Categorial Type Inference Rules

• Possible extensions to basic inference rules (ctd.)

  • Function -> relation: Z/Y/X => 2/Y/X/Z
  • n-ary operators induce generalized quantifiers
    • X/wX => X/(X/N) ; => X/(X/N)/(2N)
    • e.g. bind(plus,i,xi/i!) = sum(li.xi/i!)
  • ...

• Cognitive relevance of type inference rules

  • ”categorial” vernacular such as ”rule of composition”
  • ”common sense” maths such as n-ary/operator
  • ”convention” such as function->relation

Notes: