| Time is a mysterious concept which has drawn much attention among philosophers. For centuries, philosophers have tried very hard to grasp the meaning and to unfold the topology of time. Unfortunately, even through thousands of years of civilization, we still cannot agree on one answer about what time is, let alone a systematical means of representing temporal knowledge. As of now, we are still pondering whether time should be point-like or period-like, linear or branching, discrete or dense, foremost among other questions.; This dissertation consists of two parts and is mainly concerned with the fuzzy aspect of temporal knowledge. This first part deals with the temporal knowledge representation problem encountered in Artificial Intelligence (AI). We employ fuzzy set theory to develop five temporal logics for representing temporal knowledge. The first temporal logic we propose is a simple fuzzy temporal logic called {dollar}Fsb1{dollar}, which is a simple fuzzified version of the time line. Each point in the time line corresponds to a unique fuzzy instant with uniform spreads in {dollar}Fsb1{dollar}. The second temporal logic, {dollar}Fsb2{dollar}, and the third logic, {dollar}Fsb3{dollar}, are generalized fuzzy temporal logics that allow fuzzy instants to have different spreads. The fourth temporal logic, {dollar}Fsb4{dollar}, is a point-based fuzzy modal temporal logic; it introduces modal operators into {dollar}Fsb1{dollar} and {dollar}Fsb2{dollar}. The fifth temporal logic, {dollar}Fsb5{dollar}, is an interval-based fuzzy modal temporal logic that allows modal operators to have interval semantics.; In the second part of this dissertation, we apply the fuzzy interval concept to protocol verification for modeling timing constraints of communication protocols. Traditionally, timing constraints of protocols, such as timeout and transmission delays, are modeled by either time points or time intervals. For example, the Integrated Time Transmission Grammar ({dollar}ITTG{dollar}) model developed at the Ohio State University takes the time interval approach. Although time intervals do provide some flexibilities regarding modeling timing constraints, they still have one drawback. If optimistic bounds are specified, we need to worry about reliability. If pessimistic bounds are provided, the question is whether the results of computation are of any use. However, a fuzzy interval provides both optimistic and pessimistic bounds simultaneously. Therefore, in the second part of this dissertation, we present our work on extending the {dollar}ITTG{dollar} model to the Integrated Fuzzy Time Transmission Grammar ({dollar}IFTTG{dollar}) model for verification and performance analysis of communication protocols. |
