Classical Sequent Calculus (LK)
for Propositional Logic
CS 245
Idea: make a proof system that manipulates assumptions as well as the formula that is being proven.
Denition 1 (Sequent)
Let and be sets of formulae. We call
a sequent.
Notation: In sequents
The Completeness of Propositional Resolution
A Simple and Constructive Proof
Jean Gallier
Department of Computer and Information Science
University of Pennsylvania
Philadelphia, PA 19104, USA
jean@saul.cis.upenn.edu
September 25, 2006
Abstract. It is well
Example Grammar
V = cfw_expr, op
= cfw_ID, +
P = cfw_expr ID,
expr expr op expr,
op +
S = expr
Top-down parsing
Algorithm 1 Generic algorithm
S
while = input do
choose any A such that = A
oracle chooses such that A P or rejects
end while
Algorithm 2 Ge
Linking Algorithm
Suppose we have les f1.merl, f2.merl, . fn.merl that we wish to link together into
one le linked.merl.
1. Concatenate code:
offset[1] = 0
for i from 1 to n:
copy code from fi.merl into the file linked.merl
offset[i+1] = offset[i]+codelen
The Halting Problem for Scheme Programs
(version of November 24, 2011)
Testing Whether a Program Halts
Some Scheme programs terminate after a nite number of steps; others do not. For example,
consider the following.
( define (loop) (loop) )
With this deni
Propositional Logic
Summary of Denitions and Main Results
CS 245, SE 212
Fall 2011
1
Syntax of Propositional Logic
Statements of propositional logic come from a formal language, denoted Lp . A formal language consists
of strings over an alphabet.
Denition
Modal Logic
Summary of Denitions and Main Results
CS 245
1
Syntax of Modal Logic
The alphabet for modal (propositional) logic is the same as for propositional logic with the addition of an
additional unary connectives 2 (called necessarily or always) and
Pseudocode 1 Printing a parse tree: printTree (node )
Input: node : root of parse tree
Output: string containing printed parse tree
ret string representing node + "\n"
if node is a non-terminal node then
for each child c of node do
ret ret + printTree (c
CS246Assignment 5, Group Project (Fall 2011)
B. Lushman
R. Ahmed
Due Date 1: Friday, November 25, 5pm
Due Date 2: Monday, December 5, 11:59pm
This project is intended to be doable by two people in two weeks. Because the
breadth of students ablilities in t
CS246Assignment 4 (Fall 2011)
B. Lushman
R. Ahmed
Due Date 1: Friday, November 11, 5pm
Due Date 2: Friday, November 18, 5pm
Questions 1a and 2a are due on Due Date 1; the remainder of the assignment is
due on Due Date 2.
Note: You must use the C+ I/O stre
CS246Assignment 3 (Fall 2011)
B. Lushman
R. Ahmed
Due Date 1: Friday, October 21, 5pm
Due Date 2: Friday, November 4, 5pm
Questions 1, 2a, and 3a are due on Due Date 1; the remainder of the assignment
is due on Due Date 2.
Note: You must use the C+ I/O st
CS246Assignment 2 (Fall 2011)
B. Lushman
R. Ahmed
Due Date 1: Friday, October 7, 5pm
Due Date 2: Friday, October 14, 5pm
Questions 1, 2, 3a, 4, 5a are due on Due Date 1; the remainder of the assignment
is due on Due Date 2.
Note: On this and subsequent as
CS246Assignment 1 (Fall 2011)
B. Lushman
R. Ahmed
Due Date 1: Friday, September 23, 5pm
Due Date 2: Friday, September 30, 5pm
Questions 1 ae and 2a are due on Due Date 1; the remainder of the assignment is
due on Due Date 2.
1. Provide a Unix command line
CS246Assignment 0
B. Lushman
R. Ahmed
Due: Wednesday, September 21, 2011, 6pm
This assignment is designed to get you familiar with the most basic aspects of working with
Unix, and with assignment submission. It is not worth any marks, but you must get 100