Related papers: Quantifying over Boolean announcements
According to Aumann's celebrated theorem, rational agents cannot agree to disagree. In other words, agents who once shared a common prior probability distribution and who have common knowledge about their posteriors cannot assign different…
The concept of complementarity in combination with a non-Boolean calculus of propositions refers to a pivotal feature of quantum systems which has long been regarded as a key to their distinction from classical systems. But a non-Boolean…
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
We note the separation of a quantum description of an experiment into a statement of results (as probabilities) and an explanation of these results (in terms of linear operators). The inverse problem of choosing an explanation to fit given…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Counting propositional logic was recently introduced in relation to randomized computation and shown able to logically characterize the full counting hierarchy. In this paper we aim to clarify the intuitive meaning and expressive power of…
We introduce a probabilistic extension of Levy's Call-By-Push-Value. This extension consists simply in adding a " flipping coin " boolean closed atomic expression. This language can be understood as a major generalization of Scott's PCF…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
The term ``Boolean category'' should be used for describing an object that is to categories what a Boolean algebra is to posets. More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in…
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 article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…
Large language models (LLMs) exhibit strong general capabilities, but their deployment in high-stakes domains is hindered by their opacity and unpredictability. Recent work has taken meaningful steps towards addressing these issues by…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
This article discusses completeness of Boolean Algebra as First Order Theory in Goedel's meaning. If Theory is complete then any possible transformation is equivalent to some transformation using axioms, predicates etc. defined for this…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
Traditionally, an agent's beliefs would come from what the agent can see, hear, or sense. In the modern world, beliefs are often based on the data available to the agents. In this work, we investigate a dynamic logic of such beliefs that…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…