sjkillen/lattice-programming
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity

a

Browse source
This commit is contained in:
Spencer Killen 2023-01-19 10:53:15 -07:00
parent 4f7e85c89a
commit 9d1c717f2d
Signed by: sjkillen
GPG key ID: 2FDD7376F031D45B
1 changed files with 12 additions and 20 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

32
lattices.ipynb
View file

@ -12,16 +12,16 @@
"- Very generic math structure\n",
"- For practical purposes: just a **finite** set with a subset relation\n",
"- Paired with ``fixpoint operators``: functions that either\n",
" - Take a point and follow the lines upwards\n",
" - Stay in the same place\n",
" - Follow the lines upwards\n",
" - Stop\n",
"- Conditions above can be relaxed, but at the cost of complexity\n",
"\n",
"## Lattice programming\n",
"- Partial solutions\n",
"- Guaranteed termination\n",
"- Guaranteed termination (through monotonicity)\n",
"- Very modular / elegant\n",
"- A sane way to define recursive functions\n",
"- Not an implementation, just an underlying theory to build upon\n",
"- Sane recursive functions - no induction\n",
"- Theory, not implementation\n",
"\n",
"## Example Visualization\n",
"\n"
@ -92,14 +92,10 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"# Example Fixpoint Operator\n",
"\n",
"- Computation can start at the TOP or BOTTOM and move downwards or upwards in the lattice\n",
"- An operator is just a function that takes and element and moves in a direction consistently\n",
"\n",
"## Problem\n",
"\n",
"- A diagnostic approach to parts of speech tagging (POS tagging)\n",
"- A diagnosis approach to parts of speech tagging (POS tagging)\n",
" - Diagnostics propose a tag, then possibly refute it\n",
"- POS: noun, verb, adverb, subject\n",
"### Lattice\n",
@ -147,10 +143,8 @@
"\n",
"- Method stolen from classical linguistics ([uoa reference](https://ezpa.library.ualberta.ca/ezpAuthen.cgi?url=https://academic.oup.com/book/12008/chapter-abstract/161275349?redirectedFrom=fulltext)) ([non uoa, gated](https://academic.oup.com/book/12008/chapter/161275349?login=true))\n",
"- Rooted in generative grammar\n",
"- Don't want to misrepresent it, its a lot more sophisticated than what I'm presenting here.\n",
"- General principle is apply rules to rule out possible interpretations\n",
"- I'm not an expert of linguistic diagnosis, I just think it's cool\n",
"- Given a template sentence, decide whether it's true when instantiated\n",
"- Simplified here\n",
"- Operate on template sentences:\n",
"- E.g. \"The dog kicked the ball\" -> (\"Who kicked the ball?\", \"Dog\") is true, then dog is NOUN(SUBJECT) \n",
"- Oracle-driven\n",
" - In classical linguistics, the linguist is the oracle\n",
@ -425,13 +419,11 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"# Further Ideas\n",
"## A fuzzier approach\n",
"# A fuzzier approach\n",
"\n",
"- We're expecting a lot from a our diagnostics to have to \"entirely refute\" a POS, a graded approach would be better\n",
"- That's possible!\n",
"- Now we have triples (word, tag, confidence) and give the diagnostics the ability to lower a confidence level\n",
"- But this is no longer a simple subset relation, so it needs more general-purpose lattice theory."
"- Binary deciding expects a lot from diagnostics\n",
"- Graded approach would be beter\n",
"- Modify to use triple (word: str, tag: str, confidence: float)\n"
]
}
],