Related papers: Relational Reasoning for Markov Chains in a Probab…
Pre-trained language models (LMs) have shown remarkable reasoning performance using explanations or chain-of-thoughts (CoT)) for in-context learning. On the other hand, these reasoning tasks are usually presumed to be more approachable for…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
The role of uncertainty in data management has become more prominent than ever before, especially because of the growing importance of machine learning-driven applications that produce large uncertain databases. A well-known approach to…
In this paper, we consider the problem of lifted inference in the context of Prism-like probabilistic logic programming languages. Traditional inference in such languages involves the construction of an explanation graph for the query and…
Formal mathematics and computer science proofs are formalized using Hilbert-Russell-style logical systems which are designed to not admit paradoxes and self-refencing reasoning. These logical systems are natural way to describe and reason…
There has been substantial progress in the inference of formal behavioural specifications from sample trajectories, for example, using Linear Temporal Logic (LTL). However, these techniques cannot handle specifications that correctly…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
Symbolic event recognition systems have been successfully applied to a variety of application domains, extracting useful information in the form of events, allowing experts or other systems to monitor and respond when significant events are…
A classical approach to formal policy synthesis in stochastic dynamical systems is to construct a finite-state abstraction, often represented as a Markov decision process (MDP). The correctness of these approaches hinges on a behavioural…
Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several…
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
This paper explores several extensions of proof nets for the Lambek calculus in order to handle the different connectives of display logic in a natural way. The new proof net calculus handles some recent additions to the Lambek vocabulary…
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.…
We introduce a sound and complete equational theory capturing equivalence of discrete probabilistic programs, that is, programs extended with primitives for Bernoulli distributions and conditioning, to model distributions over finite sets…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
Recently, authors have proposed under-approximate logics for reasoning about programs. So far, all such logics have been confined to reasoning about individual program behaviours. Yet there exist many over-approximate relational logics for…