FMR: functional meaning representation

Element types in FMR

Constants: Refer to specific objects in the world. A constant can be a number, a lexical string, or an entity.
Classes: Semantic category of entities. For example: location.city, math.number
- Sub-class: math.number ⊆ math.expression
- Template classes: classes with one or more parameters, for example: t.list<c, m, n>, where c is a class, m and n are integers.
Functions: The major way to form larger language units from smaller ones. A function is comprised of a name, a list of core arguments, and a return type.
- Noun functions
  - Map entities to their properties or to other entities having specific relations withe the argument(s).
  - Are used to represent noun phrases in natural language.
  - Pronoun functions are special zero-argument noun functions.
- Verb functions
  - Act as sentences or sub-sentences
  - The most important function type?
- Modifier functions
  - Many functions can take additional extended arguments as their modifiers.
  - Modifier functions often take the role of extended arguments to modify noun function, verb functions or other modifier functions.
  - Are used in FMR as the semantic representation of adjectives, adverb phrases (including conjunctive adverb phrases), and prepositional phrases in NL
Entity Variables: Variables are assigned to FMR nodes for indicating the co-reference of sub-trees to entities.

Strongly typed language
- Type-compatibility: The type of each child of a function node should match the corresponding argument type of the function.
Open-domain type system.
- Thousands of types
- Other languages: At most 100+ in grammar level
Built-in data structures
- like t.list and nf.list

By using CFG rules to map natural language sentences and phrases to FMR

"The product of 3 consecutive number is 60" => 
vf.be.equ(nf.math.product(nf.list(math.number, 3, mf.consecutive)), 60);

NLP NLU Semantic