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Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
In economic theory, an agent chooses from available alternatives -- modeled as a set. In decisions in the field or in the lab, however, agents do not have access to the set of alternatives at once. Instead, alternatives are represented by…
We establish an assume-guarantee (AG) framework for compositional reasoning about multi-objective queries in parametric probabilistic automata (pPA) - an extension to probabilistic automata (PA), where transition probabilities are functions…
Performative predictions are forecasts which influence the outcomes they aim to predict, undermining the existence of correct forecasts and standard methods of elicitation and estimation. We show that conditioning forecasts on covariates…
J.L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e. symmetric extensions. We also provide a new…
We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative)…
The core challenge in applying abstract interpretation lies in the configuration of abstraction and analysis strategies encoded by a large number of external parameters of static analysis tools. To attain low false-positive rates (i.e.,…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
We prove that interactive learning based classical realizability (introduced by Aschieri and Berardi for first order arithmetic) is sound with respect to Coquand game semantics. In particular, any realizer of an…
Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…
The dynamics of real-world applications and systems require efficient methods for improving infeasible solutions or restoring corrupted ones by making modifications to the current state of a system in a restricted way. We propose a new…
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.…
Users of program analyses expect that results change predictably in response to changes in their programs, but many analyses fail to provide such robustness. This paper introduces a theoretical framework that provides a unified language to…
We prove a result concerning formality of the pull-back of a fibration. Our approach is to use bar complexes in the category of commutative differential graded algebras. As an application, we generalize an old result of Baum and Smith.
Realizability for knowledge representation formalisms studies the following question: given a semantics and a set of interpretations, is there a knowledge base whose semantics coincides exactly with the given interpretation set? We…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex…
We study how linear orders can be employed to realise choice functions for which the set of potential choices is restricted, i.e., the possible choice is not possible among the full powerset of all alternatives. In such restricted settings,…
This article shows a correspondence between abstract interpretation of imperative programs and the refinement calculus: in the refinement calculus, an abstract interpretation of a program is a specification which is a function. This…