def propositional logic: TBD
def predicate logic or first-order logic or first-order predicate logic: a formal language with precise rules of formation. just like computer programming languages(C, Java, etx) (Kunen, 2007:6) (Sakharov).
def proof :
def¹ (Kunen, 2007:6): a finite sequence of sentences
written in this language
that obey
a precisely defined rule of inference.
rules of inference = {modus ponens, ...}
def² (Montalban, 2020): an argument
that uses
logical steps
to show
that a mathematical statement
follows from certain axioms.
syntactic objects (Kunen, 2007:6):
- predicate logic sentences
- formal proofs
def second-order logic: TBD
def higher-order logic: TBD
def: the formal mathematical study of the methods, structure and validity of mathematical deduction and proof (Weisstein).
investigates and classifies the structure of sentences using: - formal systems of inference - analysis/study of arguments in natural language (Wikipedia)
- Weisstein, Eric W. "Logic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Logic.html
- Kunen, K. 2007. The Foundations of Mathematics.
- Sakharov, A. "First-Order Logic." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/First-OrderLogic.html.
- Montalban, A. 2020. Math 135 -- Intro to Set Theory. https://www.youtube.com/playlist?list=PLjJhPCaCziSQyON7NLc8Ac8ibdm6_iDQf
Q: Question for later research
MYINC: My Insight/Conjecture [Could Be Unoriginal/False and Likely Is]
Disclaimer: This is an ongoing and incomplete project to unpack these concepts and serve as my distributed memory.