Formal logic

Formal logic. About deductive systems from axioms.

Deductive system or formal system. From axioms equipped with rules of inference come up to theorems, and so on.

Complete formal system. A deductive system is complete when all its statements (theorems, corollaries, and so on) are derivable from axioms and rules.

Inconsistent formal system. A deductive system is inconsistent when exists contradictory theorems (A and no A).

Consistent Complete formal system.

Are the "proofs by contradiction" weaker than other proofs?

Paraconsistent logic

Syllogistic logic is a kind of logic in which the fundamental elements are terms, and arguments are evaluated depending on how the terms are arranged in the argument.

Modal logic is a kind of logic that involves such concepts as a possibility, necessity, belief, and doubt.

Entails

Implies (⇒ ) vs. Entails (⊨ ) vs. Provable (⊢ )

double turnstile.

⊢ Provable

Nederpelt, Rob (2004). "Chapter 7: Strengthening and weakening". Logical Reasoning: A First Course (3rd revised ed.). King's College Publications. p. 62. ISBN 0-9543006-7-X.

Open Logic Project, First-order logic (p.7). Accessed 4 January 2022.