FO(.)

In computer science, FO(.) (a.k.a. FO-dot) is a knowledge representation language (a.k.a. frame language) based on first-order logic.[1]

It has four types of statements:

  • Type, function and predicate declarations,
  • Axioms, i.e., logic sentences about possible worlds,
  • Definitions that specify a unique interpretation of a defined symbol, given the interpretation of its parameters. Definitions can be inductive.
  • Enumerations, i.e., definitions of symbols by enumeration.

An FO-dot knowledge base cannot be run. It is a "bag of information", to be used as input to various generic reasoning algorithms: e.g., to determine relevant questions, to compute consequences of new facts, and to explain them.

FO(.) extends first-order logic with: types, aggregates, arithmetic, (inductive) definitions, partial functions, and intensional objects.

FO-dot is used by these reasoning engines:

Example

The following voting laws

  • you must be at least 18 years old to vote;
  • if the law is prescriptive, voting is mandatory.

can represented in FO(.) as follows:

vocabulary V {
  age: () β†’ β„€                             // function declaration
  prescriptive, vote: () β†’ 𝔹              // predicate declarations
}
theory T:V {
  age() < 18 β‡’ Β¬vote().                   // axiom: if you are less than 18, you may not vote.
  prescriptive() β‡’ (age() β‰₯ 18 β‡’ vote()). // axiom: if prescriptive: if you are at least 18, you must vote
}

In this code, Aβ†’B indicates a function from A to B, denotes integers, denotes the booleans, Β¬ denotes negation, and β‡’ denotes material conditional. Predicates < and β‰₯ are built-in and have their usual meaning.

Such knowledge base can be turned automatically into an Interactive Lawyer[6] (see here[7])

References
  1. Denecker, Marc (2000). "Extending classical logic with inductive definitions". International Conference on Computational Logic: 703–717.
  2. "IDP-Z3". Retrieved 2022-02-01.
  3. De Cat, Broes; Bogaerts, Bart; Bruynooghe, Maurice; Janssens, Gerda; Denecker, Marc (2018). "Predicate logic as a modeling language: the IDP system". Declarative Logic Programming: Theory, Systems, and Applications: 279–323. doi:10.1145/3191315.3191321.
  4. "IDP". Retrieved 2022-02-01.
  5. "FOLASP". Retrieved 2022-02-01.
  6. "Interactive Consultant". Retrieved 2022-02-01.
  7. "Interactive Lawyer". Retrieved 2022-02-01.
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