Related papers: Interactive Learning-Based Realizability for Heyti…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
The theory of classical realizability is a framework in which we can develop the proof-program correspondence. Using this framework, we show how to transform into programs the proofs in classical analysis with dependent choice and the…
Learning to solve long horizon temporally extended tasks with reinforcement learning has been a challenge for several years now. We believe that it is important to leverage both the hierarchical structure of complex tasks and to use expert…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
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…
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…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
We show how the language of Krivine's classical realizability may be used to specify various forms of nondeterminism and relate them with properties of realizability models. More specifically, we introduce an abstract notion of…
Hybrid programs combine digital control with differential equations, and naturally appear in a wide range of application domains, from biology and control theory to real-time software engineering. The entanglement of discrete and continuous…
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…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
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.
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
We present realizability and realization logic, two program logics that jointly address the problem of finding solutions in semantics-guided synthesis. What is new is that we proceed eagerly and not only analyze a single candidate program…
On the ground of a general theorem concerning the admissibility of the structural rules in sequent calculi with additional atomic rules, we develop a proof theoretic analysis for several extensions of the ${\bf G3[mic]}$ sequent calculi…
We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result - which shows that the Excluded Middle principle can be used to…
We study abstract intermediate justification logics, that is arbitrary intermediate propositional logics extended with a subset of specific axioms of (classical) justification logics. For these, we introduce various semantics by combining…
For robots to perform assistive tasks in unstructured home environments, they must learn and reason on the semantic knowledge of the environments. Despite a resurgence in the development of semantic reasoning architectures, these methods…
Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential.…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…