Verifiers and Generators: Epistemic Semantics for Intuitionistic Logic (Long Version)

2026-05-15

AI Summary

This work addresses the absence of a semantic model for intuitionistic logic grounded in semi-decidable evidence by introducing a framework of *epistemic realizability*. In this framework, each proposition is paired with a verifier program—checking whether given data constitute valid evidence—and a generator program—constructing canonical evidence—forming a dual structure. This approach uniquely incorporates a verification–generation duality into the semantics of intuitionistic logic, providing a unified treatment for minimal logic as well as second- and higher-order systems. By integrating techniques from program semantics, computability theory, and type theory, the paper establishes both soundness and completeness of these logics under the proposed semantics.

Abstract

This paper explores epistemic realizability, a form of realizability in which the property that a piece of data constitutes evidence for a logical proposition is semi-decidable. In this framework, each proposition A is assigned a verifier} program that checks whether a datum X is a realizer for A, and a dual generator program that behaves as a generic realizer for X. We propose epistemic realizability interpretations for minimal logic, second-order intuitionistic logic, and higher-order intuitionistic logic, proving that each system is sound and complete under the proposed semantics.

Problem

• epistemic realizability
• intuitionistic logic
• realizability semantics
• semi-decidable evidence
• logical semantics

Innovation

• epistemic realizability
• verifier-generator duality
• intuitionistic logic
• semi-decidable evidence
• computational semantics