IKS in Computational Systems Notes | B.Sc. (Computer Science) Semester 5 | Mumbai University | munotes

Contents

Module I Sastra methodology and knowledge formalization, Pingala's Chandahsastra as binary encoding and combinatorial generation, and Panini's Astadhyayi as a generative formal grammar

1. Why a Computer Science Student Reads a Śāstra 1
2. How This Paper Is Examined, and What That Means for How You Read 4
3. Śāstra: What Makes a Body of Knowledge Formal 7
4. The Sūtra Method as Compressed Symbolic Encoding 10
5. Pramāṇa: Where Knowledge Is Allowed To Come From 13
6. Pratyakṣa: Perception, and Why It Is Defined So Narrowly 16
7. Anumāna: Inference in Outline 19
8. Āgama: Testimony, and the Trusted Source as a Design Decision 22
9. Knowledge Validation and Structured Reasoning 26
10. Knowledge Representation: The Modern Name For It 29
11. Formal Specification: Saying Exactly What a System Must Do 32
12. Computational Thinking, and the Four Habits It Names 35
13. Piṅgala's Chandaḥśāstra, and the Text We Are Reading 38
14. Syllables, Laghu and Guru: Sanskrit Metre Without Sanskrit 41
15. Laghu and Guru as One Bit 44
16. Prastāra: The Table of Every Pattern 47
17. The Prastāra Rule Read as an Algorithm 51
18. Prastāra in Code 55
19. Binary Number Systems, and Exactly Where Piṅgala's Order Agrees 59
20. Saṅkhyā: Counting the Rows Without Writing Them 63
21. Binary Exponentiation: The Same Algorithm in a Modern Textbook 67
22. Uddiṣṭa: From a Pattern to Its Row Number 70
23. Naṣṭa: From a Row Number Back to the Pattern 73
24. Index Retrieval, and Proving Two Rules Are Inverses 77
25. Recursive Enumeration 80
26. Tree Structures, and the Prastāra as a Binary Tree 83
27. Meru-Prastāra: Halāyudha's Staircase 87
28. Pascal Triangle and Combinatorics 91
29. Meru-Prastāra as a Dynamic Programming Model 95
30. Lagakriyā and Adhvayoga: The Rest of the Pratyayas 99
31. Algorithmic Generation: What Piṅgala Actually Achieved 102
32. Pāṇini's Aṣṭādhyāyī, and the Text We Are Reading 105
33. The Six Kinds of Sūtra, in Vasu's Own Words 108
34. The Fourteen Śivasūtras and the Pratyāhāra 112
35. Anubandha: The Marker Letter as a Type Tag 116
36. Rule-Based Generative Structure 119
37. Meta-Rules: Paribhāṣā, and Rules About Rules 122
38. Rule Precedence: The Four Principles 125
39. Vipratiṣedha: When Two Rules Collide, the Later Wins 128
40. Context-Sensitive Operations 131
41. Asiddhatva and the Tripādī: Ordering by Blocking 134
42. Conflict Resolution Mechanisms, Collected 137
43. Formal Grammars: Alphabet, Rule, Derivation, Language 140
44. Context-Free Grammar, and Whether Pāṇini Wrote One 143
45. The Chomsky Hierarchy, and Where the Aṣṭādhyāyī Sits 147
46. Rewrite Systems 150
47. Automata Theory Foundations: The Finite Automaton 154
48. Śāstra Rule Precedence as a Deterministic Finite Rewrite System 158
49. Parsing Algorithms 164
50. Foundations of NLP, and What Pāṇinian Grammar Contributed 168
51. Pāṇini's Aṣṭādhyāyī as a Rule-Based Grammar Engine 172
52. Practice for Module I 176

Module II Nyaya logic as structured inference, Ayurvedic classification as a rule-based expert system, and Arthasastra cryptography as a secure communication model

1. Nyāya: The School, the Sūtra and the Sixteen Categories 181
2. The Four Pramāṇas of Nyāya, and Why Charaka Has Three 184
3. Anumāna: Vyāpti, and the Three Kinds of Inference 187
4. The Five-Member Syllogism 191
5. The Five Members Worked, Three Times 195
6. Five Members Against Aristotle's Three 198
7. Hetvābhāsa: The Five Fallacies of the Reason 201
8. Chala, Jāti and Nigrahasthāna: How a Debate Is Lost 205
9. Vāda, Jalpa and Vitaṇḍā: Three Kinds of Dispute 209
10. Debate Methodology as a Validation Protocol 213
11. Padārtha: The Categories of What Exists 217
12. Padārtha Ontology as a Knowledge Representation Model 221
13. Propositional Logic: The Minimum You Need 226
14. Predicate Logic, and Why Anumāna Needs It 231
15. The Five Members Written in Logical Notation 234
16. Inference Engines: Forward and Backward Chaining 237
17. Nyāya Logic as an Inference Engine 241
18. Explainable AI, and Why a Five-Member Answer Is an Explanation 246
19. Āyurveda as a Śāstra, and What This Chapter Does Not Claim 250
20. The Tridoṣa Framework 254
21. Doṣa as a Feature Vector 258
22. Prakṛti: Constitution as a Class Label 262
23. Parīkṣā: How an Examination Is Structured 265
24. Symptom to Feature Mapping 269
25. Multi-Attribute Classification 273
26. Decision Principles in Diagnosis 276
27. Decision Trees 280
28. A Decision Tree Built From the Tridoṣa Attributes 285
29. Rule-Based Systems 289
30. Expert Systems, and MYCIN as the Comparison 293
31. Feature Engineering 297
32. Multi-Class Classification, and How It Is Scored 300
33. Ayurvedic Classification as a Rule-Based Expert System 303
34. The Arthaśāstra, and Its Intelligence Apparatus 310
35. Secret Communication: What the Text Actually Says 313
36. The Royal Writs as a Message Format 316
37. Substitution Systems 319
38. Transposition Systems 323
39. Substitution and Transposition in Code 328
40. Concealment and Coded Messaging 335
41. Basic Steganography 338
42. Information Protection Mechanisms 342
43. Symmetric Encryption 345
44. Cipher Algorithms, Classical to Modern 348
45. Breaking a Classical Cipher 351
46. Arthaśāstra-Inspired Cryptography as a Symmetric Cipher System 356
47. Secure Protocol Abstraction 360
48. Foundations of Cybersecurity 363
49. The Internal Assessment: Building and Presenting the Implementation 366
50. Practice for Module II 370
51. The Whole Paper on One Page 374