Chapter 2
Natural Deduction
Ich wollte zunchst einmal einen Formalismus aufstellen, der dem
a
wirklichen Schlieen mglichst nahe kommt. So ergab sich ein
o
,Kalkl des natrlichen Schlieens.1
u
u
Gerhard Gentzen
Untersuchungen uber das logische Schlieen [Ge
Chapter 3
Sequent Calculus
In this chapter we develop the sequent calculus as a formal system for proof
search in natural deduction. The sequent calculus was originally introduced
by Gentzen [Gen35], primarily as a technical device for proving consistency
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Draft of March 24, 2004
Chapter 4
Focused Derivations
The sequent calculus as presented in the previous chapter is an excellent foundation for proof search strategies, but it is not yet practical. For a typical sequent
there are many choices, such as w
Chapter 1
Introduction
Logic is a science studying the principles of reasoning and valid inference. Automated deduction is concerned with the mechanization of formal reasoning,
following the laws of logic. The roots of the eld go back to the end of the
la
Assignment 2
1
15-815 Automated Theorem Proving
Frank Pfenning, Spring 2004
Out Jan 29, due Feb 5
Assignment 2: A Certifying Decision Procedure
In this assignment you may work by yourself or with a partner. Library code
and signatures can be found at
http
5-815 Automated Theorem Proving
Assignment 1: Natural Deduction and
Sequent Calculus
The assignment is worth 80 pts, due Thu Jan 29
Reading: Chs. 2.1 and 3.3
Code: none
Problem 1: Deduction (35 pts)
For each of the following propositions, give proofs in t
Assignment 5
1
15-815 Automated Theorem Proving
Frank Pfenning, Spring 2004
Out Mar 3, due March 18
80 pts
Assignment 5: Quantication
In this assignment we explore the laws of quantication in rst-order logic and
logical translations.
Question 1 (10 pts):