Essay: Different logical systems
The logical analyses applied are syntactic which proofs are, the logic here is inferred in this analysis different logical systems like those of axiomatic, natural deduction are used.
In any logical reflection an argument can be deductively valid if the premises are true and the conclusion is logical, at the same time the argument may be deductively valid if the premises are false. Deductively it is more than making deductive conclusions that are based on true premises and conclusions, these deductions must also be sound. Consider this premise; all male are living, all things that live can give birth, therefore, all male can give birth. While the premises may be true, the conclusion is false, it is not logically possible. Moreover a deductive logical statement must be logically sound.
An argument must be deductively sound if and only if the argument is deductively valid and all the premises are true. An argument that is deductively unsound is not valid, if the argument has many false premises then it is deductively false Ganter and Mineau (2009).