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37 video lectures

ProLT: Propositional Logic and Topology

Explore possible states, observation, topology and inference through 37 video lectures with captions, transcripts and chapter links.

Begin with sets and truth tables, then build the topology of observation, directed distance and logical inference. The final four lectures explore further applications.

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All lectures

  1. Lecture 01Why give logic a topology?
  2. Lecture 02Sets: a language for possible states
  3. Lecture 03Propositional logic and truth tables
  4. Lecture 04From formulas to truth regions
  5. Lecture 05Partitions, minterms, and complete descriptions
  6. Lecture 06What is a distance?
  7. Lecture 07What is a topology?
  8. Lecture 08How a few sets generate a topology
  9. Lecture 09Equivalence and order: two ways to compare states
  10. Lecture 10Observation signatures: what the interface records
  11. Lecture 11Building a propositional logical topological space
  12. Lecture 12Indistinguishable states and the T0 quotient
  13. Lecture 13One-sided and two-sided observation
  14. Lecture 14The specialization preorder: preserving positive information
  15. Lecture 15AXOR and weighted Hamming distance
  16. Lecture 15BWhy symmetric distance gives a different topology
  17. Lecture 16Directed distance: the cost of losing observations
  18. Lecture 17How directed distance recovers the topology
  19. Lecture 18Interior and closure: what can observations settle?
  20. Lecture 19Boundary is ambiguity, not XOR
  21. Lecture 20Better observations: refining the topology
  22. Lecture 21Learning a premise: restricting the possible worlds
  23. Lecture 22Inference as inclusion of truth regions
  24. Lecture 23Modus Ponens and Modus Tollens, one state at a time
  25. Lecture 24Hypothetical syllogism and eight possible worlds
  26. Lecture 25Functions, inverse images, and continuity
  27. Lecture 26Continuous maps preserve the information order
  28. Lecture 27AObservable negation and double negation
  29. Lecture 27BObservable implication and the Heyting rule
  30. Lecture 28APullbacks: matching two premises to the same world
  31. Lecture 28BWhy the pullback has the induced topology
  32. Lecture 29One observation table, the whole framework
  33. Lecture 30What the paper establishes, and what remains open
  34. Lecture E1Connectedness without geometry
  35. Lecture E2Compatibility complexes and first homology
  36. Lecture E3Local contexts and global consistency
  37. Lecture E4Designing observations for a purpose