To indicate the arity of the main connective in each discharged assumption.

To indicate which assumptions are discharged, and which are still open.

To indicate which assumptions are discharged by which rules.

To count how many assumptions have been discharged at each stage.

NM has one less rule than NJ, and NK has one more rule than NJ

NM has one more rule than NJ, and NK has one more rule than NM

NM has one less rule than NJ, and NK has one more rule than NM

To show that an argument is invalid via models, you need to consider every model; to show that an argument is valid via proofs, you need to consider every proof.

Model-theoretic methods don't make use of structures, while proof-theoretic methods do.

It just takes one model to show that an argument is invalid, and it just takes one proof to show that an argument is valid.

It just takes one proof to show that an argument is invalid, and it just takes one model to show that an argument is valid.

The logic that validates no arguments at all

The logic that validates every argument with an odd number of premises, and invalidates all other arguments.

The logic that validates every argument with more than five premises, and invalidates all other arguments.

Classical logic

The logic that validates every argument

K3

Classical logic

FDRM

LP

FDE

There isn't a difference; they're two different names for the same matrix.

K3's negation takes T to F, but LP's negation takes T to *.

They use the same structure, but have different designated values.

They use the same designated values, but in different structures.

K3's negation takes * to F, but LP's negation takes * to *.

*

T

F