Related papers: Dynamic Probability Logics: Axiomatization & Defin…
We consider synthesis of control policies that maximize the probability of satisfying given temporal logic specifications in unknown, stochastic environments. We model the interaction between the system and its environment as a Markov…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
This text presents an unified approach of probability and statistics in the pursuit of understanding and computation of randomness in engineering or physical or social system with prediction with generalizability. Starting from elementary…
In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…
In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…
$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…
We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic…
The rise of parallel computing hardware has made it increasingly important to understand which nonlinear state space models can be efficiently parallelized. Recent advances like DEER (arXiv:2309.12252) and DeepPCR (arXiv:2309.16318) recast…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…
We investigate the decidability of model-checking logics of time, knowledge and probability, with respect to two epistemic semantics: the clock and synchronous perfect recall semantics in partially observed discrete-time Markov chains.…
Hay esbozos seg\'un los cuales las probabilidades se cuentan como la fundaci\'on de la teor\'i a matem\'atica de las estad\'isticas. Mas la significaci\'on f\'isica de las probabilidades matem\'aticas son oscuros, muy poco entendidos.…
Many real-world decision-making problems face the off-dynamics challenge: the agent learns a policy in a source domain and deploys it in a target domain with different state transitions. The distributionally robust Markov decision process…
We present the Sum-Product Probabilistic Language (SPPL), a new probabilistic programming language that automatically delivers exact solutions to a broad range of probabilistic inference queries. SPPL translates probabilistic programs into…
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
We consider partially observable Markov decision processes (POMDPs) with {\omega}-regular conditions specified as parity objectives. The class of {\omega}-regular languages extends regular languages to infinite strings and provides a robust…
We investigate the decidability of model-checking logics of time, knowledge and probability, with respect to two epistemic semantics: the clock and synchronous perfect recall semantics in partially observed discrete-time Markov chains.…
Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modeling of physical phenomena to computational methods. A PDMP is…