Filling in the semantics for intuitionistic conditional logic

2025/08/16 by Brendan Dufty, Dufty, Brendan, Jim de Groot +1
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Multi-Agent Systems and Negotiation #Semantic Web and Ontologies

paper · pdf · doi:10.48550/arxiv.2508.11972

openalex publication_date 2025/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove completeness results for a wide variety of intuitionistic conditional logics. We do so by first using a canonical model construction obtain completeness with respect to descriptive conditional frames, and then introducing the fill-in method to transfer this to classes of conditional frames without extra structure. The fill-in method closes the gap between descriptive conditional frames, which do not have a canonical underlying frame, and conditional frames.

Citations

• A Proof-Theoretic View of Basic Intuitionistic Conditional Logic (Extended Version)
• An intuitionistically complete system of basic intuitionistic conditional logic
• Wijesekera-style constructive modal logics
• Goldblatt-Thomason Theorems for Modal Intuitionistic Logics
• Uniform labelled calculi for preferential conditional logics based on neighbourhood semantics
• Lewisian Fixed Points I: Two Incomparable Constructions
• De Finettian Logics of Indicative Conditionals
• Intuitionistic Non-Normal Modal Logics: A general framework
• Nonmonotonic Reasoning, Preferential Models and Cumulative Logics
• Nonmonotonic reasoning, preferential models and cumulative logics
• Basic conditional logic

Related

• An intuitionistically complete system of basic intuitionistic conditional logic
• A completeness theorem in proof-theoretic semantics via set-theoretic semantics
• Post Completeness in Conditional Logic
• Proof-Theoretic Soundness and Completeness
• A basic system of paraconsistent Nelsonian logic of conditionals