Some intuitions behind realizability semantics for constructive logic: Tableaux and Läuchli countermodels

DOI10.1016/0168-0072(96)00002-4zbMath0882.03056OpenAlexW2062936207MaRDI QIDQ1923579

Michael J. O'Donnell, James Lipton

Publication date: 12 March 1998

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(96)00002-4

zbMATH Keywords

Kripke semanticsintuitionistic logicrealizability semanticsBrouwer-Heyting-Kolmogorov interpretationclassical interpretations of the negation-free part of intuitionistic propositional logicclassical metalanguageLäuchli semantics

Mathematics Subject Classification ID

Metamathematics of constructive systems (03F50)

Related Items (3)

Intuitionistic completeness of first-order logic ⋮ Läuchli's completeness theorem from a topos-theoretic perspective ⋮ \(\mathcal {BCDL}\): Basic constructive description logic

Cites Work

• The foundations of mathematics. A study in the philosophy of science
• Well-foundedness in realizability
• Constructivism in mathematics. An introduction. Volume I
• Classical recursion theory. Vol. II
• The fibrational formulation of intuitionistic predicate logic. I: Completeness according to Gödel, Kripke, and Läuchli. Part 2
• The fibrational formulation of intuitionistic predicate logic. I: Completeness according to Gödel, Kripke, and Läuchli. Part 1
• Linear Läuchli semantics
• Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
• Combinators, \(\lambda\)-terms and proof theory
• Logical relations and the typed λ-calculus
• Lambek's categorical proof theory and Läuchli's abstract realizability
• Connecting formal semantics to constructive intuitions
• Intuitive counterexamples for constructive fallacies
• The system CΔ of combinatory logic
• Semantical Analysis of Modal Logic I Normal Modal Propositional Calculi
• Propositional Calculus and Realizability
• On the interpretation of intuitionistic number theory
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