Business rules should be validated by business domain experts, and hence specified using concepts and languages easily understood by business people. This is the ninth in a series of articles on expressing business rules formally in a high-level, textual language. The first article [4] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [5] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [6] covered verbalization of basic external uniqueness constraints. Article four [7] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [8] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusive-or constraints) over sets of roles. Article six [9] considered verbalization of value constraints. Article seven [10] examined verbalization of subset constraints. Article eight [11] discussed verbalization of equality constraints. This ninth article discusses verbalization of exclusion constraints. Verbalization of exclusion constraints between single roles Figure 1 shows an ORM schema for recording when an application is submitted, and optionally when it is approved or rejected. The circled “X ” connecting the approval and rejection roles played by Application indicates that for each state of the business domain, the population of these two roles is mutually exclusive. In other words, if we record the fact that an application was approved on some date, we cannot at the same time record the fact that that application was also rejected on some (possibly other) date. This illustrates a simple exclusion constraint between two fact type roles. An exclusion constraint may be applied only if the roles are compatible (i.e. based on identical or overlapping types). Application (Nr) Figure 1 An exclusion constraint between single roles. was submitted on was approved on was rejected on

Business rules should be validated by business domain experts, and hence specified in a language easily understood by business people. This is the fourteenth in a series of articles on expressing business rules formally in a high-level, textual language. The first article [3] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [4] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [5] covered verbalization of basic external uniqueness constraints. Article four [6] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [7] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusiveor constraints) over sets of roles. Article six [8] considered verbalization of value constraints. Article seven [9] examined verbalization of subset constraints. Article eight [10] discussed verbalization of equality constraints. Article nine [11] covered verbalization of exclusion constraints. Article ten [12] dealt with verbalization of internal frequency constraints on single roles. Article eleven [13] considered verbalization of multi-role, and external, frequency constraints. Article twelve [14] discussed verbalization of ring constraints. Article thirteen [15] covered verbalization of basic subtype constraints. This article discusses why subtype definitions are needed, and how to verbalize them. Why Subtype? There are three main reasons for including subtyping in an information model. The most important reason is to constrain certain roles to be played only by specific subtypes. For example, in a hospital domain, prostate status may be recorded only for male patients, and pregnancy counts (number of pregnancies) may be recorded only for female patients. Figure 1 depicts this situation in ORM 2 [16], UML [18], and Barker ER [1] notations.

Business rules should be validated by business domain experts, and hence specified in a language easily understood by business people. This is the eleventh in a series of articles on expressing business rules formally in a high-level, textual language. The first article [2] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [3] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [4] covered verbalization of basic external uniqueness constraints. Article four [5] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [6] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusiveor constraints) over sets of roles. Article six [7] considered verbalization of value constraints. Article seven [8] examined verbalization of subset constraints. Article eight [9] discussed verbalization of equality constraints. Article nine [10] covered verbalization of exclusion constraints. Article ten [11] dealt with verbalization of internal frequency constraints on single roles. This article considers verbalization of more complex frequency constraints: multi-role frequency constraints (applying to sequences of two or more roles); and external frequency constraints (involving more than one predicate). Verbalization of multi-role frequency constraints Consider the report displayed in Table 1, which lists an extract of details about sales of computer monitors. In this domain, cities may be identified simply by their name. There are two kinds of computer monitor: cathode ray tube (CRT); and liquid crystal display (LCD). As a way of ensuring one aspect of completeness, the following business rule applies: for each year and city combination, if we record sales figures at all, we must record the sales figures for both kinds of monitor. For example, the Year-City pair

Business rules should be validated by business domain experts, and hence specified using concepts and languages easily understood by business people. This is the tenth in a series of articles on expressing business rules formally in a high-level, textual language. The first article [3] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [4] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [5] covered verbalization of basic external uniqueness constraints. Article four [6] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [7] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusive-or constraints) over sets of roles. Article six [8] considered verbalization of value constraints. Article seven [9] examined verbalization of subset constraints. Article eight [10] discussed verbalization of equality constraints. Article nine [11] covered verbalization of exclusion constraints. This tenth article deals with verbalization of internal frequency constraints on single roles. Verbalization of internal frequency constraints on single roles

Business rules should be validated by business domain experts, and hence specified in a language easily understood by business people. This is the twelfth in a series of articles on expressing business rules formally in a high-level, textual language. The first article [2] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [3] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [4] covered verbalization of basic external uniqueness constraints. Article four [5] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [6] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusiveor constraints) over sets of roles. Article six [7] considered verbalization of value constraints. Article seven [8] examined verbalization of subset constraints. Article eight [9] discussed verbalization of equality constraints. Article nine [10] covered verbalization of exclusion constraints. Article ten [11] dealt with verbalization of internal frequency constraints on single roles. Article eleven [12] considered verbalization of multi-role frequency constraints and external frequency constraints. This article discusses verbalization

Business rules should be validated by business domain experts, and hence specified in a language easily understood by business people. This is the fourteenth in a series of articles on expressing business rules formally in a high-level, textual language. The first article [2] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [3] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [4] covered verbalization of basic external uniqueness constraints. Article four [5] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [6] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusiveor constraints) over sets of roles. Article six [7] considered verbalization of value constraints. Article seven [8] examined verbalization of subset constraints. Article eight [9] discussed verbalization of equality constraints. Article nine [10] covered verbalization of exclusion constraints. Article ten [11] dealt with verbalization of internal frequency constraints on single roles. Article eleven [12] considered verbalization of multi-role, and external, frequency constraints. Article twelve [13] discussed verbalization of ring

Business rules should be validated by business domain experts, and hence specified in a language easily understood by business people. This is the fourteenth in a series of articles on expressing business rules formally in a high-level, textual language. The first article [3] discussed criteria for a business rules language, and verbalization of simple uniqueness and mandatory constraints on binary associations. Article two [4] examined hyphen-binding, and verbalization of internal uniqueness constraints that span a whole association, or that apply to n-ary associations. Article three [5] covered verbalization of basic external uniqueness constraints. Article four [6] considered relational-style verbalization of external uniqueness constraints involving nesting or long join paths, as well as attribute-style verbalization of uniqueness constraints and simple mandatory constraints. Article five [7] discussed verbalization of mandatory constraints on roles of n-ary associations, and disjunctive mandatory constraints (also known as inclusiveor constraints) over sets of roles. Article six [8] considered verbalization of value constraints. Article seven [9] examined verbalization of subset constraints. Article eight [10] discussed verbalization of equality constraints. Article nine [11] covered verbalization of exclusion constraints. Article ten [12] dealt with verbalization of internal frequency constraints on single roles. Article eleven [13] considered verbalization of multi-role, and external, frequency constraints. Article twelve [14] discussed verbalization of ring