbul University.
16. Is Classical Mathematics Appropriate for Theory of Computation?, Universal Logic 2018, (6th World Congress and school, 2018/6/28, Vichy University Campus.
17. Fuzzy Time, from Paradox to Paradox, The 50th Annual Iranian Mathematics Conferences, Shiraz, Iran, Shiraz University, 26-29 August, 2019, Shiraz University.
18. The impacts of Logic, Paradoxes in on side and Theory of Computation in the other side (Fuzzy Time Computation), (TC*، زمان فازی) تاثیر و تاثر منطق و پارادوکسها بر نظریه محاسبات عام 20 June 2022 (In Persian), https://ialogic.ir/index.php/2022-12-11-17-07--09/lectures/258--2022-06--15--05-07-35 The slides are in Philpapers.
19. About a Proof (TC + CON(TC ∗)Ͱ(P≠NP), The 10th Annual Conference of the Iranian Logic Association, February, 22, 2023-