Exercise 2.7 Nonstandard Interpretations
- Is the formula "Adjoins(b,f)" using the Geography nonstandard interpretation of
the TARSKI Blocks language true or false in the Canada geography world? F
- Is the formula "BackOf(d,e)BackOf(e,d)" using the Geogra
Philosophy 220A
Symbolic Logic I
Instructor: Richard Johns
Answers to Problem Set 3
Total: 39 marks
3.21
[1 mark each]
1
2.
(ii)
(i) Tautology, need whole table. [2 marks for table, 1 for the verdict]
Not a tautology. Row 1 is sufficient. [2 marks for tab
Philosophy 220A
Symbolic Logic I
Answers to Problem Set 5
Total: 45 marks
6.14
[5 marks]
1
6.20
[5 marks]
6.25
[5 marks]
2
6.31
[5 marks]
The argument is invalid, as the following world shows. (In this world b is a small dodec, but it
could instead be a m
Exercise 2.6 NUMBERS Logic Language
- In the world of counting numbers (the Numbers World), there is a largest
number. F
- In the world of counting numbers (the Numbers World), if one number is less
than a second, then the second must be greater than or b
Section 9: Tableau truth-functional strategies
In the previous section of this unit you learned about the truth-functional operator decomposition rules for trees. In this section
we'll look at strategies for using these rules. These strategies tell you wh
Systematic Procedure
The systematic procedure in tableau states an order in which tableau
decomposition rules should be used. It is to be used along with the hints
or heuristics about the order in which tableau decomposition rules should
be used.
Here is
Question 1
2 out of 2 points
Is the following formula in the TARSKI blocks language a logical truth, a
logical falsehood, or a contingent formula?
Formula: a=b
In this question you have to select all the correct answers and none of the incorrect ones
to
Philosophy 220A
Symbolic Logic I
Instructor: Richard Johns
Problem Set 5
Submit answers to the following questions in class on Thursday, October 15.
Warning:
At least one of the arguments in these exercises is invalid, so that all attempts at
proof will b
Section 2: Tarski Blocks artificial language
propositional
In this section you will learn about some parts of the Tarski Blocks artificial logic language. You will be learning
about the meaning or interpretation of the nonlogical symbols in this language
Section 1: What is symbolic logic?
This course studies symbolic logic. But what is symbolic logic? And how will you study it in this course?
Here are three different definitions of what logic is. They all come from different logic textbooks.
Logic and Con
Section 2: Course mechanics
In this section you'll learn something about how the course runs.
The course textbook is Barker-Plummer et al, Language Proof and Logic 2nd edn.
One computer program for doing exercises is available for download inside the UBC
Symbol
Meaning
Notes
Operators (Connectives)
negation (NOT)
The tilde ( ) is also often used.
conjunction (AND)
The ampersand ( & ) or dot ( ) are also often used
disjunction (OR)
This is the inclusive disjunction, equivalent to and/o
exclusive
disjunctio
Section 1: Introduction and learning goals for
unit
This unit will introduce you to the artificial languages for logic used in this course.
Suppose we want to decide whether a set of beliefs or statements is consistent. You should remember from the first
Section 4: Informal logical concepts
This section will introduce you to some logical concepts or notions. We'll explain how they apply in a natural
language like English. In a later section we'll explain how the logical concepts apply in the artificial la
Cemmen English Examples Tarski BIDdS Language Symbolizatien
All All tribes are small
Every 'jUbE i5 Ema" 'r-xCulJeiixji xSmall (3)
Eath tribe is small
Seme Seme tribes are small
At least one tiube is small Elxi:Cube(:-c:i rename);
There eaisb a tribe whic
Section 3: Tarski Blocks and other worlds
This section will introduce you to Tarski Blocks worlds, Geneaology worlds, and Numbers worlds. We use these
throughout the course. We'll use Tarski Blocks worlds in the next section of this unit to help explain s
Section 3: Tarski Blocks artificial language
quantificational
In this section you will learn about more parts of the Tarski or Blocks artificial logic language. There is nothing
more to learn about the meaning or interpretation of the nonlogical symbols i
Tree assumes invalidity by setting up a counterargument, closing off all branches means
argument is valid (implying a contradiction in the counterargument)
Closed Branch:
A branch containing a proposition P and its literal negation P.
Open Branch:
A branc
Section 5: Genealogy artificial language
In this section you will learn about another interpreted artificial logic language. This is the Geneaology artificial
language. You will be learning about the meaning or interpretation of the nonlogic symbols in th
Section 2: Arguments and validity
In this section we'll look at the concept of validity for arguments or reasonings. Before reading the material here it might be a
good idea to review the Learning Modules Unit 1 section 4 on the informal concept of validi
Section 2: Tarski Blocks propositional language translation
This section deals with translation or symbolization into the part of the Tarski Blocks language using the truth-functional logic
operators and identity. Nothing in this section will use the quan
Section 5: Numbers artificial language
We'll now look at the grammar or syntax for the Numbers language. The grammar breakdown parsing rules for this language will
look almost the same as those for the Tarski Blocks and Geneaology languages. The category
Section 7: Free variables and instantiation
In this section you will learn about the ideas of free occurrences of variables in a wff and instantiation of a wff. The idea of
instantiation is used in Units 7 and 8 of the course. While we don't use the idea
Question 1 2 out of 2 points
What rule name goes in the justification for line 11?
Selected Answer:
h.
INTRO
Question 2 0 out of 2 points
What rule name goes in the justification for line 18?
Selected Answer:
f. INTRO
Question 3 0 out of 2 points
What rul
Section 3: Tarski Blocks and other worlds
This section will introduce you to Tarski Blocks worlds, Geneaology worlds, and Numbers worlds. We use these throughout the course. We'll use Tarski Blocks worlds in the next section of this unit to help explain s
The following are equivalent ways of saying the same thing:
Block a isn't both a tetrahedon and a cube
and
Blocks a is not a tetrahedon or not a cube
And again so are the following
Some block is larger than block b
and
Block b is smaller than some block
O
Question 1
0 out of 2 points
The above tableau checks the set theory paradox conclusion sentence for consistency.
Which line numbers and rule name are used at
line 5 in the tableau? Your answer should be in
the form of a list of line numbers separated by
Question 1
2 out of 2 points
Is the following string
(1+3)
a (legal) term or a (legal) atomic wff or neither of the LPL FIRST-ORDER LANGUAGE
OF ARITHMETIC?
In this question you have to provide all the correct answers to get full marks
3.
It's not a term o