Related papers: Semantics of higher-order probabilistic programs w…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
Recent advances in neural symbolic learning, such as DeepProbLog, extend probabilistic logic programs with neural predicates. Like graphical models, these probabilistic logic programs define a probability distribution over possible worlds,…
We propose a new definition of higher-order DisCoCat (categorical compositional distributional) models where the meaning of a word is not a diagram, but a diagram-valued higher-order function. Our models can be seen as a variant of Montague…
Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
Programming a quantum computer, i.e., implementing quantum algorithms on a quantum processor-based copmputer architecture, is a task that can be addressed (just as for classical computers) at different levels of abstraction. This paper…
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…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
We define a class of probabilistic models in terms of an operator algebra of stochastic processes, and a representation for this class in terms of stochastic parameterized grammars. A syntactic specification of a grammar is mapped to…
This paper presents a new static analysis for deriving upper bounds on the expected resource consumption of probabilistic programs. The analysis is fully automatic and derives symbolic bounds that are multivariate polynomials of the inputs.…
This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\'etivier and Pellaumail. Those notions are…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
For encompassing the limitations of probabilistic coherence spaces which do not seem to provide natural interpretations of continuous data types such as the real line, Ehrhard and al. introduced a model of probabilistic higher order…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
This paper develops a novel minimal-state operational semantics for higher-order functional languages that uses only the call stack and a source program point or a lexical level as the complete state information: there is no environment, no…
We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with…
In this chapter, we explore how (Type-2) computable distributions can be used to give both (algorithmic) sampling and distributional semantics to probabilistic programs with continuous distributions. Towards this end, we sketch an encoding…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…