Basic Examples (2)
Basic Examples
(2)
Convert the Lukasiewicz modus ponens axiom system to equational form:
In[35]:=
Out[35]=
{imp[imp[imp[a1,imp[b,a1]],imp[imp[imp[not[c],imp[d,not[e]]],imp[imp[c,imp[d,f]],imp[imp[e,d],imp[e,f]]]],g]],imp[h,g]]imp[a,a],imp[imp[a,a],b]b,imp[imp[a,b],b]imp[imp[b,a],a]}
———
Convert to the Hilbert–Ackermann axiom system for propositional logic, giving a function for implies:
In[36]:=
Out[36]=
{or[not[or[a1,a1]],a1]or[not[a],a],or[not[a1],or[a1,b]]or[not[a],a],or[not[or[a1,b]],or[b,a1]]or[not[a],a],or[not[or[not[a1],b]],or[not[or[c,a1]],or[c,b]]]or[not[a],a],or[not[or[not[a],a]],b]b,or[not[or[not[a],b]],b]or[not[or[not[b],a]],a]}