Logics

Logics.md

Logic

Categorical Logic

Propositional Logic

variables

• q

• r

• s

• t

operations

• Negation (~) Opposite of a statement.

  E.g., ‘it is NOT raining’

• Conjunction (&) AND

  e.g., it rains AND the sun shines

• Equivalence (≡) If and only if.

  e.g., ‘if it is raining i have my umbrella therefore If I have my umbrella it is raining’

• Implication (>) If…then

  e.g., ‘if it rains I’ll bring an umbrella’

• Disjunction (v) Or statement.

  e.g., ‘it rains OR the sun shines’

Truth Tables

Arguments

• Logically Equivalent

• Contradiction

• Consistent

• Inconsistent

• Valid

Rules of implication

Only go one way, from a couple of premises to a single conclusion

• Disjunctive Syllogism (DS)

• Hypothetical Syllogism (HS)

• Modus Ponens (MP)

• Modus Tollens (MT) Opposite of MP

• Constructive Dilemma (CD)

• Conjunction (Conj)

• Simplification (Simp) Opposite of Conj

• Addition (Add)

Rules of replacement

Only has one premise and one conclusion and can go both ways