203 research outputs found
Probabilistic logics based on Riesz spaces
We introduce a novel real-valued endogenous logic for expressing properties
of probabilistic transition systems called Riesz modal logic. The design of the
syntax and semantics of this logic is directly inspired by the theory of Riesz
spaces, a mature field of mathematics at the intersection of universal algebra
and functional analysis. By using powerful results from this theory, we develop
the duality theory of the Riesz modal logic in the form of an
algebra-to-coalgebra correspondence. This has a number of consequences
including: a sound and complete axiomatization, the proof that the logic
characterizes probabilistic bisimulation and other convenient results such as
completion theorems. This work is intended to be the basis for subsequent
research on extensions of Riesz modal logic with fixed-point operators
On Counting Propositional Logic and Wagner's Hierarchy
We introduce and study counting propositional logic, an extension of propositional logic with counting quantifiers. This new kind of quantification makes it possible to express that the argument formula is true in a certain portion of all possible interpretations. We show that this logic, beyond admitting a satisfactory proof-theoretical treatment, can be related to computational complexity: the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy
On Counting Propositional Logic and Wagner's Hierarchy
We introduce an extension of classical propositional logic with counting quantifiers. These forms of quantification make it possible to express that a formula is true in a certain portion of the set of all its interpretations. Beyond providing a sound and complete proof system for this logic, we show that validity problems for counting propositional logic can be used to capture counting complexity classes. More precisely, we show that the complexity of the decision problems for validity of prenex formulas of this logic perfectly match the appropriate levels of Wagner's counting hierarchy
Human operator performance of remotely controlled tasks: Teleoperator research conducted at NASA's George C. Marshal Space Flight Center
The capabilities within the teleoperator laboratories to perform remote and teleoperated investigations for a wide variety of applications are described. Three major teleoperator issues are addressed: the human operator, the remote control and effecting subsystems, and the human/machine system performance results for specific teleoperated tasks
Foundations of Software Science and Computation Structures
This open access book constitutes the proceedings of the 22nd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2019, which took place in Prague, Czech Republic, in April 2019, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2019. The 29 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with foundational research with a clear significance for software science
Mathematical Logic: Proof Theory, Constructive Mathematics (hybrid meeting)
The Workshop "Mathematical Logic: Proof Theory,
Constructive Mathematics" focused on
proofs both as formal derivations in deductive systems as well as on
the extraction of explicit computational content from
given proofs in core areas of ordinary mathematics using proof-theoretic
methods. The workshop contributed to the following research strands: interactions between foundations and applications; proof mining; constructivity in classical logic; modal logic and provability logic; proof theory and theoretical computer science; structural proof theory
Measures and all that --- A Tutorial
This tutorial gives an overview of some of the basic techniques of measure
theory. It includes a study of Borel sets and their generators for Polish and
for analytic spaces, the weak topology on the space of all finite positive
measures including its metrics, as well as measurable selections. Integration
is covered, and product measures are introduced, both for finite and for
arbitrary factors, with an application to projective systems. Finally, the
duals of the Lp-spaces are discussed, together with the Radon-Nikodym Theorem
and the Riesz Representation Theorem. Case studies include applications to
stochastic Kripke models, to bisimulations, and to quotients for transition
kernels
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