Logic and Applications Days 2-4

I normally manage to get a post out each day I’m studying a module, but I’ve really struggled for time this time round. I’ve had a few items in my personal calendar that I didn’t want to miss, but over and above that the workload on this module is pretty intense.

There’s a coursework assignment each week, which constitutes a whole lot of work, but I’ve also chosen to switch from handwritten assignments to preparing my work in LaTeX. It’s made me pretty uncomfortable preparing extensive handwritten documents (on the order of 6-12 pages) for a few reasons. A mistake I make could involve wasting a lot of time re-writing a document, backing up a paper document regularly kinda doesn’t work, and handing in paper documents involves either physical locality or the good old Royal Mail. An electronic version has none of these drawbacks.

On the other hand, preparing this kind of material electronically is non-trivial, as there’s a lot of odd tabular layouts and logic formulae involved. I discounted anything other than LaTeX out of hand, as word processors aren’t really designed for that kind of material. Preparing this stuff electronically is more time consuming initially, but I console myself with the thought that I can correct a mistake very easily!

Anyway, Logic and Applications. We covered the relatively simple Propositional Logic in the first two weeks, and moved onto First Order Logic in weeks three and four, on into week five. So far, the idea seems to be to encode knowledge and deduce from that knowledge more information using rules that can be proven to derive correct conclusions.

Why different types of logic? Propositional logic is simplest, has certain helpful properties as a result, and has limitations you run into pretty quickly .

For example, in Propositional logic, we can encode explicit facts, like “Paul’s Mother is Helen” and “Helen is Female” and work with those facts, but we can’t generalise from there. For example, we can’t add “Jo’s Mother is Sylvia” to our system and deduce that Sylvia is female. To do that would require an ability to say something like “Mothers are Female”. We can’t do that without variables and quantifiers, so we need something more expressive. First Order logic gives us that additional expressivity, for the price of it being more difficult to learn and understand, and being undecidable. That last bit means that in general, no algorithm exists that can be guaranteed to give a yes or no answer as to the truth of a formula expressed in First Order Logic in a finite amount of time.

So, lots of fun to be had with proofs, algorithms and understanding some really abstract stuff!

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