Related papers: Probabilistic Epistemic Updates on Algebras

In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical…

In this paper, we propose a novel formalism called Probabilistic Obstruction Temporal Logic (POTL), which extends Obstruction Logic (OL) by incorporating probabilistic elements. POTL provides a robust framework for reasoning about the…

Many machine learning algorithms rely on iterative updates of uncertainty representations, ranging from variational inference and expectation-maximization, to reinforcement learning, continual learning, and multi-agent learning. In the…

Recently, several approaches to updating knowledge bases modeled as extended logic programs have been introduced, ranging from basic methods to incorporate (sequences of) sets of rules into a logic program, to more elaborate methods which…

This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…

Assessing ways in which Language Models can reduce their hallucinations and improve the outputs' quality is crucial to ensure their large-scale use. However, methods such as fine-tuning on domain-specific data or the training of a separate…

The usual epistemic model S5n for a multi-agent system is based on a Kripke frame, which is a graph whose edges are labeled with agents that do not distinguish between two states. We propose to uncover the higher dimensional information…

Probabilistic model checking has been developed for verifying systems that have stochastic and nondeterministic behavior. Given a probabilistic system, a probabilistic model checker takes a property and checks whether or not the property…

The purpose of this paper is to develop further the main concepts of Phenomena Dynamic Logic (P-DL) and Cognitive Dynamic Logic (C-DL), presented in the previous paper. The specific character of these logics is in matching vagueness or…

We study the properties of tilting modules in the context of properly stratified algebras. In particular, we answer the question when the Ringel dual of a properly stratified algebra is properly stratified itself, and show that the class of…

This work proposes a Dynamic Epistemic Logic with Communication Actions that can be performed concurrently. Unlike Concurrent Epistemic Action Logic introduced by Ditmarsch, Hoek and Kooi, where the concurrency mechanism is the so called…

Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…

A new computational method that uses polynomial equations and dynamical systems to evaluate logical propositions is introduced and applied to Goedel's incompleteness theorems. The truth value of a logical formula subject to a set of axioms…

The interpretation of propositional dynamic logic (PDL) through Kripke models requires the relations constituting the interpreting Kripke model to closely observe the syntax of the modal operators. This poses a significant challenge for an…

Probabilistic frames are a generalization of finite frames into the Wasserstein space of probability measures with finite second moment. We introduce new probabilistic definitions of duality, analysis, and synthesis and investigate their…

We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic)…

Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…

Formal, automated theorem proving has long been viewed as a challenge to artificial intelligence. We introduce here a new approach to computer theorem proving, one that employs specialized language models for Lean4 proof generation combined…

In this article, we continue the study of tense symmetric Heyting algebras (or TSH-algebras). These algebras constitute a generalization of tense algebras. In particular, we describe a discrete duality for TSHalgebras bearing in mind the…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…