12,765 research outputs found
Probabilistic Interval Temporal Logic and Duration Calculus with Infinite Intervals: Complete Proof Systems
The paper presents probabilistic extensions of interval temporal logic (ITL)
and duration calculus (DC) with infinite intervals and complete Hilbert-style
proof systems for them. The completeness results are a strong completeness
theorem for the system of probabilistic ITL with respect to an abstract
semantics and a relative completeness theorem for the system of probabilistic
DC with respect to real-time semantics. The proposed systems subsume
probabilistic real-time DC as known from the literature. A correspondence
between the proposed systems and a system of probabilistic interval temporal
logic with finite intervals and expanding modalities is established too.Comment: 43 page
Temporal Data Modeling and Reasoning for Information Systems
Temporal knowledge representation and reasoning is a major research field in Artificial
Intelligence, in Database Systems, and in Web and Semantic Web research. The ability to
model and process time and calendar data is essential for many applications like appointment
scheduling, planning, Web services, temporal and active database systems, adaptive
Web applications, and mobile computing applications. This article aims at three complementary
goals. First, to provide with a general background in temporal data modeling
and reasoning approaches. Second, to serve as an orientation guide for further specific
reading. Third, to point to new application fields and research perspectives on temporal
knowledge representation and reasoning in the Web and Semantic Web
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
Algebraic foundations for qualitative calculi and networks
A qualitative representation is like an ordinary representation of a
relation algebra, but instead of requiring , as
we do for ordinary representations, we only require that , for each in the algebra. A constraint
network is qualitatively satisfiable if its nodes can be mapped to elements of
a qualitative representation, preserving the constraints. If a constraint
network is satisfiable then it is clearly qualitatively satisfiable, but the
converse can fail. However, for a wide range of relation algebras including the
point algebra, the Allen Interval Algebra, RCC8 and many others, a network is
satisfiable if and only if it is qualitatively satisfiable.
Unlike ordinary composition, the weak composition arising from qualitative
representations need not be associative, so we can generalise by considering
network satisfaction problems over non-associative algebras. We prove that
computationally, qualitative representations have many advantages over ordinary
representations: whereas many finite relation algebras have only infinite
representations, every finite qualitatively representable algebra has a finite
qualitative representation; the representability problem for (the atom
structures of) finite non-associative algebras is NP-complete; the network
satisfaction problem over a finite qualitatively representable algebra is
always in NP; the validity of equations over qualitative representations is
co-NP-complete. On the other hand we prove that there is no finite
axiomatisation of the class of qualitatively representable algebras.Comment: 22 page
Reasoning about goal-directed real-time teleo-reactive programs
The teleo-reactive programming model is a high-level approach to developing real-time systems that supports hierarchical composition and durative actions. The model is different from frameworks such as action systems, timed automata and TLA+, and allows programs to be more compact and descriptive of their intended behaviour. Teleo-reactive programs are particularly useful for implementing controllers for autonomous agents that must react robustly to their dynamically changing environments. In this paper, we develop a real-time logic that is based on Duration Calculus and use this logic to formalise the semantics of teleo-reactive programs. We develop rely/guarantee rules that facilitate reasoning about a program and its environment in a compositional manner. We present several theorems for simplifying proofs of teleo-reactive programs and present a partially mechanised method for proving progress properties of goal-directed agents. Ā© 2013 British Computer Society
Surreal Time and Ultratasks
This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which includes one task done for each ordinal numberāthus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible
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