4. Languages on Turing machine
Turing machine
Turing
tape
Computer
Recursive
function
Kleene
Loop
C language
lambda calculus
Church
recursion
Haskell
National
deduction
Gentzen
Mathematical
recursion
Proof
Mathematical recursion
Proof
Based on natural number. We can
invoke recursive functions endlessly.
I don’t know about
flag and loop
A chain of clauses logically
connected from
Axioms.
5. Background: Resolution Principle applied
Hilbert System
Sequent calculus
Proof Theory
Gentzen System
Tableau Calculus
Resolution Principle
Applied to
computation
6. OTTER’s basic methodology
Binary resolution
Modus potens, one by one
resolution
Hyper resolution
Nucleus and satellite, All at one
Demoulation
Term rewriting
modulation
Paramodulation
Equational reasoning
list(usable).
-Greek(x) | Person(x).
-Person(x) | Mortal(x).
end_of_list.
list(sos).
Greek(sorates).
end_of_list.
|list(usable).
-Sibling(x,y) | Brother(x,y) | Sister(x,y).
end_of_list.
list(sos).
Sibling(pat, ray) | Cousin(pat, ray).
end_of_list.
list(usable).
-A(x,y) | A(x, S(y)).
end_of_list.
list(demodulators).
S(S(x)) = x.
end_of_list.
list(usable).
(a=b) | (c=d).
end_of_list.
list(sos).
P(a) | Q(n, f(c,g(d))).
end_of_list.