What is the truth-value structure of realizability? How can realizability style models be integrated with forcing techniques from Kripke and Beth semantics, and conversely? These questions have received answers in Hyland’s [33], Läuchli’s [43] and in other, related or more syntactic developments cited below. Here we re-open the investigation with the aim of providing more constructive answers t...

Abstract Non-reductive physicalists have long held that the special sciences offer explanations of some phenomena that are objectively superior to physical explanations. This explanatory “autonomy” has largely been based on the multiple realizability argument. Recently, in the face of the local reduction and disjunctive property responses to multiple realizability, some defenders of non-reducti...

We prove a soundness and completeness result for Aschieri and Berardi’s learning based realizability for Heyting Arithmetic plus Excluded Middle over semi-decidable statements with respect to 1-Backtracking Coquand game semantics. First, we prove that learning based realizability is sound with respect to 1Backtracking Coquand game semantics. In particular, any realizer of an implication-and-neg...

Argumentation is nowadays a core topic in AI research. Understanding computational and representational aspects of abstract argumentation frameworks (AFs) is a central topic in the study of argumentation. The study of realizability of AFs aims at understanding the expressive power of AFs under different semantics. We propose and study the AF synthesis problem as a natural extension of realizabi...

In this paper, we study the realizability problem for retarded functional differential equations near an equilibrium point undergoing a nonlinear mode interaction between a saddle-node bifurcation and a non-resonant multiple Hopf bifurcation. In contrast to the case of transcritical/multiple Hopf interaction which was studied in an earlier paper [4], the analysis here is complicated by the pres...

This paper is about the bar recursion operator in the context of classical realizability. The pioneering work of Berardi, Bezem, Coquand [1] was enhanced by Berger and Oliva [2]. Then Streicher [12] has shown, by means of their bar recursion operator, that the realizability models of ZF, obtained from usual models of λ-calculus (Scott domains, coherent spaces, . . . ), satisfy the axiom of depe...

3 Recursive Realizability Interpretations 16 3.1 Abstract Applicative Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Realizability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 Soundness for IZF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Term Extraction . . . . . . . . . . . . . . . . . . . . . . ...

We study the realizability problem for specifications of reactive systems expressed in real-time linear temporal logics. The logics we consider are subsets of MITL (Metric Interval Temporal Logic), a logic for which the satisfiability and validity problems are decidable, a necessary condition for the realizability problem to be decidable. On the positive side, we show that the realizability of ...

We apply to the semantics of Arithmetic the idea of “finite approximation” used to provide computational interpretations of Herbrand’s Theorem, and we interpret classical proofs as constructive proofs (with constructive rules for ∨, ∃) over a suitable structure N for the language of natural numbers and maps of Gödel’s system T . We introduce a new Realizability semantics we call “Interactive le...

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language – the input of the problem – and fixed language called filter is non-empty. We consider two kind of problems depending on representation of regular language. If a regular language on input is represented by a DFA, then we obtain (deterministic) regular realizability...