THE LOGIC BOOK, 4TH EDITION: CHAPTER FIVE: SL DERIVATIONS Whales breathe by lungs and whales are warm-blooded. If whales breathe by lungs, then whales are not fish. Whales are warm-blooded and whales are not fish. 1. Whales breathe by lungs and whales are
UNIT 1
REASON AND ARGUMENT
1.1 WHAT IS MODERN SYMBOLIC LOGIC?
Logic.
The Study & Evaluation of Reasoning & Argument
An argument probably seems logical if it look likes the conclusion
must be true, based on what you are told is the case and what you
alread
PHL 245: Second Practice Test Answers
A1: a advertises. D1: a has diamonds on it. G1: a is a restaurant M2: a is getting married to b. a0: Tiffany's d1: the fianc of a 1. B1: E1: H1: N2: a is a business a is an engagement ring. a stays in business. a is m
UNIVERSITY OF TORONTO
Faculty of Arts and Science
EXAMINATION APRIL 2013
PHL 245 HIS
L0101 - Niko Scharer
Duration - 3 hours
Examination Aid: Sheet with rules (provided)
Last Name
First Name
Student Number
Answer all questions on the exam paper.
WHAT IS ON THE EXAM? Anything we have studied can be on the exam. Derivations: approximately 35% of the exam. Focus on questions from the second half of the course. PANIC ATTACKS A VICIOUS CIRCLE When you don't see the solution, you panic. When you panic,
University of Toronto PHL 245 Modern Symbolic Logic Staple this page with your answers. St. # First name:
Test 2 Instructor Sorin Bangu
August 4th, 2005 - LM 159 45 minutes (8:10 8:55 PM) Worth 30% of the final grade. Answer all questions. Rules provided.
PHL245: Truth Tables Handout
Recall our definition of validity:
an argument is valid if and only if the conclusion is true if the premises are true
We used derivations as one test for validity. By showing
The Basic Grammar of SL
1
The Alphabet
The alphabet of SL consists of the following symbols:
1. Sentence Letters: P, Q, R, S. . . X, Y, Z and P1 etc.
2.
3.
4.
5.
6.
7. and (,).
A sequence of SL is any string of characters from the alphabet.
2
Useful
PHLB50 Unit 3 Part 2
SL Derivations Contd
0. Re-cap
Derivations are one of the basic techniques we will use for testing validity.
A derivation is a special way of representing an argument we start by
specifying our premises and which conclusion we want to
Modern Symbolic Logic
Week II: Sentential Logic - Getting Started
Kevin Kuhl
Department of Philosophy
University of Toronto
Announcements
Assignment 1: Rescheduled - details to follow on
Blackboard (still setting up online database for Logic2010)
Logic2
Unit 3 Part 2: Derivation Exercises
Derivations with AND, OR and BICONDITIONAL
NOTE: there are 3 sections. Make sure you do a good number from each section. (In
each section, the first ones tend to be easier than the later ones.)
SECTION 1: Construct deri
Sentential Derivation Problems
BASIC DERIVATION PROBLEMS NO SUBDERIVATIONS
These questions just use MP, MT, DN and R. They require no subderivations.
They are meant to help those who want more exercises to get used to the basic rules and derivation types.
UNIT 5 Part 1
SYMBOLIZATION: PREDICATES AND QUANTIFIERS
5.1: THE LOGIC OF SUB-SENTENTIAL RELATIONS
Consider this argument:
All humans are mortal.
Socrates is human.
_
Socrates is mortal.
It is clearly a valid argument, but if we try to symbolize it using
To Apply
Application information is available online at www.bsmeducation.com.
Early application is encouraged.
Costs
BSME tuition is lower than tuition at many American colleges and universities.
Furthermore, Budapest has a modest cost of living. Current
Handout for PHL245: Predicate Logic and Symbolizations
Exercise:
Symbolize the following argument in SL
All mental states are brains states.
Pain is a mental state.
All brain states have locations.
Pain is a brain state._
Therefore, pain has a location.
I
Last Name _
First Name _
PHL245H1Y (Spring/Summer 2015)
Midterm 1: Tuesday, June 30, 2012
Aids: List of rules and theorems (provided by instructor).
NO OTHER AIDS ALLOWED
Instructions: READ CAREFULLY BEFORE THE TEST
This is a somewhat lengthy test, so
Deriving a Tough Theorem!
Part 1
Lets take a closer look at the theorem that was our participation task.
(PQ) v (QP)
As I said, its a tough one! When we think about our initial derivation techniques,
we have two options for starting a derivation whe
Modern Symbolic Logic Week 2
Kevin Kuhl
Department of Philosophy
University of Toronto
Outline
1
Symbolizations in Sentential Logic
Complex Sentences
Consider:
Either Kevin is 6ft tall or Kevin is not 6ft tall
How does the Either.or. contribute to the mea
CSC384. Propositional Logic
February 16, 2016
1. Using Truth Tables, are the following statements equivalent?
(a) > and
2. Using Truth Table, is the following logical expression correct?
(a) (x S1 ) (x S2 ) > S1 S2
(b) (X (Y X) > Y
3. If a triangle is eq
UNIT 7
INTERPRETATIONS AND MODELS: SEMANTICS FOR PREDICATE LOGIC
7.3 EG1
a)
On the interpretations below, is the following true or false?
~Fa x(Fx G(xa)
Universe: positive integers
F1: a is a multiple of 4.
a0: 2
G2: a is divisible by b
The first conjunct
DERIVATIONS WITH AND, OR AND BICONDITIONAL
NATURAL DEDUCTION
Part 2
3.11 Derivations with AND, OR and BICONDITIONAL
So far weve learned how to derive any sentence from any set of sentences that entails it, provided that
the sentences are symbolized using
S 2.9 E1a
U: Determinism is true. V: I am free.
Determinism is true but I am free.
Basic Page 1
S 2.9 E1c
U: Determinism is true.
V: I am free.
Determinism is false, however I am not free.
Basic Page 2
S 2.9 E1e
P: I exist.
I exist if I think.
Basic Page
Modern Symbolic Logic
PHL245H1F
Instructor:
Alex Koo
alex.koo@utoronto.ca
Jackman Humanities Building, 170 St. George St., Room 512
Lectures:
M2-4 in MS 2158, W2-3 in PB B150
Office Hours:
Wednesday 12-1 or by appointment
Course Description:
Modern symbol
Scharer 4.4 EG1
Tautology, Contradiction, or Contingent
(~PQ)(PQ)
P
Q
(~
P
Q)
(P
Q)
T
T
F
T
T
T
T
T
T
T
T
F
F
T
F
F
T
T
F
F
F
T
T
F
T
T
T
F
T
T
F
F
T
F
T
F
T
F
T
F
Truth Tables Page 1
Scharer 4.4 EG2 c
Consistent, Equivalent, or Neither
cfw_(~PQ), (QP)
P
S 2.10 E3e
R: Robin is present.
S: Sonia is present.
T: The meeting will take place.
The meeting will take place only if both Robin and Sonia
are present.
Medium Page 1
S 2.10 E3f
P: Paul is present.
U: The meeting will start on time.
W: Somebody is going
Scharer 4.5 EG1
Not a contradiction
Shortened Truth Tables Page 1
Scharer 4.5 EG2
Not a tautology
Shortened Truth Tables Page 2
Old Test 2015F 2
September 15, 2016
9:35 AM
Construct a shortened truth-table that
demonstrates that the following argument
i
For questions 1-3, symbolize the English sentence using the abbreviation scheme provided for each
question.
1.
Unless drinking coffee is necessary for Tom to be alert, he will pass the test even though he
neither studied nor slept. (4)
P: Tom drinks coffe
Derivation Types:
Direct Derivation (DD or dd)
Conditional Derivation (CD or cd)
Indirect Derivation (ID or id)
10 Basic Rules for Sentential Logic:
Modus Ponens (MP or mp)
( )
Double Negation (DN or dn)
~
~
Simplification (S/SL/SR or s/sl/sr)
Addition
1)
Not all soccer players try hard even though nobody likes losing. (3)
A: a is a person. C: a is a soccer player. D: a tries hard. F: a likes losing.
~x(CxDx) ~x(AxFx)
x(Cx~Dx)
x(Ax~Fx)
2)
Amongst amusement parks and zoos, those that have lions are popul
1.
Consider the following argument:
If an argument is valid, then it has a true conclusion.
Arguments with a contradiction in the premises are valid.
Therefore, arguments with a contradiction in the premises have a true conclusion.
a)
Is the argument vali
CSC363 Tutorial 5
Reductions
Tutor: Assimakis Kattis
Scribe: Robert Robere
February 9, 2016
In this tutorial we classified the following two languages with respect to the computability
classes D, SD, coSD:
EMPTY = cfw_hM i | M is a TM that does not accept