12. Glossary

This glossary contains brief definitions for terms used in the PowerLoom User’s Manual and/or used by the knowledge representation community. It is impractical to give a logically precise definition for many of these terms, because their interpretation varies quite a bit. In this case, the glossary attempts to indicate a range of interpretations consistent with their use in PowerLoom.

Assertion: An assertion states that a particular proposition is True or False.

Backward and Forward Inference: ???

BACKWARD RULE: ???

Binary Relation: A relation having two arguments (arity equals two), often as a mapping from one concept domain to another. This is by far the most common form of relation.

Classifier: A classifier is a type of an inference engine that implements efficient strategies for computing subsumption relations between pairs of concepts, or for computing instance-of relations between a concept an a set of instances. PowerLoom implements a classifier that can be explicitly invoked by an application program.

Clipping: If a function or single-valued binary relation maps an instance to two or more other instances, a logical contradiction (a clash) exists. If clipping is enabled, PowerLoom will automatically retract all assertions but the last that lead to a clash. Clipping can be toggled on or off; it is enabled by default.

Closed-World Semantics: Under closed-world semantics it is assumed that “if proposition P cannot be proved True, then assume that P is False.” PowerLoom gives programmers the option to explicitly declare that concept or a relation operates under the assumption of closed-world semantics (See also Open-World Semantics).

Concept: A concept defines a category or class of individuals. PowerLoom categorizes a concept as a special kind of relation. The distinction between a concept and a unary relation is subtle (some logicians do not believe that there is any distinction(10)). In linguistics, the distinction is that between a noun and an adjective. In logic, the test we favor is whether or not the relation has a domain — a unary relation has a domain, while a concept does not. For example, the relation ‘married’ has domain ‘person’, while the concept ‘married-person’ does not have a domain (or is its own domain).

Constraint: “Constraint” at its most general is a synonym for “rule”. Often a constraint is conceptualized as a rule that restricts the types of the arguments that can appear within a tuple.

Context: ???

Default Rule: A default rule expresses an conditional implication that applies only when its consequent is consistent with current state of the knowledge base. In other words, the rule applies only when it will not lead to a contradition.

Definition: A definition binds a name to a logical expression. PowerLoom syntax defines several operators with names of the form defxxx (e.g., defconcept and defrule) that declare definitions for various types of entities.

Description: A “description” is an expression that defines a particular logical relation (e.g., the class of all three-legged black cats). In PowerLoom, the terms “concept” and “relation” generally refer to named relations, while a description may or may not have a name. The KIF operators kappa and setofall are used to define unnamed descriptions.

Description Logic: The term “description logic” refers to a logic that focuses on descriptions as its principal means for expressing logical expressions. A description logic system emphasises the use of classification and subsumption reasoning as its primary mode of inference. Loom and Classic were two early examples of knowledge representation systems that implement description logics.

Domain Model: A collection of definitions, rules, and facts that characterizes the possible states of some real or imagined world. The domain model specifies a terminology (of concepts and relations) that is useful for describing objects in that world. Often “domain model” refers to that portion of a world’s representation that does not change over time.

Extension: Given a relation R with arity N, the extension of R is the set of ground propositions of the form (R x1 ... xN) whose truth value is true. If R is a concept, then its extension of often considered to be, not a set of unary tuples, but the set of argument fillers of those tuples, i.e., the set of instances that belong to the concept.

Fact: A fact is a proposition that has been asserted to be either True or False. The term “fact” usually refers to a “ground proposition”, i.e., a proposition that can be represented as a predicate applied to a sequence of instances or literals.

Filler: The second argument to a binary tuple is often refered to as its “filler”. When a multiple-valued binary relation maps an instance to a set of values, these values are also called “fillers”.

Forward Rule: ???

Function: Formally, a function is a relation such that the value of the last (nth) argument of a relational tuple is a function of the values of the first n-1 arguments. This definition coincides with the notion of a “single-valued relation”. PowerLoom (and KIF) support specialized syntax that allows functions that have been defined using the operator deffunction to appear in term expressions (e.g., (= (f ?x) 42))).

Instance: An instance denotes an entity within a domain model, a member of the concept Thing. Depending on ones interpretation, this could include almost everything. Often the term “instance” is used more narrowly, to exclude literals and other objects whose properties do not change over time. PowerLoom assumes that concepts and relations are instances.

KIF: Short for “Knowledge Interchange Format”, KIF is a language that defines a Lisp-like syntax for the predicate calculus. There is an ANSII-standard that defines the KIF syntax and semantics. PowerLoom adopts KIF as its representation language, and adds a few extensions.

Knowledge Base: A knowledge base attempts to capture in abstract (machine interpretable) form a useful representation of a physical or virtual world. The entities in that world are modeled in the knowledge base by objects we call terms. Examples of terms are “Georgia” (denoting the U.S., state), “BenjaminFranklin” (denoting the historical person by that name), the number three, the string "abc", and the concept “Person”.

Literal: A logically static constant. Examples are numbers, strings, quantities, and truth values.

Module: ???

Open-World Semantics: PowerLoom assumes an open-world semantics, unless a user explicitly specifies that it use closed-world semantics. Under this assumption, if PowerLoom cannot prove or disprove a proposition, then it assigns that proposition the value Unknown (See also Closed-World Semantics).

Predicate:. The term predicate is a syntactic notion that refers to the zeroth arguments of a proposition. Predicates denote relations and properties, i.e., sets.

Proposition:. A logical sentence whose truth value can be evaluated with respect to some context. Each PowerLoom assertion assigns the value True or False to some proposition.

Primitive Relation: P is a primitive concept or relation if and only if a proof that (P x1 ... xn) is true exists only for the case that there exists an explicit assertion of a proposition (Q x1 ... xn) and either Q equals P or Q is a proper subrelation of P. In otherwords, the only rules that imply membership in P are those that relate P to one of its (proper) subconcepts or subrelations.

Query: A query probes the informational state of a knowledge base. An ask query test the truth of its propositional argument. A retrieve asks for sets of constants (bindings) that make its propositional argument true when the constants are substituted in place of its variables. The propositional argument to ask and retrieve arbitrary expression in the first-order predicate calculus. Because of constraints imposed either by resource limitations or inherent undecidability, PowerLoom cannot guarantee the completeness of its inferences.

Relation: ???

Retraction: A retraction changes the truth value of a proposition from either True or False to the value Unknown. Retraction is a procedural (non-declarative) operation.

Rule: A “rule” is any universally-quantified proposition, i.e., a proposition of the form (forall (?x1 ... ?xn) <logical sentence with free variables ?x1 ... ?xn). PowerLoom supports several different syntactic constructs for defining rules. (See also Forward Rule and Backward Rule).

Subsumption: A subsumption relation specifies the relative generality of two concepts. A concept A subsumes a concept B if the definitions of A and B logically imply that members of B must also be members of A.

Truth-Maintenance: ???

Type: Often used a synonym for the term concept. The phrase “a type of an instance” generally refers to (one of) the concepts that the instance belongs to. The phrase “nth domain type” refers to a concept that contains all instances of the nth column of a relation.

World: ???

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