Related papers: Dynamic Probability Logics: Axiomatization & Defin…

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…

The notion of probability plays an important role in almost all areas of science and technology. In modern mathematics, however, probability theory means nothing other than measure theory, and the operational characterization of the notion…

The aim of this paper is to extend probability theory from the classical to the product t-norm fuzzy logic setting. More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called…

This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…

In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…

We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…

What are the functionals of the reward that can be computed and optimized exactly in Markov Decision Processes?In the finite-horizon, undiscounted setting, Dynamic Programming (DP) can only handle these operations efficiently for certain…

In this paper, we investigate arithmetical completeness with respect to finite Kripke models of quantified modal logic. We adapt the finite-model embedding techniques of Artemov and Japaridze to two settings involving finite Kripke models.…

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…

We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…

This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…

Probabilistic programming languages (PPLs) are an expressive and intuitive means of representing complex probability distributions. In that realm, languages like Dice target an important class of probabilistic programs: those whose…

In spite of the rapidly increasing number of applications of machine learning in various domains, a principled and systematic approach to the incorporation of domain knowledge in the engineering process is still lacking and ad hoc solutions…

A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…

In this paper, we prove measurability of event for which a general continuous-time stochastic process satisfies continuous-time Metric Temporal Logic (MTL) formula. Continuous-time MTL can define temporal constrains for physical system in…

In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a…

This paper proposes a notion of branching bisimilarity for non-deterministic probabilistic processes. In order to characterize the corresponding notion of rooted branching probabilistic bisimilarity, an equational theory is proposed for a…

In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. We prove the finite-iteration and asymptotic l\infty-norm…

This work proposes a view of probability as a relative measure rather than an absolute one. To demonstrate this concept, we focus on finite outcome spaces and develop three fundamental axioms that establish requirements for relative…

The central open question in Descriptive Complexity is whether there is a logic that characterizes deterministic polynomial time (PTIME) on relational structures. Towards this goal, we define a logic that is obtained from first-order logic…