For a general introduction to sentence rules see What are sentence rules? The basic simple implication rule is described there in detail. Sentence rules are classified as follows:

Rules can not be directly or indirectly recursive. This is related to the processing of the rules by the sentence derivation process.

Generalization Rules - Rules with logical OR (v)

The generalization rule is mainly a rule editor input-concept, since all rules containing logical OR-operators (v) are stored in the KB as a OR-free sub-rules (the OR-operators are eliminated during translation to internal format). Consequently, rules with OR are not supported in PR-format. The above rule is represented as three sub-rules in the KB, corresponding to the three branches of the OR-operator. The following sub-rule represents the first branch of the OR-operator:

Type="expense" (i.e. the assignment of the literal "expense" to the variable named Type, is an example of a variable condition component of a rule).

Rules with open entity type arguments

Note that rules with open entity arguments only can be interpreted via the sentence derivation process. The rules can not be handled by the inference engine directly.

Function calls in sentence rules

Note the following restrictions in calling functions:

• functions can only be called in the rule's condition;
• function calls can only be "assigned" to a simple variable (directly or via an expression);
• a function-call can not be used as actual parameter in another function call.

REFERRING INDIVIDUAL ELEMENTS IN LISTS

Individual list elements (values) can only be accessed indirectly by using the built-in function list element no:

Rules Working On Sets Of Sentences

Set rules conclude sentences which are derived in various ways from sets of other sentences (or sentence combinations ANDed together). Set rules use (call) at least one of Pro/3's procedures in the rule's conclusion. This call looks superficially like a function call, but has otherwise no similarity with such calls. The inference engine's processing of a set rule can be more easily understood in relational database terms: 

• The condition part of the rule defines a condition set, a (usually) non-normalized table where each row either is a sentence or two or more sentences joined  together. 
• The condition set is sometimes viewed as two or more condition sub-sets. Sub-sets are defined as rows in the table with the same value for one or more of the data element types (columns).
• The procedures refer to various type of operations on the data element types of the condition (sub-)set. These operations include sums, averages, minimums. maximums and several other. There are two sub-types of set rules: statistical rules and selection, interpolation, ranking, correlation and accumulation rules. 

The following discusses the set rules in somewhat summarized manner. A comprehensive set of examples with explanation of the different rules in more detail, is mandatory to fully understand the concept and workings of the set rules. 

Note the following restrictions in using procedures:

• procedures can only be used in the rule's conclusion;
• procedures are normally assigned directly to a data element type, however some procedures can form part of an expression (assigned to a data element type);
• a procedure can not be used as actual parameter to another procedure.

Statistical Rules

The statistical rules assign values to the data elements in the concluded sentence by using one or more of the statistical procedures. The value assigned to one or more of the data elements in the conclusion, is determined through a call to one of the statistical procedures. There are 13 statistical procedures in addition to the TIMESERIES_OF-procedure (described under).

The statistical procedures take one, two or no parameters. No parameters are needed by the SENTENCE_COUNT procedure since it simply returns the number of sentences in the  condition (sub-)set. All other procedures require the argument-parameter i.e. the data element from the condition sentence set which is computed on. The procedures which require two parameters view the sentences in condition set as an ordered set. The second parameter (series) is the data element which defines the order (sequence) of the sentences in the condition set.

There is no limit the number or combination of procedure calls in the conclusion. However, the series-parameter must always be the same data element. The inference will check this integrity constraint upon execution of the rule.

Selection, interpolation, ranking, correlation and accumulation rules

The model for Pro/3's interpretation (processing) of a selection/interpolation/accumulation rule is as follows:

1. The condition part of the rule, in a relational database analogy, defines a condition set, a (usually) non-normalized table joined  together of known sentences (tables). The condition sentence set is generated as defined by the rule's condition part. The procedure calls do not have any significance in generating the condition set. (The condition set (depending on the actual rule), may or may not be viewed as two or more condition sub-sets. Sub-sets are defined as condition sentences with same value for on or more of the data elements. ).
2. An adjusted condition set is generated from the set in (1), and manipulated according to the the procedure calls. This set is a subset of the condition set when the MAXIMUM_OF, MINIMUM_OF or UNIQUE_OF procedures are used. It can be either a subset or a superset when the INTERPOLATION or DATE_INTERPOLATION procedures are used. The adjusted condition set has the same number of sentences when the ACCUMULATION_OF, STANDARD_RANKING or CORRELATION_OF procedures are used.
3. The concluded sentences are generated from the adjusted condition set.

A rule must include one, and only one, of the following five procedure call types (corresponding to the five main procedure types):

• one or more calls to the ACCUMULATION_OF procedure - whereby given data element(s) are accumulated over a series of sentences;
• one call to the MAXIMUM_OF procedure - whereby a sentence with the highest value of a given data element in set of sentences is selected. The MAXIMUM_OF procedure can optionally be used in combination with any number of calls to the SELECT sub-procedure;
• one call to the MINIMUM_OF procedure - whereby a sentence with the lowest value of a given data element in set of sentences is selected. The MINIMUM_OF procedure can optionally be used in combination with any number of calls to the SELECT sub-procedure;
• one or more call to the UNIQUE_OF procedure - whereby sentences with unique values for given data elements are selected from a set of sentences. The UNIQUE_OF procedure can optionally be used in combination with any number of calls to the SELECT sub-procedure;
• one call to the INTERPOLATION or DATE_INTERPOLATION procedure - whereby gaps in an ordered set of sentences are filled through interpolation. the INTERPOLATION procedure can optionally be used in combination with any number of calls to the MIDPOINT, PREDECESSOR, SUCCESSOR and FIXED sub-procedures.
• one call to the STANDARD_RANKING or STATISTICAL_RANKING procedure and one or more calls to the SORT procedure, whereby the sentences are assigned a rank depending on the sequence of sentences after sorting.
• one call to the CORRELATION_OF procedure.

Note that the series-parameter must always be the same data element in rules where more than one procedure uses this parameter. 

The selection, interpolation and accumulation procedures can best be understood by considering examples.

Rules calling inexact rules

Inexact rules are used (called) in exactly the same way as functions in sentence rules, with the difference that inexact rule calls require a different internal processing of the rule. The rule is processed as if was a statistical rule. The certainty factor returned by the called rule is either assigned directly to a data element in the conclusion, or indirectly in an expression.

Note that Pro/3 is unconcerned with the semantic interpretation of the returned certainty factor. This is just another data element value. The certainty factor may state the certainty of the sentence as a whole (this might be the typical way of using certainty data elements), but this is not necessarily so. The correct interpretation is only known by the KE.

Note the following restrictions in calling inexact rules:

• inexact rule calls can only be called in the rule's conclusion, i.e. rule calls are "assigned" to a simple data element type (directly or via an expression);
• an inexact rule call can not be used as actual parameter in another inexact rule call.