** Bibliography **
The perspective—that logic is discovered rather than invented—aligns with the Platonist view in the philosophy of mathematics and logic. This stance posits that logical truths exist independently of human thought, and through reasoning, we uncover these pre-existing structures.
Key References Supporting This View:
1. Plato’s Theory of Forms: Plato suggested that abstract entities, including logical forms, exist in a non-physical realm and are more real than the tangible world. Humans access these forms through intellectual insight, implying that logical truths are eternal and unchanging.
2. Kurt Gödel’s Platonism: Gödel, a prominent logician, believed in an objective mathematical reality. He argued that mathematical and logical entities exist independently of our knowledge of them, and through intuition, we can perceive these truths.3. Frege’s Realism: Gottlob Frege, a foundational figure in logic, maintained that numbers and logical laws are objective, existing outside human cognition. He contended that humans discover these truths rather than create them.
4. Charles Sanders Peirce’s Semiotics: Peirce viewed logic as rooted in the social principle, suggesting that inference depends on a standpoint that, in a sense, is unlimited. He regarded logic as a normative science based on aesthetics and ethics, more fundamental than metaphysics.
5. Hegel’s Science of Logic: Georg Wilhelm Friedrich Hegel’s concept of logic differs from the ordinary sense of the term. He presents logic as a presupposition-less science that investigates the most fundamental thought-determinations, constituting the basis of philosophy.
6. Wittgenstein’s Perspective: Ludwig Wittgenstein, in his later works, suggested that logical structures are inherent in our language and forms of life. He implied that by examining our linguistic practices, we reveal the logical relationships that pre-exist our explicit recognition of them.
7. Contemporary Discussions: Modern debates continue to explore whether logic is a human construct or an intrinsic aspect of reality. Some argue that logical principles are embedded in the fabric of the universe, awaiting discovery through human inquiry.
Quantum Cryptography:
1. Bennett, C. H., & Brassard, G. (1984). “Quantum Cryptography: Public Key Distribution and Coin Tossing.” Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, pp. 175–179.
2. Shor, P. W. (1994). “Algorithms for Quantum Computation: Discrete Logarithms and Factoring.” Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134.
3. Gisin, N., Ribordy, G., Tittel, W., & Zbinden, H. (2002). “Quantum Cryptography.” Reviews of Modern Physics, 74(1), 145–195.
4. Scarani, V., Bechmann-Pasquinucci, H., Cerf, N. J., Dušek, M., Lütkenhaus, N., & Peev, M. (2009). “The Security of Practical Quantum Key Distribution.” Reviews of Modern Physics, 81(3), 1301–1350.
5. Pirandola, S., Andersen, U. L., Banchi, L., Berta, M., Bunandar, D., Colbeck, R., … & Wehner, S. (2020). “Advances in Quantum Cryptography.” Advances in Optics and Photonics, 12(4), 1012–1236.
Temporal Logic:
1. Prior, A. N. (1967). Past, Present and Future. Oxford University Press.
2. Pnueli, A. (1977). “The Temporal Logic of Programs.” Proceedings of the 18th Annual Symposium on Foundations of Computer Science, pp. 46–57.
3. Emerson, E. A. (1990). “Temporal and Modal Logic.” In Handbook of Theoretical Computer Science, Vol. B, pp. 995–1072. Elsevier.
4. Lamport, L. (1994). “The Temporal Logic of Actions.” ACM Transactions on Programming Languages and Systems, 16(3), 872–923.
5. Gabbay, D. M., Hodkinson, I., & Reynolds, M. (1994). Temporal Logic: Mathematical Foundations and Computational Aspects. Oxford University Press.
Integrating Temporal Logic in Computation:
1. Alur, R., & Henzinger, T. A. (1992). “Logics and Models of Real Time: A Survey.” In Real-Time: Theory in Practice, Lecture Notes in Computer Science, Vol. 600, pp. 74–106. Springer.
2. Huth, M., & Ryan, M. (2004). Logic in Computer Science: Modelling and Reasoning about Systems (2nd ed.). Cambridge University Press.
3. Baier, C., & Katoen, J.-P. (2008). Principles of Model Checking. MIT Press.
4. Demri, S., Goranko, V., & Lange, M. (2016). Temporal Logics in Computer Science: Finite-State Systems. Cambridge University Press.
5. Lamport, L. (2002). Specifying Systems: The TLA+ Language and Tools for Hardware and Software Engineers. Addison-Wesley.
Recent Advances and Applications:
1. Bozzio, M., Crépeau, C., Wallden, P., & Walther, P. (2024). “Quantum Cryptography Beyond Key Distribution: Theory and Experiment.” arXiv preprint arXiv:2411.08877.
2. Takagi, T. (2023). “Semantic Analysis of a Linear Temporal Extension of Quantum Logic and Its Dynamic Aspect.” ACM Transactions on Computational Logic, 24(3), 1–21.
3. Rozier, K. Y. (2019). “From Simulation to Runtime Verification and Back: Connecting Single-Run Verification Techniques.” Proceedings of the 11th Working Conference on Verified Software: Theories, Tools, and Experiments (VSTTE), Lecture Notes in Computer Science, Vol. 12031, pp. 180–192. Springer.
4. Alur, R., & Henzinger, T. A. (1994). “A Really Temporal Logic.” Journal of the ACM, 41(1), 181–204.
5. Kretschmer, W. (2023). “Founding Quantum Cryptography on Quantum Advantage, or: How to Construct Quantum Protocols from Post-Quantum Assumptions.” arXiv preprint arXiv:2409.15248.