Logic-based approach

The rationale of logical-based approach is to exploit the formal representation of the logical knowledge of a given activity, sensor data modelling and to use logical reasoning to perform activity recognition. The researchers have integrated various activity theories to create logical

rules based on the models such as situation theory, lattice theory (Description logic (DL)), and event theory (event calculus (EC) [61]). In general, procedure creating a logical-based model includes:

1. Logical formalism to explicitly define and describe a library of activity models for all possible activities in a domain

2. Aggregate and transform sensor data into logical terms and formula 3. Performing logical reasoning, e.g., deduction, abduction and subsumption

High-quality ontologies are important for many applications. The Description Logics (DLs) have been recognised to be an ideal candidate as an ontology language in the past. However, there were restricted expressivity features and limited collection of knowledge-based ontology models. Nevertheless, recent research in DLs have aided to bridge this gap. The suitability of DLs as ontology languages has been highlighted by the inclusion in the several web ontology languages (OWLs), including OWL (OWL DL in specific). OWL is based on the resource description framework (RDF) schema syntax, which uses DL SHIQ to achieve a balance between expressiveness and the complexity level for the reasoning. Although the SHIQ presents high complexity for decision-making problems, many reasoning engines such as FaCT++, RACER, and Pallet have been used with impressive results. Therefore, allowing one to describe countless numbers of real-world facts as a set of rules. The inference engines can then be applied to deduce implicit knowledge data from the explicitly represented knowledge data model. The inferencing engines apply the set of rules to all the relationships, classes, methods and objects and instances.

Description Logics (DLs) are a family of knowledge representation language to explicitly represent the concepts and relations in a structured and formal means. For example, let’s assume the following relationship “A man that is married to a female who is an accountant has at least

three children together, and all of whom are a musician”. Figure 2.10 describes the above

notion in a simple statement. It uses various formal notations such as the conjunction (∩), negation (¬), the existential restriction constructor (∃R.C), the value restriction constructor (∀R.C), and the number restriction constructor (≥ n R). To apply this rule, let’s say Bob is married to Alice, who is an accountant, and all of their three children are musicians.

Figure 2.10. An example of Description Logics (DLs) statement using formal notations Human ∩ ¬Female ∩ ∃married.Accountant ∩ (≥3 hasChild) ∩ ∀hasChild.Musician

Similarly, more axioms can be defined using Description Logic Program (DLP) and

ALCIO TBox syntax; see Table 2.4 for more details.

Table 2.4. More example of representing axioms using DLP and ALCIO TBox syntax

Simple axioms Description Logic Program (DLP) ALCIO TBox (1) Every man or woman is an adult

(2) A grown-up is a human who is an adult

(3) A woman who has somebody as a child is a mother

(4) An orphan is the child of humans who are dead

(5) A lonely child has no siblings (6) AI researchers are employed by

the IBM

Man ⊆ Adult (1) Woman ⊆ Adult (1) GrownUp ⊆ Human (2) GrownUp ⊆ Adult (2)

Woman ∩ ∃childOf−.T ⊆ Mother (3) Orphan ⊆ ∀childOf.Dead (4) Orphan ⊆ ∀childOf.Human (4) LonelyChild ⊆ ∀siblingOf.⊥ (5)

AIResearcher ⊆ ∃employedBy.{IBM} (6)

Man ∪ Woman ⊆ Adult (1) GrownUp ⊆ Human Adult (2) Woman ∃ childOf−. ⊆ Mother (3) Orphan ⊆ ∀childOf.(Dead ∩ Human) (4)

LonelyChild ⊆ ¬∃siblingOf.T (5) AIResearcher ⊆ ∃employedBy.{IBM} (6)

In general, the reasoning can be performed in many ways; the two common approaches are consequence-based and tableau-based. The consequence-based approach which uses horn fragment, whereas the tableau-based approach computes the classification from the given completion rules to infer additional facts. The logic ALC is one of the basic logic, which can be further extended for better expressivity, i.e. SHOIN. More detailed information about the family of DLs can be obtained from [62]–[65].

Furthermore, a knowledge representation system based on DL has two main components, terminological axioms (Tbox) and assertions formalism (Abox). The Tbox is a terminology used to define concepts and roles definition (i.e. classes, properties, and relationships in the ontology), whereas Abox can be used to describe an individual or the class by enumerating the individual instances[62], [66]. The Tbox can be used to introduce names or an abbreviation for a complex description. For example, we could introduce the abbreviation HappyMan for the concept described above. More expressive terminological formalisms allow the statement of constraints such as ∃hasChild.Human ⊆ Human, which says that only humans can have human children. Abox can be used to state the properties of individuals. For example, the assertions HappyMan(BOB), hasChild(TOM, JESS) state that Tom belongs to the concept HappyMan and that Jess is one of his children. A set of such assertions is called an ABox, and the named individuals that occur in ABox assertions are called ABox individuals[62], (See Table 2.5).

The logical rules are now being combined with ontologies to formally represent knowledge. For instance, RuleML language is being used in [67] this study to represent points of interest to a targeted group. In addition, semantic web rule language (SWRL) was created with the combination descriptive logic and production of external logic, i.e. OWL DL, OWL Lite, and Rule ML, see more [65], [68], [69]. In general, the logical-based modelling and reasoning approach has its own benefits and limitations. This has been summarised in Table 2.6.

Table 2.5. Example of Terminological axioms (Tbox) and Assertions formalism (Abox)

Tbox axioms Abox formalism

∃hasChild.Human ⊆ Human HappyMan(BOB), hasChild(TOM, JESS)

Table 2.6. Key strengths and weakness of knowledge-driven logical-based modelling and reasoning Logical-based modelling and reasoning

Strength Weaknesses

- Semantically clear and elegant for reasoning.

- Easy to incorporate domain knowledge and heuristics for activity models.

- Ability to represent fuzziness and uncertainty. - Minimal support for measuring the efficiency

of the models

- Lack of learning ability and the evolution of the rules.