These videos introduce the basic framework for our discussion of propositional logic. This includes a universe of things, and a collection of predicates, which are properties a thing might have. We look at a chess set as a first example of a universe, and then introduce an even simpler example, which we use to introduce propositions, which are statements we may make about the universe.
In the last video, Lecture-1x-models, we represent a universe as a type in
Haskell. If our things have type Thing then a predicate
is a function from Thing to Bool.
type Predicate = Thing -> Bool
If that doesn't yet
make sense, don't worry; come back to the last video once you're a bit
more familiar with Haskell.
You should complement your watching of these videos by reading
Chapter 4, Venn diagrams and Logical Connectives, and Chapter
6, Features and Predicates, in The Book.
In this video we introduce
binary data as a simple example of information, and show how
apparently more-complex examples can be encoded as binary data. This
video uses a chess set as a worked example to show how we can encode
information in binary form. In this video, we revisit
the chess set to introduce another encoding. We introduce decision
trees and compare the two codings. In
this video, we revisit the chess set to introduce another encoding. We
introduce decision trees and compare the two codings. Propositions say something about the world. In this video we define
the meanings of some Aristotelian propositions. The meaning is given
by defining the validity of a proposition in a universe. This
formal notion of validity represents the informal notion of truth.
Once you have listened to the videos above, you may want to listen to
the first part of this recording of a lecture delivered in 2019. There is a slight glitch in
the rendering of the second slide in the video below. Don't let it
distract you! Once you have understood how our universe can be
represented in Haskell, you may also want to revisit the legacy
video from 2019 introduced above. This takes the Haskell representation a
step further, starting from 7m20s. In this video I introduce some important
questions about mathematical, logical and computational models.
Nothing technical here. It's intended to
get you thinking $mdash& about the relationship between the virtual
worlds, created by the models we will study in logic and implement
in software, and the material world we inhabit in real life (IRL).
Lecture-1a-data
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Lecture-1b-questions
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Lecture-1c-encodings
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Lecture-1d-a-universe
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Lecture-1e-propositions
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Legacy recording from 2019
Up to 7m20s this is another presentation of the materials covered in
this and the preceding videos. Beyond that it goes into the Haskell
representation of our small universe (see below).Video
Lecture-1h-haskell
We represent our small universe in Haskell. You can look at this
now if you're eager, but you will will probably find
that it doesn't yet make sense; don't worry, that's expected.
It's here just to keep it close to the ideas it refers to.
Come back to this once you're a bit more familiar with Haskell.
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Lecture-1x-models
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