Related papers: Interactive Realizability, Monads and Witness Extr…
This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive…
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…
We consider the problem of finding pre-fixed points of interactive realizers over arbitrary knowledge spaces, obtaining a relative recursive procedure. Knowledge spaces and interactive realizers are an abstract setting to represent learning…
Realizability interprets propositions as specifications for computational entities in programming languages. Specifically, syntactic realizability is a powerful machinery that handles realizability as a syntactic translation of propositions…
Counterfactual reasoning, a hallmark of intelligence, consists of three steps: inferring latent variables from observations (abduction), constructing alternatives (interventions), and predicting their outcomes (prediction). This skill is…
We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…
We introduce the notion of implicative algebra, a simple algebraic structure intended to factorize the model constructions underlying forcing and realizability (both in intuitionistic and classical logic). The salient feature of this…
We consider a randomised version of Kleene's realisability interpretation of intuitionistic arithmetic in which computability is replaced with randomised computability with positive probability. In particular, we show that (i) the set of…
As modern computing moves towards smaller devices and powerful cloud platforms, more and more computation is being delegated to powerful service providers. Interactive proofs are a widely-used model to design efficient protocols for…
The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are…
In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.
Interactive proofs are often considered as costs of formal modelling activity. In an incremental development environment such as the Rodin platform for Event-B, information from proof attempts is important input for adapting the model. This…
Evidential reasoning is cast as the problem of simplifying the evidence-hypothesis relation and constructing combination formulas that possess certain testable properties. Important classes of evidence as identifiers, annihilators, and…
Juba recently proposed a formulation of learning abductive reasoning from examples, in which both the relative plausibility of various explanations, as well as which explanations are valid, are learned directly from data. The main…
This draft introduces the technical machinery of a semantic framework for potentialist truthmaking based on our innovation of intentic states, which are structured partial models accounting for our distinction between non-hypothetical and…
We use the technique of "classical realizability" to build new models of ZF + DC in which R is not well ordered. This gives new relative consistency results, probably not obtainable by forcing. This gives also a new method to get programs…
In previous work [Lewitzka, Log. J. IGPL 2017], we presented a hierarchy of classical modal systems, along with algebraic semantics, for the reasoning about intuitionistic truth, belief and knowledge. Deviating from G\"odel's interpretation…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
Interpretability aims to explain the behavior of deep neural networks. Despite rapid growth, there is mounting concern that much of this work has not translated into practical impact, raising questions about its relevance and utility. This…
We develop a realizability model in which the realizers are the reals not just Turing computable in a fixed real but rather the reals in a countable ideal of Turing degrees. This is then applied to prove several separation results involving…