Reasoning about time intervals of processes and events is propounded by Allen. His theory of time and action is based on intervals as primitive rather than as derived structure from points (Allen, 1984) as in McDermott's case. A set of 13 mutually exclusive binary relations between two intervals are introduced, i.e., EQUALS, BEFORE, AFTER, MEETS, MET BY, OVERLAPS, OVERLAPPED BY, STARTS, STARTED BY, DURING, CONTAINS, FINISHES and FINISHED_BY. Unlike McDermott's dichotomy of facts and events with respect to time, Allen introduces three ontological categories, i.e., properties, events and processes , to time intervals over which they hold or occur. He denotes the assertion that property p holds over interval i by the formula HOLDS ( p, i ), using axiomatic theorems.

Ma and Knight (1996) proposed Reification approach which serves as a sort of bridge with respect to synthesis of both McDermott's and Allen's theories; as well as to semantics (power of expressiveness) of logical assertions.  It allows one to reason about the truth of assertions over time while preserving the first-order structure of the propositions. It is meant for representing and reasoning about temporal and non-temporal relationships between non-temporal assertions, and for expressing the temporal relations between actions and effects. We consider next a number of applications that adopt temporal reasoning.

## 2.4.1 Existing Systems Applying Temporal Reasoning

Chen worked on uncertain temporal knowledge management (Chen, 1992). The emphasis is on the use of fuzzy logic to handle uncertain (imprecise time-stamp) temporal events: represented in form of possibility distributions. KM involves the creation, acquisition, organization, storage and exploitation of knowledge. The author claimed to manage temporal knowledge but his approach is different from that of KM practice since his focus was mainly on computing intervals between imprecise periods (several hours, long time etc.) of processes' events.

Another direction is that which centers on reasoning about processes in distributed system with emphasis on the sets of states of processes, runs
(execution of network process or protocol) and time points of the runs (Fagin & Halpern, 1994). Their approach is based on Kripke structure (Kripke, 1963) which formalizes intuitions behind event occurrence (possible world). They were able to model and prove the correctness of the probability spaces among processes' states using a language of axiomatization. Also, decision procedures are obtained from the reasoning process.

The common feature of their work with this one is the fact that both reason on knowledge i.e. events and also consider time points of events' states.

However, the discrepancy is that there is no provision for capitalization of knowledge. An apparently similar application is another instance of workflow system.

Workflow system is a complete or partial automation of a business process, in which participants (humans or machine) are involved in a set of activities according to certain procedural rules and constraints (Bettini et al., 2002). Their work aimed at reasoning about the quantitative temporal constraints on the duration of activities and the required synchronization in order to enhance capability of workflow systems. However, they only concentrate on the temporal issue of workflow specification. The notion and framework of flexible temporal properties is applied to scheduling of activities in an office environment and for representing preferences among solutions and possible priorities of the temporal properties (Badaloni et al., 2000). Another system which integrates temporal reasoning and maintenance in medical applications is considered next.