Related papers: Induction and Recursion Principles in a Higher-Ord…
The paper extends the expectation transformer based analysis of higher-order probabilistic programs to the quantum higher-order setting. The quantum language we are considering can be seen as an extension of PCF, featuring unbounded…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…
We study which standard operators of probabilistic process calculi allow for compositional reasoning with respect to bisimulation metric semantics. We argue that uniform continuity (generalizing the earlier proposed property of…
We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…
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…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…
We present Coneris, the first higher-order concurrent separation logic for reasoning about error probability bounds of higher-order concurrent probabilistic programs with higher-order state. To support modular reasoning about concurrent…
We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
We present a denotational semantics for higher-order probabilistic programs in terms of linear operators between Banach spaces. Our semantics is rooted in the classical theory of Banach spaces and their tensor products, but bears…
This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main…
We consider the task of performing probabilistic inference with probabilistic logical models. Many algorithms for approximate inference with such models are based on sampling. From a logic programming perspective, sampling boils down to…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
Probabilistic couplings are the foundation for many probabilistic relational program logics and arise when relating random sampling statements across two programs. In relational program logics, this manifests as dedicated coupling rules…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
Coinduction is a widely used technique for establishing behavioural equivalence of programs in higher-order languages. In recent years, the rise of languages with quantitative (e.g.~probabilistic) features has led to extensions of…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…