Related papers: A logic for reasoning about upper probabilities
We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
This paper argues for a modal view of probability. The syntax and semantics of one particularly strong probability logic are discussed and some examples of the use of the logic are provided. We show that it is both natural and useful to…
This contribution derives from a rather extensive study on the foundations of probability. We start by discussing critically the two main models of the random event in Probability Theroy and cast light over a number of incongruities. We…
Recent advances in AI have been significantly driven by the capabilities of large language models (LLMs) to solve complex problems in ways that resemble human thinking. However, there is an ongoing debate about the extent to which LLMs are…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most…
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…
We consider team semantics for propositional logic, continuing our previous work (Yang & V\"a\"an\"anen 2016). In team semantics the truth of a propositional formula is considered in a set of valuations, called a team, rather than in an…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The propositional logic is generalized on the real numbers field. The logical analog of the Bernoulli independent tests scheme is constructed. The variant of the nonstandard analysis is adopted for the definition of the logical function,…
Argumentation is a non-monotonic process. This reflects the fact that argumentation involves uncertain information, and so new information can cause a change in the conclusions drawn. However, the base logic does not need to be…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
This paper considers the challenges Large Language Models (LLMs) face when reasoning over text that includes information involving uncertainty explicitly quantified via probability values. This type of reasoning is relevant to a variety of…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
I introduce PEDAL -- a probabilistic epistemic logic meant to capture, in propositional dynamic terms, the epistemic state of an agent engaged in checking whether a program meets its specification. Semantically, PEDAL is built `on top of'…
This paper considers the notion of possible events which are insignificant in probabilistic analysis (i.e. events that have zero probability). The paper discusses the method of modal logic based on "possible worlds" and discusses a…
We introduce an expressive probabilistic temporal epistemic logic PTEL suitable to reason about uncertain knowledge of a non-rigid set of agents that can be changed during time. We define semantics for PTEL as Kripke models with epistemic…
We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly…