The Reasoning Operators ⇒ and ⇔
`rArr` and `hArr` are not propositional operators
- different syntax:
is the same as
above
is a syntax
error
- so negation cannot be applied to `rArr` and
`hArr`
- different meaning of chains:
is valid for
every `x in RR`
yields
F when `x ne 3`
- different reaction to context information
We must — and can — and do — have
U`hArr`F
- `sqrt(x) = 2 hArr x=4` yields it when `x = -1`
`rArr` | F |
U | T |
|
`hArr` | F |
U | T |
F | ✓ | ✓ | ✓ |
|
F | ✓ | ✓ | – |
U | ✓ | ✓ | ✓ |
|
U | ✓ | ✓ | – |
T | – | – | ✓ |
|
T | – | – | ✓ |