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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 time-dependent 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 meta-predicates 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 non-temporal 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 eigen-decomposition graph matching algorithm and the symmetric polynomial transform graph matching algorithm are critically examined and improved as two new algorithms named meta-basis graph matching algorithm and sort based graph matching algorithm respectively, where the meta-basis graph matching algorithm works better for 0-1 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
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
An Integrated First-Order Theory of Points and Intervals over Linear Orders (Part II)
There are two natural and well-studied approaches to temporal ontology and
reasoning: point-based and interval-based. Usually, interval-based temporal
reasoning deals with points as a particular case of duration-less intervals. A
recent result by Balbiani, Goranko, and Sciavicco presented an explicit
two-sorted point-interval temporal framework in which time instants (points)
and time periods (intervals) are considered on a par, allowing the perspective
to shift between these within the formal discourse. We consider here two-sorted
first-order languages based on the same principle, and therefore including
relations, as first studied by Reich, among others, between points, between
intervals, and inter-sort. We give complete classifications of its
sub-languages in terms of relative expressive power, thus determining how many,
and which, are the intrinsically different extensions of two-sorted first-order
logic with one or more such relations. This approach roots out the classical
problem of whether or not points should be included in a interval-based
semantics. In this Part II, we deal with the cases of all dense and the case of
all unbounded linearly ordered sets.Comment: This is Part II of the paper `An Integrated First-Order Theory of
Points and Intervals over Linear Orders' arXiv:1805.08425v2. Therefore the
introduction, preliminaries and conclusions of the two papers are the same.
This version implements a few minor corrections and an update to the
affiliation of the second autho
Modal Logics of Topological Relations
Logical formalisms for reasoning about relations between spatial regions play
a fundamental role in geographical information systems, spatial and constraint
databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's
modal logic of time intervals based on the Allen relations, we introduce a
family of modal logics equipped with eight modal operators that are interpreted
by the Egenhofer-Franzosa (or RCC8) relations between regions in topological
spaces such as the real plane. We investigate the expressive power and
computational complexity of logics obtained in this way. It turns out that our
modal logics have the same expressive power as the two-variable fragment of
first-order logic, but are exponentially less succinct. The complexity ranges
from (undecidable and) recursively enumerable to highly undecidable, where the
recursively enumerable logics are obtained by considering substructures of
structures induced by topological spaces. As our undecidability results also
capture logics based on the real line, they improve upon undecidability results
for interval temporal logics by Halpern and Shoham. We also analyze modal
logics based on the five RCC5 relations, with similar results regarding the
expressive power, but weaker results regarding the complexity
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