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A modal logic that is strong enough to fully characterize the behavior of a system is called expressive. Recently, with the growing diversity of systems to be reasoned about (probabilistic, cyber-physical, etc.), the focus shifted to…
Given a logic presented in a sequent calculus, a natural question is that of equivalence of proofs: to determine whether two given proofs are equated by any denotational semantics, ie any categorical interpretation of the logic compatible…
We spell out the paradigm of exact conditioning as an intuitive and powerful way of conditioning on observations in probabilistic programs. This is contrasted with likelihood-based scoring known from languages such as Stan. We study exact…
We introduce a language for formally reasoning about programs that combine differential constructs with probabilistic ones. The language harbours, for example, such systems as adaptive cruise controllers, continuous-time random walks, and…
In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type…
Recent findings in multi-agent deep learning systems point towards the emergence of compositional languages. These claims are often made without exact analysis or testing of the language. In this work, we analyze the emergent language…
The field of probabilistic logic programming (PLP) focuses on integrating probabilistic models into programming languages based on logic. Over the past 30 years, numerous languages and frameworks have been developed for modeling, inference…
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…
Formalisms for specifying statistical models, such as probabilistic-programming languages, typically consist of two components: a specification of a stochastic process (the prior), and a specification of observations that restrict the…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
Recent contributions address the problem of language coexistence as that of two species competing to aggregate speakers, thus focusing on the dynamics of linguistic traits across populations. They draw inspiration from physics and biology…
The probability theory is a well-studied branch of mathematics, in order to carry out formal reasoning about probability. Thus, it is important to have a logic, both for computation of probabilities and for reasoning about probabilities,…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
Although randomization has long been used in distributed computing, formal methods for reasoning about probabilistic concurrent programs have lagged behind. No existing program logics can express specifications about the full distributions…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
The behavior of a quantum system depends on how it is measured. How much of what is observed comes from the structure of the quantum system itself and how much from the observer's choice of measurement? We explore these questions by…
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
There is a subset of computational problems that are computable in polynomial time for which an existing algorithm may not complete due to a lack of high performance technology on a mission field. We define a subclass of deterministic…
In this paper we deal with a new approach to probabilistic reasoning in a logical framework. Nearly almost all logics of probability that have been proposed in the literature are based on classical two-valued logic. After making clear the…
This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based…