Related papers: Can Uncertainty Management be Realized in a Finite…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
Despite widespread success in language understanding and generation, large language models (LLMs) exhibit unclear and often inconsistent behavior when faced with tasks that require probabilistic reasoning. In this work, we present the first…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is well known that both problems are undecidable.…
We study decision dependent distributionally robust optimization models, where the ambiguity sets of probability distributions can depend on the decision variables. These models arise in situations with endogenous uncertainty. The developed…
We explore new interactions between finite model theory and classical streams of universal algebra and semigroup theory. A key result is an example of finite algebras whose variety is not finitely axiomatisable in first order logic, but…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this…
In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A…
This paper addresses two central problems for probabilistic processing models: parameter estimation from incomplete data and efficient retrieval of most probable analyses. These questions have been answered satisfactorily only for…
Several Artificial Intelligence schemes for reasoning under uncertainty explore either explicitly or implicitly asymmetries among probabilities of various states of their uncertain domain models. Even though the correct working of these…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
This paper presents formulae that can solve various seemingly hopeless philosophical conundrums. We discuss the simulation argument, teleportation, mind-uploading, the rationality of utilitarianism, and the ethics of exploiting artificial…
Over time, there have hen refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distributions depict a complete ordering among the propositions of interest, yet…