924,781 research outputs found
Stream Reasoning in Temporal Datalog
In recent years, there has been an increasing interest in extending
traditional stream processing engines with logical, rule-based, reasoning
capabilities. This poses significant theoretical and practical challenges since
rules can derive new information and propagate it both towards past and future
time points; as a result, streamed query answers can depend on data that has
not yet been received, as well as on data that arrived far in the past. Stream
reasoning algorithms, however, must be able to stream out query answers as soon
as possible, and can only keep a limited number of previous input facts in
memory. In this paper, we propose novel reasoning problems to deal with these
challenges, and study their computational properties on Datalog extended with a
temporal sort and the successor function (a core rule-based language for stream
reasoning applications)
Classical Mathematics for a Constructive World
Interactive theorem provers based on dependent type theory have the
flexibility to support both constructive and classical reasoning. Constructive
reasoning is supported natively by dependent type theory and classical
reasoning is typically supported by adding additional non-constructive axioms.
However, there is another perspective that views constructive logic as an
extension of classical logic. This paper will illustrate how classical
reasoning can be supported in a practical manner inside dependent type theory
without additional axioms. We will see several examples of how classical
results can be applied to constructive mathematics. Finally, we will see how to
extend this perspective from logic to mathematics by representing classical
function spaces using a weak value monad.Comment: v2: Final copy for publicatio
Picturing perturbative parton cascades in QCD matter
Based on parametric reasoning, we provide a simple dynamical picture of how a
perturbative parton cascade, in interaction with a QCD medium, fills phase
space as a function of time.Comment: 9 pages, 3 figure
Refactoring pattern matching
Defining functions by pattern matching over the arguments is advantageous for understanding and reasoning, but it tends to expose the implementation of a datatype. Significant effort has been invested in tackling this loss of modularity; however, decoupling patterns from concrete representations while maintaining soundness of reasoning has been a challenge. Inspired by the development of invertible programming, we propose an approach to program refactoring based on a right-invertible language rinv—every function has a right (or pre-) inverse. We show how this new design is able to permit a smooth incremental transition from programs with algebraic datatypes and pattern matching, to ones with proper encapsulation, while maintaining simple and sound reasoning
Quantum Barnes function as the partition function of the resolved conifold
We suggest a new strategy for proving large duality by interpreting
Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau
threefold as different characterizations of the same holomorphic function. For
the resolved conifold this function turns out to be the quantum Barnes
function, a natural -deformation of the classical one that in its turn
generalizes Euler's gamma function. Our reasoning is based on a new formula for
this function that expresses it as a graded product of -shifted
multifactorials.Comment: 47 pages, 7 figure
Knowledge-based Autonomous Test Engineer (KATE)
Mathematical models of system components have long been used to allow simulators to predict system behavior to various stimuli. Recent efforts to monitor, diagnose, and control real-time systems using component models have experienced similar success. NASA Kennedy is continuing the development of a tool for implementing real-time knowledge-based diagnostic and control systems called KATE (Knowledge based Autonomous Test Engineer). KATE is a model-based reasoning shell designed to provide autonomous control, monitoring, fault detection, and diagnostics for complex engineering systems by applying its reasoning techniques to an exchangeable quantitative model describing the structure and function of the various system components and their systemic behavior
Exploration of high school students' reasoning in solving trigonometric function problems
Reasoning has been extensively studied by many experts. However, Research on student reasoning in trigonometric problem solving, particularly those related to logical thinking skills is still sorely needed. This study aimed to explore students' reasoning in solving trigonometric function problems regarding logical thinking skills. The research was conducted using a qualitative approach. The research subjects involved high school students in Palopo, Indonesia. Based on the logical ability test results, three subjects were selected, namely students with high, medium, and low logical abilities. Research instruments in mathematical problem-solving tasks and interview guidelines are valid and reliable. Data collection was carried out through task-based interviews and think-aloud. The results of the study: (1) the reasoning subjects with high and moderate logical abilities in solving trigonometric function problems are the same in every type of question, always starting with inductive reasoning and then doing deductive reasoning (2) the reasoning of subjects with high and medium logical abilities is different in solving trigonometric function problems in the initial identification. Subjects with low logical ability showed no mental activity in solving trigonometric function problems. The research finding is that the subject has a high logical ability and is solving trigonometric function problems first by inductive reasoning and then deductive reasoning. In general, it is concluded that students with high and moderate logical abilities use inductive and deductive thinking patterns interchangeably in solving trigonometric function problems
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