Open World Assumption
Encyclopedia
In formal logic
, the open world assumption is the assumption that the truth-value of a statement
is independent of whether or not it is known by any single observer or agent to be true. It is the opposite of the closed world assumption
, which holds that any statement that is not known to be true is false. The open world assumption (OWA) is used in knowledge representation
to codify the informal notion that in general no single agent or observer has complete knowledge, and therefore cannot make the closed world assumption. The OWA limits the kinds of inference and deductions an agent can make to those that follow from statements that are known to the agent to be true. In contrast, the closed world assumption allows an agent to infer, from its lack of knowledge of a statement being true, anything that follows from that statement being false.
Heuristically, the open world assumption applies when we represent knowledge within a system as we discover it, and where we cannot guarantee that we have discovered or will discover complete information. In the OWA, statements about knowledge that are not included in or inferred from the knowledge explicitly recorded in the system may be considered unknown, rather than wrong or false.
Semantic Web
languages such as OWL
make the open world assumption. The absence of a particular statement within the web means, in principle, that the statement has not been made explicitly yet, irrespectively of whether it would be true or not, and irrespectively of whether we believe (or would believe) that it is (or would be) true or not. In essence, from the absence of a statement alone, a deductive reasoner cannot (and must
not) infer that the statement is false.
Many procedural programming languages and database
s make the closed world assumption. For example, if a typical airline database does not contain a seat assignment for a traveler, it means the traveler has not checked in. The closed world assumption typically applies when a system has complete control over information; this is the case with many database applications where the database transaction
system acts as a central broker and arbiter of concurrent requests by multiple independent clients (e.g., airline booking agents). There are however many databases with incomplete information: one cannot assume that because there is no mention on a patient's history of a particular allergy, that the patient does not suffer from that allergy.
Example
Statement: "Mary" "is a citizen of" "France"
Question: Is Paul a citizen of France?
"Closed world" (for example SQL) answer: No.
"Open world" answer: unknown.
Under OWA, failure to derive a fact does not imply the
opposite. For example, assume we only know that Mary is a citizen of France. From this information we can neither conclude that Paul is not a citizen of France, nor that he is. Therefore, we admit the fact that our knowledge of the world is incomplete. The open world assumption is closely related to the monotonic
nature of first-order logic
: adding new information never falsifies a previous conclusion. Namely, if we subsequently learn that Paul is also a citizen of France, this does not change any earlier positive or negative conclusions.
The language of logic programs with strong negation allows us to postulate the closed world assumption for some predicates and leave the other predicates in the realm of the open world assumption.
Formal logic
Classical or traditional system of determining the validity or invalidity of a conclusion deduced from two or more statements...
, the open world assumption is the assumption that the truth-value of a statement
Statement (logic)
In logic a statement is either a meaningful declarative sentence that is either true or false, or what is asserted or made by the use of a declarative sentence...
is independent of whether or not it is known by any single observer or agent to be true. It is the opposite of the closed world assumption
Closed world assumption
The closed world assumption is the presumption that what is not currently known to be true, is false. The same name also refers to a logical formalization of this assumption by Raymond Reiter. The opposite of the closed world assumption is the open world assumption , stating that lack of knowledge...
, which holds that any statement that is not known to be true is false. The open world assumption (OWA) is used in knowledge representation
Knowledge representation
Knowledge representation is an area of artificial intelligence research aimed at representing knowledge in symbols to facilitate inferencing from those knowledge elements, creating new elements of knowledge...
to codify the informal notion that in general no single agent or observer has complete knowledge, and therefore cannot make the closed world assumption. The OWA limits the kinds of inference and deductions an agent can make to those that follow from statements that are known to the agent to be true. In contrast, the closed world assumption allows an agent to infer, from its lack of knowledge of a statement being true, anything that follows from that statement being false.
Heuristically, the open world assumption applies when we represent knowledge within a system as we discover it, and where we cannot guarantee that we have discovered or will discover complete information. In the OWA, statements about knowledge that are not included in or inferred from the knowledge explicitly recorded in the system may be considered unknown, rather than wrong or false.
Semantic Web
Semantic Web
The Semantic Web is a collaborative movement led by the World Wide Web Consortium that promotes common formats for data on the World Wide Web. By encouraging the inclusion of semantic content in web pages, the Semantic Web aims at converting the current web of unstructured documents into a "web of...
languages such as OWL
Web Ontology Language
The Web Ontology Language is a family of knowledge representation languages for authoring ontologies.The languages are characterised by formal semantics and RDF/XML-based serializations for the Semantic Web...
make the open world assumption. The absence of a particular statement within the web means, in principle, that the statement has not been made explicitly yet, irrespectively of whether it would be true or not, and irrespectively of whether we believe (or would believe) that it is (or would be) true or not. In essence, from the absence of a statement alone, a deductive reasoner cannot (and must
not) infer that the statement is false.
Many procedural programming languages and database
Database
A database is an organized collection of data for one or more purposes, usually in digital form. The data are typically organized to model relevant aspects of reality , in a way that supports processes requiring this information...
s make the closed world assumption. For example, if a typical airline database does not contain a seat assignment for a traveler, it means the traveler has not checked in. The closed world assumption typically applies when a system has complete control over information; this is the case with many database applications where the database transaction
Database transaction
A transaction comprises a unit of work performed within a database management system against a database, and treated in a coherent and reliable way independent of other transactions...
system acts as a central broker and arbiter of concurrent requests by multiple independent clients (e.g., airline booking agents). There are however many databases with incomplete information: one cannot assume that because there is no mention on a patient's history of a particular allergy, that the patient does not suffer from that allergy.
Example
Statement: "Mary" "is a citizen of" "France"
Question: Is Paul a citizen of France?
"Closed world" (for example SQL) answer: No.
"Open world" answer: unknown.
Under OWA, failure to derive a fact does not imply the
opposite. For example, assume we only know that Mary is a citizen of France. From this information we can neither conclude that Paul is not a citizen of France, nor that he is. Therefore, we admit the fact that our knowledge of the world is incomplete. The open world assumption is closely related to the monotonic
Monotonicity of entailment
Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions. In sequent calculi this property can be captured by an inference rule called weakening, or sometimes thinning, and in such...
nature of first-order logic
First-order logic
First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
: adding new information never falsifies a previous conclusion. Namely, if we subsequently learn that Paul is also a citizen of France, this does not change any earlier positive or negative conclusions.
The language of logic programs with strong negation allows us to postulate the closed world assumption for some predicates and leave the other predicates in the realm of the open world assumption.