Title:

A complete reified temporal logic and its applications

Temporal representation and reasoning plays a fundamental and increasingly important role in some areas of Computer Science and Artificial Intelligence. A natural approach to represent and reason about timedependent knowledge is to associate them with instantaneous time points and/or durative time intervals. In particular, there are various ways to use logic formalisms for temporal knowledge representation and reasoning. Based on the chosen logic frameworks, temporal theories can be classified into modal logic approaches (including prepositional modal logic approaches and hybrid logic approaches) and predicate logic approaches (including temporal argument methods and temporal reification methods). Generally speaking, the predicate logic approaches are more expressive than the modal logic approaches and among predicate logic approaches, temporal reification methods are even more expressive for representing and reasoning about general temporal knowledge. However, the current reified temporal logics are so complicate that each of them either do not have a clear definition of its syntax and semantics or do not have a sound and complete axiomatization. In this thesis, a new complete reified temporal logic (CRTL) is introduced which has a clear syntax, semantics, and a complete axiomatic system by inheriting from the initial first order language. This is the main improvement made to the reification approaches for temporal representation and reasoning. It is a true reified logic since some metapredicates are formally defined that allow one to predicate and quantify over prepositional terms, and therefore provides the expressive power to represent and reason about both temporal and nontemporal relationships between prepositional terms. For a special case, the temporal model of the simplified CRTL system (SCRTL) is defined as scenarios and graphically represented in terms of a directed, partially weighted or attributed, simple graph. Therefore, the problem of matching temporal scenarios is transformed into conventional graph matching. For the scenario graph matching problem, the traditional eigendecomposition graph matching algorithm and the symmetric polynomial transform graph matching algorithm are critically examined and improved as two new algorithms named metabasis graph matching algorithm and sort based graph matching algorithm respectively, where the metabasis graph matching algorithm works better for 01 matrices while the sort based graph matching algorithm is more suitable for continuous real matrices. Another important contribution is the node similarity graph matching framework proposed in this thesis, based on which the node similarity graph matching algorithms can be defined, analyzed and extended uniformly. We prove that that all these node similarity graph matching algorithms fail to work for matching circles.
