diff --git a/lattices.ipynb b/lattices.ipynb
index b16e4f6..98c6d0b 100644
--- a/lattices.ipynb
+++ b/lattices.ipynb
@@ -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"
    ]
   }
  ],