Truth, Deduction,
Computation
Introduction
Vlad Patryshev
SCU
2013
http:/tinyurl.com/coen260-1
Variety of Interpretations
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Modern Europe
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Truth, Deduction,
Computation
Lecture 2
First Order Languages
Vlad Patryshev
SCU
2013
In chapter 1 of LPL book.
the world consists of existing objects
some of them have names
some of them have more than one name
objects can participate in n-ary
relati
Chapter 7
The Application Layer
DNS The Domain Name System
The DNS Name Space Resource Records Name Servers
The DNS Name Space
A portion of the Internet domain name space.
Resource Records
The principal DNS resource records types.
Resource Records (2)
A
Chapter 8
Network Security
Cryptography
Introduction to Cryptography
Substitution Ciphers
Transposition Ciphers
One-Time Pads
Two Fundamental Cryptographic Principles
Need for Security
Some people who cause security problems and why.
An Introduction to Cr
Physical Layer
The physical layer deals with transporting bits between two machines. How do we communicate 0's and 1's across a medium? By varying some sort of physical property such as voltage or current. Moreover, by representing the property as a funct
Chapter 6
The Transport Layer
The Transport Service
Services Provided to the Upper Layers Transport Service Primitives Berkeley Sockets An Example of Socket Programming:
An Internet File Server
Services Provided to the Upper Layers
The network, transpor
Chapter 5
The Network Layer
Network Layer Design Isues
Store-and-Forward Packet Switching Services Provided to the Transport Layer Implementation of Connectionless Service Implementation of Connection-Oriented Service Comparison of Virtual-Circuit and Da
Chapter 3
The Data Link Layer
Data Link Layer Design Issues
Services Provided to the Network Layer
Framing
Error Control
Flow Control
Functions of the Data Link Layer
Provide service interface to the network layer
Dealing with transmission errors
Regulati
Chapter 2
The Physical Layer
The Theoretical Basis for Data
Communication
Fourier Analysis
Bandwidth-Limited Signals
Maximum Data Rate of a Channel
Bandwidth-Limited Signals
A binary signal and its root-mean-square Fourier amplitudes.
(b) (c) Successive a
Chapter 4
The Medium Access Control
Sublayer
The Channel Allocation Problem
Static Channel Allocation in LANs and MANs
Dynamic Channel Allocation in LANs and MANs
Dynamic Channel Allocation in LANs and MANs
1.
Station Model.
2.
Single Channel Assumption.
Chapter 19: Hints and Selected Solutions
Section 19.2 (page 531)
19.1 1. cLarger(a,x) has date of birth = 1. This constant is also called c1 later in the exercise. 2. cLarger(c1 ,x) has date of birth = 2. This constant is also called c2 later in the exerc
Chapter 17: Hints and Selected Solutions
Section 17.1 (page 470)
17.1 Here for your convenience is the truth table (P, Q, R): P t t t t f f f f Q t t f f t t f f R t f t f t f t f (P, Q, R)
T T F F T F T F
This can be nicely captured as follows: h(P, Q, R
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Chapter 18: Hints and Selected Solutions
Section 18.1 (page 498)
18.2 1. This is an allowable change. The language in question does not have any position predicates, so the model for the original world and the modied world are identical. 4. If we make the
Chapter 16: Hints and Selected Solutions
Section 16.1 (page 449)
16.3 You are asked to give two distinct derivations of the ambig-w A1 A2 A2 . Here is one. You should be able to think of another. By the basis clause, A2is an ambig-w. Hence, by the inducti
Chapter 8: Hints and Selected Solutions
Section 8.1 (page 203)
8.1 1. Arming the consequent is invalid. 4. Weakening the Antecedent invalid. 7. Constructive Dilemma is valid. 8.4 Here is an informal proof of the argument: The unicorn, if horned, is elusiv
Chapter 12: Hints and Selected Solutions
Section 12.3 (page 327)
12.1 The argument is valid and the proof is a good one. In the following, we repeat the proof, but being explicit about the proof methods being used. x [(Brillig(x) Tove(x) (Mimsy(x) Gyre(x)
Chapter 14: Hints and Selected Solutions
Section 14.1 (page 371)
14.1 One way to do the You Try It is shown in the two worlds below. You
should submit dierent looking worlds.
1
14.2
1. There is exactly one tove.
4. All toves are identical (=).
14.3
1. xy
Chapter 15: Hints and Selected Solutions
Section 15.1 (page 411)
15.1 Hint: The exercise is to test your understanding of the axiom of extensionality. According to that axiom, sets are identical if and only if they have the same members, regardless of how
Chapter 13: Hints and Selected Solutions
Section 13.1 (page 346)
13.2 Hint (ll in the supports):
13.7 Hint:
1
Section 13.2 (page 350)
13.11 A counterexample:
13.14 Hint:
2
Section 13.3 (page 337)
13.20 The following proof formalizes the informal proof we
Chapter 11: Hints and Selected Solutions
Section 11.1 (page 291)
11.4 1. xy [(Small(x) Large(y) FrontOf(x, y) 4. xy (Tet(x) Tet(y) SameCol(x, y) 7. xy (Tet(x) Tet(y) x = y SameSize(x, y) 11.7 2. Some of the parties are not lonely. 4. There is a lonely par
Chapter 9: Hints and Selected Solutions
Section 9.3 (page 234)
9.1 The rst four sentences:
9.2 Here is one possible way of xing up the odd numbered sentences:
1
Section 9.4 (page 238)
9.7 According to the formation rules, quantiers can combine with variab
Chapter 10: Hints and Selected Solutions
Section 10.1 (page 264)
10.1 The following lls in some of the rows for you. Be sure you understand these. Annotated sentence Truth-functional form 1. 4. 7. 10 x (x = x)A x (Cube(x) Small(x)A x (Small(x) Cube(x)B [z
Chapter 7: Hints and Selected Solutions
Section 7.2 (page 183)
7.2 The truth table for this Exercise is shown below. Since all the entries
in the main columns for each sentence are the same, row by row, the
sentences are tautologically equivalent.
7.5 The
Chapter 3: Hints and Selected Solutions
Section 3.1 (page 70)
3.2 1. True 4. To see why this sentence is false, you may need to switch to the 2D view, since the label f is barely visible in the 3D view. 5. This is false since it claims that a and b are no
Chapter 6: Hints and Selected Solutions
Section 6.2 (page 154)
6.2
6.4
1
6.9
Section 6.3 (page 161)
6.10 One of many possible counterexamples to the following argument is shown below. Cube(a) Cube(b) (Cube(c) Cube(b) Cube(c) You should turn in a dierent c
Chapter 2: Hints and Selected Solutions
Section 2.1 (page 44)
2.1 Sound in Socrates World? Yes Sound in Wittgensteins World? No
Argument 1. 2. 3. 4. 5. 6. 7. 8. 2.2 1.
Valid? Yes
Yes
Yes
No
No
No
No
Anyone who wins an academy award is famous Meryl Streep
Chapter 4: Hints and Selected Solutions
Section 4.1 (page 104)
4.2 1. The truth table for (A B) (A B) is shown in Figure ?. Since all the entries under the main connective () are T, it shows that the sentence is a tautology.
4.5 The truth table is shown b
Chapter 5: Hints and Selected Solutions
Section 5.1 (page 131)
5.1 The pattern From P Q and P, infer Q is valid. If P Q is true, then by the truth table for , at least one of P or Q must be true. But if P is true, then by the truth table for, P must be fa