Definition of Semantic Decision Table
An SDT uses the tabular presentation as a decision table does. Following the de facto international standard [CSA 1970], three groups of information in a decision table are the basic decision table elements: the conditions, the actions (or decisions), and the rules that describe which actions might be taken based on the combination of conditions. A condition stub contains a statement of a condition and each condition entry indicates the relationship between the various conditions in the condition stub. Each action stub has a statement of each action to be taken and the action entries specify whether (or in what order) the action is to be performed for the combination of conditions that are actually met in the rule column. Accordingly, a decision table can be defined as:
Definition 1. A decision table is a triple <C,A,R>, where C is the set of conditions, A is the set of actions aiÎA, and R the set of rules. Each condition ci, ciÎC is defined as <ni,vi> where niÎN is a condition stub label, and viÎV is a condition entry value. Each rule rjÎR is defined as a function rj: (set of) VN -> A.
Table 1. A simple decision table example.
|
Condition |
Column 1 |
… |
Column n |
|
has driver’s license |
yes |
… |
No |
|
Action / Decision |
|
|
|
|
a driver |
* |
… |
|
|
not a driver |
|
... |
* |
Table 1 demonstrates a very simple decision table to check whether a person can be driver or not. Based on Definition 1, the condition “has driver’s license” can be written as - n1: driver’s license (with two condition entries - v1: yes, v2: no). Actions (or decisions) “a driver” and “not a driver” are written as - a1: a driver, a2: not a driver. The decision rule in the Column 1 in Table 1 can be constructed as - r1: <n1, v1>->a1. Or r1: <driver’s license, yes> -> a driver.
Similar to traditional decision tables, SDT is a powerful tool to assist implementing the complex logic of many application domains with a simple and clear tabular presentation. However, often the definition of concepts, variables and rules that underlie traditional decision tables remain or become implicit. A properly annotated SDT, of which rules are generated through a formal ontological commitment, contains semantically rich decision rules.
SDT is modeled in the DOGMA framework, which formulates ontology-based applications as three layers: 1) the ontological lexon base ∑ that consists of lexical representation of concepts and their inter-relations (lexons); 2) the ontological commitment layer that includes lexon interpretation, axioms and domain rules; 3) the application layer that comprises application specific rules.
Initiatively, a lexon l Î∑ is defined as a plausible binary fact-type. It is formalized as a quintuple < γ, t1, r1, r2, t2 > where t1 and t2 are terms[1] that represent two elementary concepts in some language. r1 and r2 are roles referring to the relationships between t1 and t2. γ is a context identifier[2] to disambiguate t1 and t2 and to make r1 and r2 meaningful. For example, we have a lexon <γ, driver’s license, is issued to, has, driver> indicates that a driver’s license is issued to a driver.
Though ontologies can differ in structure and semantics, they are all built on a shared lexon base ∑ through the commitment layer. A commitment is a first-order logical theory, of which the models that connect lexons are interpreted with respect to the application Universe of Discourse. It can be expressed in a commitment language. For example, we apply the uniqueness constraint to describe the fact “each driver’s license is issued to at most one driver” as:
P1 = [γ, driver’s license, is issued to, has, driver]: UNIQ (P1)[3].
An SDT is formalized as:
Definition 2. An SDT is < Γ,Cl,Al,Rl>. γÎΓ is a context identifier pointing to the original decision table and its documents. CL is the set of condition lexons and
The formalization in Definition 2 represents an SDT into two dimensions: in one dimension, an SDT keeps tabular structure. In the other dimension, it is constructed in the DOGMA framework: the lexon base layer that contains decision and action lexons, the ontological commitment layer and the decision rule layer. In the next subsection, we will model the interorganizational ontology engineering with the integration of SDT.
Useful links:
[1] t1 is sometimes called head term and t2 tail term.
[2] As the discussion of how to define a proper context identifier is out of the paper scope, we refer to Pieter's work for the issue on how to disambiguate concepts with the context identifier.
[3] P1 is a semantic path. The semantic path represents the construction direction of a lexon. Each lexon has two construction directions. P1 is the forward construct direction of the lexon <r, driver’s license, is issued to, has, driver>. The backward construction direction is P2=[r, driver, has, is issued to, driver’s license]. We use ORM constraints to constrain the semantic paths. More details can be found in.