Frame Logic

Origin. Kifer, Lausen, Wu (1995). Object-oriented knowledge representation. Frames with logic. Methods and inheritance. Foundation for F-logic systems.

Models. Objects with attributes. Class hierarchy. Method definitions. Nonmonotonic inheritance. Combines frames with first-order logic.

Formalism.

Objects and classes: o : c — object o is instance of class c c :: d — class c subclass of d o[m → v] — object o has method m with value v o[m →→ v] — inheritable method

Signatures and data: c[m ⇒ t] — instances of c have m of type t c[m ⇒⇒ t] — inheritable signature o[m → v] — actual data value

Rules: H :- B₁, ..., Bₙ Deductive rules. Logic programming style.

Inheritance: Nonmonotonic: overridable. Multiple inheritance with conflict resolution. ISA hierarchy.

Path expressions: o.m.n — chained access o[m → X][n → Y] — conjunctive

Molecules: Combine facts about one object: o[m₁ → v₁; m₂ → v₂; ... ; mₙ → vₙ]

Example: bob : person. person :: being. person[age ⇒ integer]. bob[age → 30].

Query: ?- X : person[age → Y], Y > 25.

Symbols.

Symbol	Unicode	Name	Meaning
:	—	IsA	Instance of
::	—	SubClass	Subclass of
→	U+2192	Data	Value
⇒	U+21D2	Signature	Type
→→	—	Inheritable	Inherited value

Metatheory. Model-theoretic semantics. Fixpoint semantics for rules. Decidable fragments. Inheritance nonmonotonic.

Applies to. Deductive databases. Knowledge bases. Semantic Web (Flora-2). Object-oriented reasoning. Ontologies.

Limitations. Nonmonotonicity complex. Inheritance conflicts. Performance issues. Less standard than OWL.