Related papers: Full abstraction for probabilistic PCF
The paper is about a class of languages that extends context-free languages (CFL) and is stable under shuffle. Specifically, we investigate the class of partially-commutative context-free languages (PCCFL), where non-terminal symbols are…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…
After Dung's founding work in Abstract Argumentation Frameworks there has been a growing interest in extending the Dung's semantics in order to describe more complex or real life situations. Several of these approaches take the direction of…
Large language models have demonstrated impressive performance on commonsense tasks; however, these tasks are often posed as multiple-choice questions, allowing models to exploit systematic biases. Commonsense is also inherently…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
We settle an old question about the existence of certain "sums-of-squares" formulas over a field F (which are the simplest examples of composition formulas for quadratic forms). A classical theorem says that if such a formula exists over a…
We investigate the formal semantics of a simple imperative language that has both classical and quantum constructs. More specifically, we provide an operational semantics, a denotational semantics and two Hoare-style proof systems: an…
We give a new construction of free distributive p-algebras. Our construction relies on a detailed description of completely meet-irreducible congruences, so it is purely universal algebraic. It yields a normal form theorem for p-algebra…
Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive…
We present a full-spectrum dependently typed core language which includes both nontermination and computational irrelevance (a.k.a. erasure), a combination which has not been studied before. The two features interact: to protect type safety…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
We study the category Cstabm of measurable cones and measurable stable functions, which is a denotational model of an higher-order language with continuous probabilities and full recursion. We look at Cstabm as a model for discrete…
Current probabilistic programming languages and tools tightly couple model representations with specific inference algorithms, preventing experimentation with novel representations or mixed discrete-continuous models. We introduce a factor…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their…
Representing a word by its co-occurrences with other words in context is an effective way to capture the meaning of the word. However, the theory behind remains a challenge. In this work, taking the example of a word classification task, we…
Much of the power of probabilistic methods in modelling language comes from their ability to compare several derivations for the same string in the language. An important starting point for the study of such cross-derivational properties is…
We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the…
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…
The class of Basic Feasible Functionals BFF is the second-order counterpart of the class of first-order functions computable in polynomial time. We present several implicit characterizations of BFF based on a typed programming language of…
While a large body of work has scrutinized the meaning of conditional sentences, considerably less attention has been paid to formal models of their pragmatic use and interpretation. Here, we take a probabilistic approach to pragmatic…