Post by Eugene 2.0 on Aug 31, 2022 7:38:59 GMT
According to the implicit rule in Predicate Logic:
1. ∀х¹, х², х³... хⁿ(Р1х¹х²х³... хⁿ) (instantiation х¹)
2. ∀х², х³... хⁿ(Р2х²х³... хⁿ) (instantiation х²)
3. ∀х³... хⁿ(Р3х³... хⁿ) (instantiation х³)
...
N. ∀хⁿ(Рnхⁿ) (instantiation хⁿ)
The same is for:
1. ∃х¹, х², х³... хⁿ(Р1х¹х²х³... хⁿ) (instantiation х¹)
2. ∃х², х³... хⁿ(Р2х²х³... хⁿ) (instantiation х²)
3. ∃х³... хⁿ(Р3х³... хⁿ) (instantiation х³)
...
N. ∃хⁿ(Рnхⁿ) (instantiation хⁿ)
Any property ∀х(Рх) or ∃х(Рх) is a function of instantiation of the plural predicates, or, shortly, is a union relation to the other atoms (variables) within the system of relations.
This is a quite interesting feature that demonstrate that any property is just an element of the system of relations, or that a proepris defined only within a system of relations.
1. ∀х¹, х², х³... хⁿ(Р1х¹х²х³... хⁿ) (instantiation х¹)
2. ∀х², х³... хⁿ(Р2х²х³... хⁿ) (instantiation х²)
3. ∀х³... хⁿ(Р3х³... хⁿ) (instantiation х³)
...
N. ∀хⁿ(Рnхⁿ) (instantiation хⁿ)
The same is for:
1. ∃х¹, х², х³... хⁿ(Р1х¹х²х³... хⁿ) (instantiation х¹)
2. ∃х², х³... хⁿ(Р2х²х³... хⁿ) (instantiation х²)
3. ∃х³... хⁿ(Р3х³... хⁿ) (instantiation х³)
...
N. ∃хⁿ(Рnхⁿ) (instantiation хⁿ)
Any property ∀х(Рх) or ∃х(Рх) is a function of instantiation of the plural predicates, or, shortly, is a union relation to the other atoms (variables) within the system of relations.
This is a quite interesting feature that demonstrate that any property is just an element of the system of relations, or that a proepris defined only within a system of relations.