Definitions

An ad-hoc table is a ST-table in a SQL database which contains all sentences of a sentence type in unpacked NL-format. The sentences (rows) in the table have been exported from the knowledge base (ad-hoc).

and rule [Pro/3]

A certainty rule which returns the lowest certainty of its argument certainty rules.

annotation [Pro/3]

annotations

Annotations are "comments" (explanatory texts) associated with knowledge nodes. Annotations play no role in knowledge inference.

arithmetical operators [Pro/3]

arithmetical operators

Operators used in forming arithmetical expressions.

assignment operators [Pro/3]

assignment operators

Operators used to assign values to a variable.

axiom

A well formed formula (wff) of a theory.

atomic formula

An atomic formula consists of a predicate and terms which act as arguments.

atomic entity type [Pro/3]

An entity type with only one data element type.

bayesian rule

A class of certainty rules which derive the return value from a bayesian combination of two or more certainties returned by other certainty rules.

binary predicate type [Pro/3]

A predicate type which takes two entity arguments.

built-in function [Pro/3]

A function which is built into the inference engine, and thus execute much faster than KE-defined functions which are interpreted by the inference engine.

certainty factor

A certainty factor is a measure of certainty in the range [-1.0,1.0] where -1.0 represents absolutely not certain, 1.0 absolutely certain and 0.0 neither certain nor not certain. Certainty factors are computed by certainty rules.

certainty rule [Pro/3]

A class of inexact rules which conclude (return) a certainty factor value (data element) from n parameters. Certainty rules are divided into bayesian rules, and-rules, or-rules, not-rules and combination rules.

chain [Pro/3]

A chain is a collection of KB records, either

all sentence records with the same predicate type and all sentence rules with the same predicate type in the conclusion
all definitions of a function
all inexact rules of the same class

chain location file [Pro/3]

A KB based on 3kb-type databases has a corresponding chain location file which lists all external database files, their corresponding DB identifier used in the opening KB and the external chains used in each external DB and their access mode.

chain table [Pro/3]

A chain table is a table in a SQL database which contains either:

all sentence records with the same predicate type and all sentence rules with the same predicate type in the conclusion
all definitions of a function
all inexact rules of the same class

clausal form

A clausal form wff ("well formed formula") or a predicate logic wff, is symbolic format where only the connectives and, or and not are used, i.e. a set of clauses connected by and. Synonymous with normal form wff.

A and B
A or B
not A
A=B
A+B (expressions)
_ (open variable)

clause

A clause is a set of positive or negative atomic formulas connected by or (with no explicit variable quantification - universal quantification is assumed).

clausal form wff is synonymous with normal form wff .

closed world assumption (in Prolog)

An instance of a relation in Prolog which can not be proven is considered false (i.e. no distinction between unknown relations and provable false relations).

combination rule

A class of certainty rules which returns a certainty factor (or probability) from two or more called rules (which return certainty factors (or probabilities)) according to the formula:

CF₁>0,CF₂>0 : CF₁+CF₂- CF₁*CF₂
CF₁<0,CF₂<0 : CF₁+CF₂+ CF₁*CF₂
CF₁=-CF₂,CF₁+CF₂0: 0
else : (CF₁+CF₂) / (1-min(|CF₁|,|CF₂|))

comparison operators [Pro/3]

comparison operators

Operators which are used to compare to expressions.

complement rule [Pro/3]

A class of fuzzy set rules which computes the membership grade for the complement of a fuzzy set.

cyclic multi-KB configurations [Pro/3]

See multi-KB configurations.

cyclic rules [Pro/3]

A rule where the same sentence type occurs both in condition and conclusion. Cyclic rules are not allowed in Pro/3.

data element [Pro/3]

A value belonging to a defined data element type.

data element reference [Pro/3]

A reference in a function, certainty rule or query to a data element (value) in a sentence. References can be deterministic or non-deterministic.

data element type

A open class of data elements defined by a name, a domain, a format and a field width.

database (DB) identifier [Pro/3]

A one-letter identifier associated with a database and used in the KB to locate records. The DB identifiers used in a KB must uniquely identify the main and the external databases.

data rule [Pro/3]

A sub-class of certainty rules. Data rules are either a query-type or a question-type of data rule.

DB address [Pro/3]

A database record is associated with a unique variable length hexadecimal address (DB address) - prefixed with a ~ character in outputs (for example "~2100E4"). See also KB addresses.

DDE

Acronym for dynamic data exchange. DDE is a protocol for exchanging data between two executing Windows programs. Pro/3 supports DDE of sentences to/from Excel.

deletion filter [Pro/3]

A sentence-rule like construct which is used\to achieve incremental sentence derivation (an optimizaton feature applicable to very big KBs). DELETION FILTERS ARE NO LONGER SUPPORTED BY PRO/3!

dependency graph [Pro/3]

An acyclic directed graph which defines the dependencies between knowledge nodes in the KB (functions, certainty rules, sentence rules, sentence types and sentence groups)

derivation [Pro/3]

The process of deriving sentences (facts) from rules (and other sentences).

derivation graph [Pro/3]

An acyclic directed graph used when deriving facts. The derivation graph is generated from the dependency graph.

derived rule [Pro/3]

sentence derivation

Rules with open (variable) entity argument(s) in the conclusion cannot be interpreted directly by the inference engine. Rather, Pro/3 determines all relevant entity type arguments in the conditions (from the dependency graph) prior to rule processing. Rules with corresponding entity type argument(s) are then derived from the original rule. These derived rules are then processed.

disjunctive normal form wff

Clause wff's with the general form AvBvC & DvEv... & ... (synonymous with clausal form wff).

domain [Pro/3]

domains

A finite or infinite set of values of a certain type i.e. integers, numbers, strings, identifiers, dates, list of integers, list of strings etc.

entity [Pro/3]

An object consisting of an ordered set of value elements (data elements) and belonging to a defined entity type.

entity type [Pro/3]

An open class of entities defined by a name and an ordered set of data element types.

export table [Pro/3]

multi-database confirgurations

An export table is a ST-table in a SQL database which contains all sentences of a sentence type in unpacked NL-format. The sentences (rows) in the table have been exported from the knowledge base (and is automatically refreshed each time the sentence type is re-derived).

external database [Pro/3]

A KB consists of a main database (file) and zero, one or more external databases. All databases are technically KBs in themselves.

field [Pro/3]

A fixed sub-set of a KB record.

FileScanner [Pro/3]

FileScanner

A java application which translates/reformats HTML-files to another format, e.g. a format which can be used as sentence-input to Pro/3 (PR, NL or delimited format). FileScanner can be invoked from Pro/3.

function [Pro/3]

functions

A mapping from n members of a domain of interpretation (parameters) onto one member of the domain of interpretation (return value). A function can also retrieve data elements and sentences from the KB during its execution. Pro/3 functions are either built-in or KE-defined. Built-in functions are embedded in the Pro/3 executable, while KE-defined functions are stores as knowledge in the KB.

fuzzy set

fuzzy set concepts

An essential assumption in traditional "crisp" logic is that something (an element belonging to a certain universe) either is a member of a given set or it is not a member, in which case it is a member of the complement set (in the universe). In fuzzy set theory this is not so. Fuzzy set membership is qualified by a degree of membership, given by the set's membership function, which is a mapping from an element (represented by a parameter or parameters) to a real number in the range [0,1]. This number is the membership degree, where 0 means that the element is not a member of the set, 1 means that element definitely is a member of the set, while values in the range <0,1> mean that the element is a member to a degree. The higher the value, the higher the degree of membership. An element can both be a member of a fuzzy set and its complement.

fuzzy set membership grade

A fuzzy set membership grade is a measure of the degree of membership in a fuzzy set. The grade is in the range [0.0,1.0] where 0.0 represents absolutely not a member, 1.0 absolutely a member and values in between member to some degree. Membership degrees are computed by fuzzy set rules.

fuzzy set rule [Pro/3]

A class of inexact rules which conclude (return) a a fuzzy set membership grade value (data element) from n parameters. Fuzzy set rules are divided into complement rules, intersection rules, union rules and ordered weighted averaging rules.

generalization rule [Pro/3]

A rule which defines how one sentence type is a generalization of another sentence type. Generalization rules can define multi-level hierarchies of more and more general sentence types. Generalization rules are logically a sub-set of simple implication rules.

Horn clause

A Horn clause is a clause with only one positive literal. Example: Av~Bv~Cv~D v B&C&D=>A or in Prolog syntax A :- B, C, D.

identifier [Pro/3]

Identifiers are a domain of data elements (values). An identifier correspond to a syntagm, i.e. it is represented by a "sequence of tokens (words)" in NL and a KB name in the KB (IF format).

import table [Pro/3]

An import table is a ST-table in a SQL database which contains all sentences of a sentence type in unpacked NL-format. The sentences (rows) in the table are automatically imported into the knowledge base each time the sentence type is to be re-derived.

incremental sentence derivation [Pro/3]

sentence derivation

The first step in the derivation of a sentence type is the deletion of all existing derived sentences of the given type. Incremental sentence derivation uses partial deletion where the selection of the sentences to be deleted is determined by a sentence rule-like construct called a deletion filter. The rule(s) concluding the sentence type is constructed to work in tandem with the deletion filter.

inexact rule [Pro/3]

A class of rules used for inexact reasoning. Inexact rules are divided into certainty rules (which return a certainty factor), fuzzy set rules (which return a membership degree), and support rules. An inexact rule always return one and only one simple value.

inexact rule association [Pro/3]

inexact rule evaluation

A simple value found in the KB which is associated with an inexact rule. The value is typically a measurement relating to the evaluation of the rule and is optionally shown in inexact rule trees.

inexact rule reasoning tree [Pro/3]

An inexact rule reasoning tree corresponds to an inexact rule tree. The reasoning tree represents an instantiation of the rule tree for a given set of call parameters. The reasoning tree shows the value returned by each rule. Rules called by out-of-context rules are not shown in the reasoning tree.

inexact rule tree [Pro/3]

Inexact rules can call other inexact rules in various ways. The root of a ineaxt rule tree is an inexact rule while the branches are calls. The rules called by the root rule form the second level of nodes in the tree etc.

inference engine

The part of an "intelligent system" which deals with knowledge representation is usually separate from the part which deals with "reasoning". The knowledge representation part is referred to as the knowledge base, while the reasoning part is referred to as the inference engine.

internal format (IF) [Pro/3]

The internal knowledge representation format used in the knowledge base.

intersection rule [Pro/3]

A class of fuzzy set rules which computes the membership grade for the intersection of two or more fuzzy sets (by using one of the four intersection methods standard intersection, algebraic product intersection, bounded difference intersection or drastic intersection).

KB address [Pro/3]

A database record is associated with a unique variable-length hexadecimal address (DB address) - prefixed with a ~ character in outputs (for example "~2100E4"). A KB address has additionally the database identifier as suffix (for example "~2100E4B"). The distinction between the DB address and the KB address is only significant in a multi-database configuration, since DB address does not specify which of KB's databases the address refers to.

KB name [Pro/3]

An internal name (internal identifier) used in the knowledge base (KB) to represent a syntagm and its synonyms (if any).

knowledge base (KB)

A Pro/3 knowledge base is in theoretical terms a theory.

knowledge dependencies [Pro/3]

Knowledge dependencies refer to interrelationships between different types of knowledge components in the KB. These dependencies are represented in Pro/3 as two graphs: the dependency graph and the sentence model graph. These graphs are used by Pro/3 to prevent updates which would cause KB integrity errors. The dependency graph is also used to administer the derivation of facts.

knowledge engineer (KE) [Pro/3]

The person(s) who construct a Pro/3 model.

knowledge node [Pro/3]

An element of knowledge (in the KB). The exact meaning of knowledge node depends on the context. Knowledge nodes in the dependency graph (or derivation graph) include:

sentence groups
sentence types
sentence rules
certainty rules
functions

The sentence model graph additionally includes:

entity types
predicate types
data element types

Knowledge nodes to which annotations can be made also include:

realms
databases
segments

main database [Pro/3]

A KB consists of a main database (file) and optionally, one or more external databases. See KB internals for details.

map-rule [Pro/3]

A class of certainty rules which derives its return value mapping the certainty returned by another certainty rule into another value (i.e. by using a numerical or a discrete map).

meta characters

names - NL-syntax

Meta characters are used in various places in the Pro/3 dialogs (windows) and outputs, and also in the the KB itself, as delimiters. Avoid using meta characters in strings.

meta data

Meta data means "data about data" and is used in terms such as meta model ("a model of a model").

multi-DB configurations [Pro/3]

A multi-DB configuration refers to any configuration where one or more external DBs are used. A multi-DB configuration is either cyclic or non-cyclic. Cyclic multi-DB configurations are (in the simplest case) structured such that derivation of sentences in DB "A" is dependent on sentences in DB "B", while derivation of sentences in DB "B" likewise depends sentences in DB "A". Non-cyclic multi-DB configurations do not have such dependency cycles.

natural language format (NL) [Pro/3]

NL interface

The natural language-like knowledge specification language used for input and output to a Pro/3 knowledge base.

NL name [Pro/3]

The syntagm (natural language representation) corresponding to a KB name.

non-cyclic multi-DB configuration [Pro/3]

See multi-DB configurations

non-deterministic assignment [Pro/3]

Assignments have the general format: <variable> <assignment_operator> <expression>. A deterministic assignment assigns one value to the left-side variable. A non-deterministic assignment might assign several values to the left-side variable( consequtively). This is carried out repeatedly through a processing logic known as back-tracking. A non-deterministic assignment is specified by using a non-deterministic assignment operator and a non-deterministic expression. Non-deterministic expressions are variable ranges, non-deterministic data element references and calls to non-deterministic functions.

normalization

The processing of reformulating a predicate logic wff to clausal form wff. The following steps are involved:

1. reformulate equivalence using
(AvB) v (A->B)&(B=>A)
2. reformulate implication using
(A=>B) v(~AvB)
3. move negation inwards using
~(A&B) v (~Av~B) and
~(AvB) v (~A&~B)
4. remove existential quantifiers using
X: pred(X) replaced by pred(func())
5. move universal quantifiers outward using
predA(X) & ("Y: predB(Y)) replaced by
"Y:(predA(X)&predB(Y))
6. group into clauses using
(A&B)vC v (AvC)&(BvC)

normal form wff is synonymous with clausal form wff.

not-rule [Pro/3]

A class of certainty rules which derives its return value by negating the certainty returned by another certainty rule.

operators [Pro/3]

Operators in Pro/3 include comparison operators, assignment operators, arithmetical operators and string operators.

or-rule [Pro/3]

A class of certainty rules which derives its return value by a logical OR-type of operation of two or more certainties returned by other certainty rules.

ordered weighted averaging rule [Pro/3]

A class of fuzzy set rules which computes the membership grade for the resulting fuzzy set through an averaging operation, where a weighting factor is applied to the contributing sets.

parameter rule [Pro/3]

A class of inexact rules (support rules) which calls one or more rules, and uses the values returned by these rules as actual parameters in a call to another rule. The value returned by this last rule is the value returned by the parameter rule.

parameterized predicate [Pro/3]

A predicate which has one or more data elements.

predicate

A predicate is a mapping from one or several arguments onto a boolean value (i.e. TRUE or FALSE). Arguments are data elements and/or entities.

A Pro/3 predicate is either unary (one entity argument - cardinality one) or binary (two entity arguments - cardinality two). Parameterized predicates have one or more data elements. Un-parameterized predicates do not have data elements.

predicate calculus

A complete set of inference rules for predicate logic.

predicate logic wff

A predicate logic wff consists of atomic formulas and connectives:

~ not
& and
v or
=> implication
= equivalence
$ existential quantifier
A universal quantifier

predicate type [Pro/3]

An open class of predicates defined by a name, its cardinality (unary or binary) and an ordered set of data element types (possibly empty). Refer to sentence modeling.

PR-format [Pro/3]

A PROLOG-like format used as a translation step between natural language format and internal format. PR-format can also be used as input and output directly.

procedure [Pro/3]

A Pro/3 procedure is used in statistical rules, accumulation rules and selection rules, to specify how data element values are implied from sets of data element values.

property

A relation with one argument.

propositional calculus

A complete set of inference rules for propositional logic.

propositional logic wff

A propositional logic wff consists of atomic propositions and connectives:

~ not
& and
v or
=> implication
= equivalence

A propositional logic wff does not contain variables.

query [Pro/3]

queries

An expression which can be processed by Pro/3's inference engine, and to which the inference engine will respond either a set of sentences or simple value(s).

query rule [Pro/3]

inexact rules

A class of inexact rules which derives its return value from the response to a query to the KB (made during the interpretation of the rule).

question cluster [Pro/3]

question clusters

A sentence type used to improve the evaluation of question rules.

question rule [Pro/3]

inexact rules

A class of inexact rules which derives its return value from the answer to a question put interactively to the KE during interpretation of the rule.

question series [Pro/3]

question series

A sentence type used to improve the evaluation of question rules.

RAM

Random access memory (as opposed to disk memory/storage).

RAM database [Pro/3]

The main KB database can be stored in RAM (for performance reasons). See KB internals for details.

realm [Pro/3]

A realm is a collection of KB records (with the same realm name record field). The realm concept is a tool to classify and find KB records for easier KB administration. There is no particular knowledge semantic attached to the realm concept. Refer to KB internal structure.

record [Pro/3]

A KB record is either of the following:

one sentence
one sentence rule
one function definition
one certainty rule

recursion

See acyclicity requirement.

recursive function

A function which calls itself directly or indirectly.

refutation procedure

A procedure to prove if a wff is a consequence of a theory by showing that a contradiction can be derived by adding the negation of the wff to the theory.

root rule [Pro/3]

A certainty rule which is not called by any other certainty rules. A Pro/3 model with certainty rules must have at least one root rule. Refer to certainty rules.

rule [Pro/3]

Pro/3 supports three classes of rules: sentence-rules, inexact rules and functions.

segment [Pro/3]

All structure entities in the KB i.e. syntagms, synonyms, data element types, entity types, predicate types and function declarations, with the same segment name.

segment context [Pro/3]

One or more segments are (during a session with Pro/3) designated as the current segment context. Windows and reports inputting or outputting structure entities will filter out structure entities which are outside the current segment context.

segment name [Pro/3]

All structure entities in the KB i.e. syntagms, synonyms, data element types, entity types, predicate types and functions are assigned a segment name. The segment names serve as simple categorizations of different structure entities. Pro/3's internal or meta entities are assigned segment name "Pro/3", while other are assigned to a model or sub-model segment name defined by the KE. All structure entities with the same name is referred to as a segment.

selection rule [Pro/3]

A class of set implication rules which conclude sentences based on selections based on minimum or maximum values.

sentence [Pro/3]

A knowledge specification which describes "one piece of factual knowledge". A sentence consists of a predicate and a subject and optionally an object. Subjects and objects are both referred as entities.

sentence group [Pro/3]

All factual sentences with the same predicate type belong to the same sentence group.

sentence model [Pro/3]

A model of the sentence structures in a Pro/3 model. The sentence model includes the definitions of data element types, entity types, predicate types and function declarations.

sentence model graph [Pro/3]

An acyclic directed graph which defines the dependencies between sentence model entities and factual sentences in the KB (data element types, entity types, entity keys, predicate types and sentence types).

sentence rule [Pro/3]

A class of rules where the conclusion of the rule is a sentence-like structure. Sentence rules specify how sentences can be derived from other sentences. Sentence rules can refer to certainty rules and functions as sub-specifications (sub-rules). Sentence rules are classified into set rules and simple rules.

sentence type [Pro/3]

All sentences with the same predicate type and the same entity type argument(s) (in the same sequence) belong to the same sentence type.

set implication rule [Pro/3]

Set implication rules define how a set of sentences can be derived from another set of sentences. Set implication rules use one or more of Pro/3's procedures. There are three classes of set rules: statistical rules, accumulation rules and selection rules. Set implication rules are a sub-set of sentence rules.

simple implication rule [Pro/3]

A rule which defines how sentences are derived from other sentences. Procedures cannot be used in simple implication rules.

SQL-type database format [Pro/3]

SQL-type database internals

A Pro/3 knowledge base storage format based on SQL (as opposed native 3kb-type database format).

statistical rule [Pro/3]

A class of set implication rules which conclude statistical-type observations on sets of sentences.

string [Pro/3]

Strings are a domain of data elements (values). Strings are enclosed in quotes (both in NL and in IF) and can contain any characters except the Pro/3 meta-characters. Strings have the same representation both in NL and in IF.

structure knowledge [Pro/3]

A Pro/3 model consists of structural knowledge and application knowledge. The structure knowledge is a meta model which defines the structure of the application knowledge. The structural knowledge consists of terminology knowledge and a sentence model.

string operators [Pro/3]

string operators

Operators which are used to form string expressions.

ST-table [Pro/3]

A ST-table is a table in a SQL database which contains all sentences of a sentence type in unpacked NL-format. The sentences (rows) in the table have either been exported (export table or ad-hoc table) from the knowledge or are being used as an import table.

support rule [Pro/3]

what is inexact rules

A class of inexact rules i.e. used to support computation of certainty factors in certainty rules or membership grades in fuzzy set rules. Support rules are divided into switch rules, map rules, parameter rules and data rules.

suspended record [Pro/3]

KB internals

A KB record which is kept in the KB, but which is ignored by all inference (querying, derivation) type of activities. The suspended record typically has integrity errors (due to change in related meta-data subsequent to its creation), and it needs to revised in connection with the removal of the suspension status.

switch rule [Pro/3]

A class of certainty rules which derives its return value from a switching-type of selection of the certainty returned by either another certainty rule (rule-type switch) or from one of the input parameters (parameter-type switch).

symbol [Pro/3]

Symbols are a domain of data elements (values). A symbol is a hybrid between a string and an identifier. Symbols are enclosed in quotes (both in NL and IF). Symbols can contain multiple elements (separated by |), and each element can correspond to a string or an identifier. Identifier components have a different representation in NL and IF (corresponding to the difference in the representations of identifiers). String components have the same representation in NL and IF.

synonym [Pro/3]

A synonym is an alternative natural language representation of a syntagm (an alternative sequence of natural language tokens (words)) .

syntagm [Pro/3]

A sequence of one or more "natural language tokens" representing one syntactic concept, and this concept's mapping into a word triplet (KB name, a syntax class and syntax form). Sometimes "syntagm" refers only to the word sequence.

syntax tree [Pro/3]

An intermediary knowledge representation format used during translation from natural natural language format to internal format or rule-tree format.

system realm [Pro/3]

A pre-defined set of realms with names starting with $.

term

A constant, a variable or the application of a function.

terminology [Pro/3]

A "complete" set of syntagms and synonyms in a given natural language which defines all syntagms in a Pro/3 model. A KB model can contain two or more alternative terminologies. One terminology is designated as the current terminology during a session with Pro/3. The current terminology can be changed any time.

theory

A set of axioms describing a field of knowledge.

un-parameterized predicate [Pro/3]

A predicate which does not have data elements.

unary predicate [Pro/3]

A predicate which takes one entity argument.

union rule [Pro/3]

A class of fuzzy set rules which computes the membership grade for the union of two or more fuzzy sets (by using one of the four union methods standard union, algebraic product union, bounded difference union or drastic union).

value [Pro/3]

A literal value, either (i) a simple literal of any of Pro/3's domain; or (ii) a list of simple literals

word [Pro/3]

NL interface

A word (or word triplet) consists of a KB name, a syntax class and a syntax form. See also syntagm.

work database [Pro/3]