Related papers: Contextual Equivalence for a Probabilistic Languag…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
We study bisimulation and context equivalence in a probabilistic $\lambda$-calculus. The contributions of this paper are threefold. Firstly we show a technique for proving congruence of probabilistic applicative bisimilarity. While the…
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
We define a probabilistic programming language for Gaussian random variables with a first-class exact conditioning construct. We give operational, denotational and equational semantics for this language, establishing convenient properties…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
A noncontextual system of random variables may become contextual if one adds to it a set of new variables, even if each of them is obtained by the same context-wise function of the old variables. This fact follows from the definition of…
This paper provides a systematic yet accessible presentation of the Contextuality-by-Default theory. The consideration is confined to finite systems of categorical random variables, which allows us to focus on the basics of the theory…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…
Contextual situations are those in which seemingly "the same" random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is…
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
There is no known way of giving a domain-theoretic semantics to higher-order probabilistic languages, in such a way that the involved domains are continuous or quasi-continuous - the latter is required to do any serious mathematics. We…
Equality saturation is a powerful technique for program optimization. Contextual equality saturation extends this to support rewrite rules that are conditioned on where a term appears in an expression. Existing work has brought contextual…
Contextual equivalence equate terms that have the same observable behaviour in any context. A standard contextual equivalence for CCS is the strong barbed congruence. Configuration structures are a denotational semantics for processes in…
Probabilistic programming languages rely fundamentally on some notion of sampling, and this is doubly true for probabilistic programming languages which perform Bayesian inference using Monte Carlo techniques. Verifying samplers - proving…
Abstract Contextuality is a property of systems of random variables. The identity of a random variable in a system is determined by its joint distribution with all other random variables in the same context. When context changes, a variable…