David Agler
Propositional Logic: Semantics, Part 1. Covers functions, the interpretation function, and the valuation functions for well-formed formulas.
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Propositional Logic: Semantics, Part 1 (Interpretations and Valuations)
Thnx for sharing!
When you say , each input is related to one and only one output
it seems unnecessary to add 'and only one'.
or worse it might imply the constant function.
It seems sufficient to say a function is a relationship between two sets such that each input has one output.
But I understand what you mean.
A slightly better definition might be,
in a function the number of outputs relating to a specific input is always exactly one.
If we think of general relations between two sets with arrows coming out from points in the domain set to the target set (codomain), then in a function at most one arrow can come out of each input, and there must be at least one arrow that comes out of each input (oh no, i think this is shorthand for one and only one, but it seems better to say 'at least one and at most one output')
A rough example of a function is a soda pop machine.
When you put in a dollar, the machine pops out a single soda – not two sodas.
(also we must imagine this machine is infinitely stocked, so it always pops out a soda if you place a dollar in).
great video!
Excellent, the explanation is so clear! Thanks!
When it comes to interpretation functions, i_1 and i_2 … i_n, is one of way of thinking about these interpretation functions (for simplicity) as being "the interpretation function for a specific universe"?
For example, let's say I have a premise p, "All pigs fly"
if I have i_1, which we will call "real world interpretation function", then i_1 (p) = F
if I have i_2, which we will call "fantasy world where pigs fly interpretation function", then i_2 (p) = T
Is this the correct way of thinking about different interpretation functions?
Thanks a lot!