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In logic, we call the things in the universal model valuations; they are Boolean-values functions defined on the set of predicates.In computer science we often call these states, because, as we will…

We begin by revisiting the idea of a universal model. If we have only n predicates then we can distinguish only 2n kinds of individual. So we only need to consider 2^{2n} universes. For example, for…

Venn diagrams on a sphere.

In this video, we try to arrive at the disjunction rule.

In this video, we try to arrive at the conjunction rule.

Our first video is a recap of last week's materials.

In this video, we label each region in the Venn diagram with a number from 0 to 7. We can then present our justifications and counter-examples by referring to those 8 regions.

Given a syllogistic rule, how do we show that it is sound? Here we show that using Venn diagrams.

In this video, we get syllogisms for free! We see how some simple reasoning allows us to derive three more syllogisms.

In this video on syllogisms, we present a new form of proposition -- universal denial. Introducing negation gives a new syllogism as an instance of barbara.

This is the third video on Syllogisms. We use Venn diagrams to show that barbara is sound.

This is the second video on Syllogisms. We return to discuss the relationship between Euler and Venn diagrams, and introduce some notation.Having watched this video, you should be able to count…

This is the first video on Syllogisms. We start by introducing barbara, the simplest classical syllogism, and the proposition, "all a are b", known as universal affirmation. We briefly …

This video gives the background to set theory which is fundamental for dealing with probability more generally. The video discusses using Venn diagrams as a simple way of proving a number of…