Introduction to Symbolic Logic
Department of Philosophy
Spring, 2016
University of California, Davis
Assignment 4 (Covers Chapter 4)
1.
Explicate in terms of open and/or closed truth-trees:
a.
Truth-functional consistency*
b.
Truth-functional truth
c.
Tru
ASSIGNMENT 5
1. Define
a. Inconsistency in SD
b. Equivalence in SD
2. Construct derivations in SD that establish parts a and b below.
a. The following sentence is a theorem in SD:
( A B) (A B)
b. The following claim holds:
[( A & B) (A & B)] (A B)
3. Show
ASSIGNMENT 4 ANSWERS
1. a. A sentence P of SL is truth-functionally true if and only if the set cfw_ P has a closed truthtree.
b. An argument of SL is truth-functionally valid if and only if the set consisting of the premises
and the negation of the concl
ASSIGNMENT 3 ANSWERS
1. a. Sentences P and Q of SL are truth-functionally equivalent if and only if there is no truthvalue assignment on which P and Q have different truth-values.
b. An argument of SL is truth-functionally valid if and only if there is no
ASSIGNMENT 2 ANSWERS
1. a. If Mary is here then Mary will tell us how to set the lenses.
MT
b. It is not the case that both Bill will be able to come today and Rob
will be able to come today.
(B & R)
c. Both if food prices decline then wholesale costs de
Chapter
1
Basic Notions of Logic
1.1 Background
Sentential
logic: this is the branch of
symbolic deductive logic that takes
sentences as the fundamental unit of logical
analysis.
Predicate logic: this is the branch of
symbolic deductive logic that takes
Chapter
3
Sentential Logic:
Semantics
3.1 Truth-Value Assignments and
Truth-Tables for Sentences
We shall develop formal tests for truth-functional
versions of logical concepts:
i) truth-functional truth, falsity, and
indeterminacy
ii) truth-functional co
Chapter
5
Sentential Logic:
Derivations
5.1 The Derivation System SD
When evaluating an argument we often try to
show that its conclusion can be deduced or
derived from its premises.
Semantics is concerned with the interpretation of
a language, i.e., with
Chapter 4
Sentential Logic:
Truth-Trees
4.1 The Truth-Tree Method
In Chapter 3 we saw that the semantic
concepts of sentential logic can be
explicated in terms of truth-functional
consistency.
In this Chapter we provide an additional
method, the truth-tr
Chapter
2
SL: Symbolization and
Syntax
2.1 Symbolization and TruthFunctional Connectives
SL: branch of symbolic deductive logic in which
sentences are the basic units of logical analysis.
Recall: we are dealing only with sentences that
have truth-values,
ASSIGNMENT 1 ANSWERS
1. a. An argumentis a set of sentences one of which (the conclusion) is taken to be supported by
the remaining sentences (the premises).
b. A sentence is logically falseif and only if it is not possible for the sentence to be true.
c.
ASSIGNMENT 5 ANSWERS
1. a. A set of sentences of SL is inconsistent in SD if and only if a sentence P and its negation
P are derivable in SD from .
b. Sentences P and Q of SL are equivalent in SD if and only if Q is derivable in SD from cfw_P and P
is de
Philosophy 12
INTRODUCTION TO SYMBOLIC LOGIC
Winter 2017
Homework 1
1. Define the following: (2 pts. each)
a. Argument: an argument is a series of statements typically used to
persuade someone of something or to present reasons for accepting a
conclusion.
Introduction to Symbolic Logic
Department of Philosophy
Spring 2016
University of California, Davis
Assignment 2 Solutions (The Logic Book, Chapter 2)
1.
Give a truth-functional paraphrase of each of the following. Then symbolize each
paraphrase in SL, be