Abstract Completeness: A formalization of an abstract property of possibly infinite derivation trees (modeled by a codatatype), representing the core of a proof (in Beth/Hintikka style) of the first-order logic completeness theorem, independent of the concrete syntax or inference rules. This work is described in detail in the IJCAR 2014 publication by the authors. The abstract proof can be instantiated for a wide range of Gentzen and tableau systems as well as various flavors of FOL---e.g., with or without predicates, equality, or sorts. Here, we give only a toy example instantiation with classical propositional logic. A more serious instance---many-sorted FOL with equality---is described elsewhere [Blanchette and Popescu, FroCoS 2013].
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References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Schlichtkrull, Anders: Formalization of the resolution calculus for first-order logic (2018)
- Biendarra, Julian; Blanchette, Jasmin Christian; Bouzy, Aymeric; Desharnais, Martin; Fleury, Mathias; Hölzl, Johannes; Kunčar, Ondřej; Lochbihler, Andreas; Meier, Fabian; Panny, Lorenz; Popescu, Andrei; Sternagel, Christian; Thiemann, René; Traytel, Dmitriy: Foundational (co)datatypes and (co)recursion for higher-order logic (2017)
- Blanchette, Jasmin Christian; Popescu, Andrei; Traytel, Dmitriy: Soundness and completeness proofs by coinductive methods (2017)
- Blanchette, Jasmin Christian; Popescu, Andrei; Traytel, Dmitriy: Unified classical logic completeness. A coinductive pearl (2014)