CSI5110 Term Project - Natural Deduction Proof Assistant

    CSI5110 Term Project
    Made by Zhiheng Yi (7475788)
    Email:zyi093@uottawa.ca

    Logical Connectives in this program:

    • Conjunction: &
    • Disjunction: v
    • Not: ~
    • Implication: =>

    This proof assistant implements 11 basic natural deduction rules from the text book, which are shown on the right panel.

    Rules patterns:

    • And Intro (&I) : p, q |- q & q
    • And Elim 1 (&E1) : p & q |- p
    • And Elim 2 (&E2) : p & q |- q
    • Or Intro 1 (vI1) : p |- p v q
    • Or Intro 2 (vI2) : p |- q v p
    • Or Elim (vE) : p v q, p => a, q => a |- a
    • Implication Intro (=>I) : (p |- q) |- p => q
    • Implication Elim (=>E) : p, p => q |- q
    • Not Intro (~I) : p => (q & ~q) |- ~p
    • Double Not Intro (~~I) : p |- ~~p
    • Double Not Elim (~~E) : ~~p |- p
    1. input: p&(qvr) ; click premise
    2. input: p ; click premise
    3. input: qvr ; click premise
    4. input: q ; click assumption
    5. input: &I 2,4 ; click conclude
    6. input: vI1 4.1,(p&r) ; click conclude
    7. input: =>I 4,4.2 ; click conclude
    8. input: r ; click assumption
    9. input: &I 2,6 ; click conclude
    10. input: vI2 6.1,(p&q) ; click conclude
    11. input: =>I 6,6.2 ; click conclude
    12. input: vE 3,5,7 ; conclude
    1. input: (p & ~q) => r ; click premise
    2. input: ~r ; click premise
    3. input: p ; click premise
    4. input: ~q ; click assumption
    5. input: &I 3,4 ; click conclud
    6. input: "=>E 4.1,1" ; click conclude
    7. input: &I 4.2,2 ; click conclude
    8. input: =>I 4,4.3 ; click conclude
    9. input: ~I 5 ; click conclude
    10. input: ~~E 6 ; click conclude