Re: completeness what is it exactly

Ahh

At least two different kinds of completeness.

In this post I stick to (modal) propositional logic

A (Uppercase) is a well formed formula
p (lowercase) is a propositional variable




1 the opposite of soundness

|= A -> |-A

if (using a truthtable, or other mechanical means) a formula is always
true then that formula is provable .

also
if a formula A is unsatisfiable (never true) then |- ~A

(or is this a step to far)


2 negation completeness

All well formed formula's are (provable) true or false.

for every A |-A or |- ~A

this is more complicated.

for this
all propositional variables need to have a fixed truth value
(otherwise neither |-p or |- ~p can be deduced)


am i forgetting something?

On Jul 16, 10:35 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

That is a DIFFERENT sense of completeness. We're not talking about
that sense of completeness. Also, it does not make sense to talk about
a formula being true if it is not known that the formula is a
sentence. Open formulas are not true or false in a model; rather open
formulas are satifisfied or not satisified in a model with an
assignment to the variables.


My question was about completeness in any sense.


.

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