Welcome to Logic, Language and Information
1
brought to you from the University of
Melbourne.
I'm Craig Restall.
>> And I'm Jen Devron.
We're both passionate about logic and it's
applications.
We have backgrounds in philosophy,
mathematics, computer science, and
electronic engineering.
We've been teaching logic at Melbourne for
the last
ten years to students from the humanities,
sciences, and engineering.
And now, we're excited to bring
this to a new audience from all over the
world.
>> Now, logic is the study of
information, wherever we find it.
The features it has, how it's represented,
and how we can manipulate it.
Learning logic helps you formulate and
answer all sorts of questions about
information.
>> Logic plays a foundational role in
several different disciplines including
linguistics, philosophy, electronic
engineering,
computer science, and mathematics.
Logic provides a bridge linking these
disparate disciplines and as well as
giving
an access route into these individual
disciplines
by providing a common language and
approach.
>> Now over five weeks, we'll introduce
you
to propositional logic and some of its
applications.
We begin by introducing a formal symbolic
language as a means to identify logical
structure.
Many of the sentences we speak and
write contain logical structure words like
if then,
‘and’, ‘unless’, ‘or’, ‘not’ and things like this
which play an important role in combining
information.
Our formal language will help us precisely
represent and understand and manipulate
logical structure.
You'll learn how the truth or falsity of a
complex
proposition like this one, depends on the
meaning of the logical
connectives, together with the truth or
falsity of its simplest parts.
>> In developing the semantics or
meaning of logical connectives,
we use structures called truth tables to
make precise the way
in which the truth or falsity of a
compound proposition depends
on it's parts, the logical connectives and
the simplest propositions.
By convention
we use the symbol 1 for true and 0 for
false.
You'll learn how to use truth tables
to make logical classifications and
assessments, such as
when one proposition is a logical
consequence of
another, or when two propositions are
logically equivalent.
In this example, the two highlighted
columns of 0s and 1s match exactly.
And this
shows that the two formulas are logically
equivalent.
>> Now truth variables are fine when
it comes to small, not too complicated
formulas.
But they quickly become unworkable when
things get larger or more complex.
You'll learn an alternative means of
making these logical classifications
called proof trees,
which are diagrams like the one that you
can see next to us here.
Crucially, you'll also learn why the
method of proof trees always and
only gives the correct answer.
The so-called soundness and completeness
of the proof tree method.
>> We cover core propositional logic in
the
first two weeks, and then in the remaining
weeks
three to five, we offer four applications
of propositional logic: electronic
engineering, philosophy, linguistics, and
in computer science.
You are encouraged
to choose two or more of the four
application areas.
All of the material for these applications
will be released
at the beginning of week three, so that
you can
choose which order you take them in, and
you'll have
flexibility in completing the graded
assessment for each of them.
Digital systems is a core area within
electronic engineering.
And it is grounded in logic.
The term digital systems covers the
computer hardware inside
all the communications and computing
technology that we use everyday.
And which has changed our lives so
dramatically over the last few decades.
In this section of the course, we will
introduce the simplest class called
combinational digital systems.
The most basic components are called 
‘and’, ‘or’, and ‘not’ gates 
and these behave exactly as the
logical connectives you will have learned
of in
the core part of the course.
You'll be introduced to several different
ways of representing combinational
systems, including circuit diagrams and
logic formulas like the ones here.
>> The philosophy application section
tackles
the topic of vagueness, where a meaning
isn't determined precisely
enough for us to be able to decide every
case.
This is different from ambiguity, where a
word has several different meanings.
Now you'll remember when we saw truth
tables just before, they divided
the world into cases where things are
true and things are false.
But if you look at this strip shading from
red to yellow that's
next to us, it's very hard to spot what
place in the strip
it makes a transition from saying it's
true that
this is red to no, it's false that it's
red.
The topic of vagueness makes people think
that, well, maybe we've got to expand our
understanding of truth values to have
things
beyond the truth values of true or false.
At the very least, looking at vagueness
helps us look critically at how
the technology of truth tables and proof
trees, how that applies to the world
around us, which is sometimes hard to
categorize.
Now in the next section, the Linguistics
section, we're
going to be addressing the topic of
Implicature and Implication.
These are different ways of distinguishing
what's implied in what people have said.
So for example, if somebody asks me, do I
have any children, and I say in answer
to them, I have a son, you'll often make
the inference from this that
I don't have any other children.
But maybe I do.
Literally, all that I said here in giving
the answer is that I said, I have a son.
And that would be true if I have two
children, three children, or more.
But for some reason, for some good reason,
when we say things like, I have a son,
in answer to questions like this, you make
inferences from what we say, which goes
beyond the logical content of what it is
that we've said.
In this topic we're going to use the
techniques that we've
had in logic to begin to analyse this
and understand
how dialogue works, and how we go beyond
what we say
to infer other things on the basis of what
we've said.
>> And in the computer science
application section of
the course, we're going to consider the
task of automated reasoning,
which is required of any artificial
intelligence system.
This is when and how we can program a
computer to correctly calculate when
a proposition is a logical consequence of
a database of knowledge.
You'll be introduced to 
logic programming using a language called
Prolog.
And you'll learn how Prolog works, and
when it can fail.
Prolog is used in the automated reasoning
component of
IBM's top of the line artificial
intelligence system called Watson.
Watson's most public achievement was to
recently beat all of
its human competitors on a US TV game show
called Jeopardy.
So how will we do all this?
Well, there are video lessons, many of
them with quizzes.
Then there's the course notes for each
section, which build up to make a text
book.
Discussion boards are places where you can
engage with other students.
There are quizzes for each section.
First, an ungraded practice quiz that you
can
take multiple versions of before sitting
the graded quiz.
And then, some peer assessment tasks,
which
are short 500 word or so writing tasks.
>> Now, now the grading
of the course breaks down as 40% for the
core areas of propositional logic,
40% for the different application areas,
and then 20% for the final writing exam.
The application score comes from taking
your best two application
marks out of 20, plus half of any
additional application
marks that you achieve, so that
you'll get
a reward for taking on one or more extra
application topics.
The final exam is peer-assessed using a
well-structured
grading rubric that you'll see online.
A score of 50 out of 100 is required for a
statement of accomplishment in this
course, and a score of 70 out of 100 is
great and you'll get a distinction.
We have really enjoyed preparing this
course.
And we're looking forward to joining you.
And we hope that you enjoy studying it
with us.