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Welcome to Logic, Language and Information
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brought to you from the University of
Melbourne.

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I'm Craig Restall.
>> And I'm Jen Devron.

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We're both passionate about logic and it's
applications.

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We have backgrounds in philosophy,

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mathematics, computer science, and
electronic engineering.

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We've been teaching logic at Melbourne for
the last

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ten years to students from the humanities,
sciences, and engineering.

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And now, we're excited to bring

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this to a new audience from all over the
world.

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>> Now, logic is the study of
information, wherever we find it.

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The features it has, how it's represented,
and how we can manipulate it.

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Learning logic helps you formulate and

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answer all sorts of questions about
information.

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>> Logic plays a foundational role in

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several different disciplines including

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linguistics, philosophy, electronic
engineering,

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computer science, and mathematics.

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Logic provides a bridge linking these

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disparate disciplines and as well as
giving

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an access route into these individual
disciplines

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by providing a common language and
approach.

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>> Now over five weeks, we'll introduce
you

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to propositional logic and some of its
applications.

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We begin by introducing a formal symbolic

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language as a means to identify logical
structure.

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Many of the sentences we speak and

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write contain logical structure words like
if then,

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‘and’, ‘unless’, ‘or’, ‘not’ and things like this

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which play an important role in combining
information.

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Our formal language will help us precisely

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represent and understand and manipulate
logical structure.

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You'll learn how the truth or falsity of a
complex

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proposition like this one, depends on the
meaning of the logical

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connectives, together with the truth or
falsity of its simplest parts.

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>> In developing the semantics or
meaning of logical connectives,

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we use structures called truth tables to
make precise the way

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in which the truth or falsity of a
compound proposition depends

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on it's parts, the logical connectives and
the simplest propositions.

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By convention

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we use the symbol 1 for true and 0 for
false.

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You'll learn how to use truth tables

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to make logical classifications and
assessments, such as

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when one proposition is a logical
consequence of

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another, or when two propositions are
logically equivalent.

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In this example, the two highlighted
columns of 0s and 1s match exactly.

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And this

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shows that the two formulas are logically
equivalent.

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>> Now truth variables are fine when

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it comes to small, not too complicated
formulas.

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But they quickly become unworkable when
things get larger or more complex.

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You'll learn an alternative means of

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making these logical classifications
called proof trees,

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which are diagrams like the one that you
can see next to us here.

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Crucially, you'll also learn why the
method of proof trees always and

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only gives the correct answer.

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The so-called soundness and completeness
of the proof tree method.

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>> We cover core propositional logic in
the

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first two weeks, and then in the remaining
weeks

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three to five, we offer four applications
of propositional logic: electronic

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engineering, philosophy, linguistics, and
in computer science.

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You are encouraged

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to choose two or more of the four
application areas.

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All of the material for these applications
will be released

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at the beginning of week three, so that
you can

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choose which order you take them in, and
you'll have

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flexibility in completing the graded
assessment for each of them.

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Digital systems is a core area within
electronic engineering.

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And it is grounded in logic.

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The term digital systems covers the
computer hardware inside

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all the communications and computing
technology that we use everyday.

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And which has changed our lives so
dramatically over the last few decades.

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In this section of the course, we will

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introduce the simplest class called
combinational digital systems.

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The most basic components are called 

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‘and’, ‘or’, and ‘not’ gates 
and these behave exactly as the

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logical connectives you will have learned
of in

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the core part of the course.

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You'll be introduced to several different
ways of representing combinational

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systems, including circuit diagrams and
logic formulas like the ones here.

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>> The philosophy application section
tackles

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the topic of vagueness, where a meaning
isn't determined precisely

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enough for us to be able to decide every
case.

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This is different from ambiguity, where a
word has several different meanings.

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Now you'll remember when we saw truth
tables just before, they divided

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the world into cases where things are
true and things are false.

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But if you look at this strip shading from
red to yellow that's

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next to us, it's very hard to spot what
place in the strip

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it makes a transition from saying it's
true that

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this is red to no, it's false that it's
red.

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The topic of vagueness makes people think
that, well, maybe we've got to expand our

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understanding of truth values to have
things

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beyond the truth values of true or false.

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At the very least, looking at vagueness
helps us look critically at how

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the technology of truth tables and proof
trees, how that applies to the world

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around us, which is sometimes hard to
categorize.

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Now in the next section, the Linguistics
section, we're

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going to be addressing the topic of
Implicature and Implication.

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These are different ways of distinguishing
what's implied in what people have said.

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So for example, if somebody asks me, do I
have any children, and I say in answer

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to them, I have a son, you'll often make
the inference from this that

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I don't have any other children.
But maybe I do.

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Literally, all that I said here in giving
the answer is that I said, I have a son.

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And that would be true if I have two
children, three children, or more.

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But for some reason, for some good reason,
when we say things like, I have a son,

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in answer to questions like this, you make
inferences from what we say, which goes

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beyond the logical content of what it is
that we've said.

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In this topic we're going to use the
techniques that we've

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had in logic to begin to analyse this
and understand

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how dialogue works, and how we go beyond
what we say

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to infer other things on the basis of what
we've said.

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>> And in the computer science
application section of

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the course, we're going to consider the
task of automated reasoning,

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which is required of any artificial
intelligence system.

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This is when and how we can program a
computer to correctly calculate when

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a proposition is a logical consequence of
a database of knowledge.

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You'll be introduced to 

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logic programming using a language called
Prolog.

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And you'll learn how Prolog works, and
when it can fail.

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Prolog is used in the automated reasoning
component of

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IBM's top of the line artificial
intelligence system called Watson.

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Watson's most public achievement was to
recently beat all of

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its human competitors on a US TV game show
called Jeopardy.

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So how will we do all this?

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Well, there are video lessons, many of
them with quizzes.

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Then there's the course notes for each

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section, which build up to make a text
book.

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Discussion boards are places where you can
engage with other students.

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There are quizzes for each section.

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First, an ungraded practice quiz that you
can

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take multiple versions of before sitting
the graded quiz.

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And then, some peer assessment tasks,
which

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are short 500 word or so writing tasks.

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>> Now, now the grading

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of the course breaks down as 40% for the
core areas of propositional logic,

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40% for the different application areas,
and then 20% for the final writing exam.

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The application score comes from taking
your best two application

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marks out of 20, plus half of any
additional application

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marks that you achieve, so that
you'll get

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a reward for taking on one or more extra
application topics.

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The final exam is peer-assessed using a
well-structured

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grading rubric that you'll see online.

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A score of 50 out of 100 is required for a
statement of accomplishment in this

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course, and a score of 70 out of 100 is
great and you'll get a distinction.

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We have really enjoyed preparing this
course.

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And we're looking forward to joining you.

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And we hope that you enjoy studying it
with us.