Objects, properties and relations added onto propositional logic. Allows for making statements about what is true/false for some, all or no objects

First-order logic

Propositions and connectives are used to make compound propositions. One can make deductions and proofs drawing from the structure of propositions

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A declarative statement that is either true or false

Propositions (mathematics)

University of Michigan EECS 203 Lecture Notes

- Two parallel lines on a plane have a point in common : (FALSE)

- Ann Arbor is the capital of America : (FALSE)

- 2 + 3 + 5 = 10 : (TRUE)

Examples of propositions

Propositional Logic

Built from multiple propositions using logical operators to connect the propositions

Compound proposition

If the proposition is not a contradiction then it is satisfiable, otherwise it is not.

How can we know if a proposition is satisfiable?

If two compound propositions have the same truth table they are logically equivalent (p $$\equiv$$ q).
- ((p $$\rightarrow$$ q) $$\land$$ (q $$\rightarrow$$ p) $$\equiv$$ p $$\leftrightarrow$$ q is a tautology)

Logically Equivalent

A proposition that is always false (e.g. $$\lnot$$ p $$\land$$ p)

Contradiction (propositions)

A proposition that is always true (e.g. $$\lnot$$ p $$\lor$$ p)

Tautology (propositions)

Axioms (propositions)

A chain of logical deductions that leads to a proposition form an original (base) set of axioms.

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