The Logic of Space

In my search for a Quantum Logic I've started looking at formalisations of logic for classical mechanics. This seems like a reasonable place to start.

Of course some of you know that you can easily get an intuisionistic logic from spatial operations where where meet and join are specified by intersection and union (almost, we have to be careful about boundaries). For more on how this is done and it's connection with modal logic, look at thatlogicblog.

This is nearly enough to start reasoning about classical mechanics since we can view space as 4 dimensionally static. I haven't worked through it yet since I've been a bit busy. I'll update you later.

[Update: See The Logic of Space Part II ]

Comments

Decidable Equality in Agda

So I've been playing with typing various things in System-F which previously I had left with auxiliary well-formedness conditions. This includes substitutions and contexts, both of which are interesting to have well typed versions of. Since I've been learning Agda, it seemed sensible to carry out this work in that language, as there is nothing like a problem to help you learn a language. In the course of proving properties, I ran into the age old problem of showing that equivalence is decidable between two objects. In this particular case, I need to be able to show the decidability of equality over types in System F in order to have formation rules for variable contexts. We'd like a context Γ to have (x:A) only if (x:B) does not occur in Γ when (A ≠ B). For us to have statements about whether two types are equal or not, we're going to need to be able to decide if that's true using a terminating procedure. And so we arrive at our story. In Coq, equality is ...

Total Functional Programming

Recently on Lambda the Ultimate there was a post called "Total Functional Programming". The title didn't catch my eye particularly, but I tend to read the abstract of any paper that is posted there that doesn't sound terribly boring. I've found that this is a fairly good strategy since I tend to get very few false positives this way and I'm too busy for false negatives. The paper touches directly and indirectly on subjects I've posted about here before. The idea is basically to eschew the current dogma that programming languages should be Turing-complete, and run with the alternative to the end of supplying "Total Functional Programming" . At first glance this might seem to be a paper aimed at "hair-shirt" wearing functional programming weenies. My reading was somewhat different. Most hobbiest mathematicians have some passing familiarity with "Turing's Halting Problem" and the related "Goedel's Inco...

Managing state in Prolog monadically, using DCGs.

Prolog is a beautiful language which makes a lot of irritating rudimentary rule application and search easy. I have found it is particularly nice when trying to deal with compilers which involve rule based transformation from a source language L to a target language L'. However, the management of these rules generally requires keeping track of a context, and this context has to be explicitly threaded through the entire application, which involves a lot of irritating and error prone sequence variables. This often leads to your code looking something a bit like this: compile(seq(a,b),(ResultA,ResultB),S0,S2) :- compile(a,ResultA,S0,S1), compile(b,ResultB,S1,S2). While not the worst thing, I've found it irritating and ugly, and I've made a lot of mistakes with incorrectly sequenced variables. It's much easier to see sequence made explicitly textually in the code. While they were not designed for this task, but rather for parsing, DCGs turn out to be a conveni...

Rubrication

Search This Blog