First-Order Logic Formalization

Core Statements

1. All devotees are ISKCON acharyas:
∀x (Devotee(x) → ISKCONAcharya(x))

2. There exists one devotee who is Srila Prabhupada:
∃x (Devotee(x) ∧ IsSrilaPrabhupada(x))

Disjunction Forms

Inclusive Disjunction (∨)

∀x (Devotee(x) → ISKCONAcharya(x)) ∨ ∃x (Devotee(x) ∧ IsSrilaPrabhupada(x))

Exclusive Disjunction (⊕)

[∀x (Devotee(x) → ISKCONAcharya(x)) ∨ ∃x (Devotee(x) ∧ IsSrilaPrabhupada(x))]
∧
¬[∀x (Devotee(x) → ISKCONAcharya(x)) ∧ ∃x (Devotee(x) ∧ IsSrilaPrabhupada(x))]

Universal Quantifiers (∀)

#	Statement	Formula
1	All devotees are ISKCON acharyas	∀x (Devotee(x) → ISKCONAcharya(x))
2	Srila Prabhupada is the founding acharya and diksha guru	∀x (IsSrilaPrabhupada(x) → (FoundingAcharya(x) ∧ DikshaGuru(x)))
3	Only Srila Prabhupada is the founding acharya	∀x (FoundingAcharya(x) → IsSrilaPrabhupada(x))
4	Srila Prabhupada is an ISKCON acharya	∀x (IsSrilaPrabhupada(x) → ISKCONAcharya(x))
5	Exclusion rule for XOR	∀x ¬(Devotee(x) ∧ IsSrilaPrabhupada(x) ∧ ISKCONAcharya(x))

Note: The exclusive disjunction (⊕) ensures that both conditions cannot be true simultaneously.

Predicate Definitions

• Devotee(x): x is a devotee
• ISKCONAcharya(x): x is an ISKCON acharya
• IsSrilaPrabhupada(x): x is Srila Prabhupada
• FoundingAcharya(x): x is the founding acharya of ISKCON
• DikshaGuru(x): x is a diksha guru