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Counting the maximal intermediate constructive logics

Mauro Ferrari & Pierangelo Miglioli

Journal of Symbolic Logic 58 (4):1365-1401 (1993)

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On maximal intermediate predicate constructive logics.Alessandro Avellone, Camillo Fiorentini, Paolo Mantovani & Pierangelo Miglioli - 1996 - Studia Logica 57 (2-3):373 - 408.details We extend to the predicate frame a previous characterization of the maximal intermediate propositional constructive logics. This provides a technique to get maximal intermediate predicate constructive logics starting from suitable sets of classically valid predicate formulae we call maximal nonstandard predicate constructive logics. As an example of this technique, we exhibit two maximal intermediate predicate constructive logics, yet leaving open the problem of stating whether the two logics are distinct. Further properties of these logics will be also investigated. Download Export citation Bookmark 1 citation
Proof analysis in intermediate logics.Roy Dyckhoff & Sara Negri - 2012 - Archive for Mathematical Logic 51 (1):71-92.details Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink) Download Export citation Bookmark 29 citations
On Harrop disjunction property in intermediate predicate logics.Katsumasa Ishii - 2023 - Archive for Mathematical Logic 63 (3):317-324.details A partial solution to Ono’s problem P54 is given. Here Ono’s problem P54 is whether Harrop disjunction property is equivalent to disjunction property or not in intermediate predicate logics. As an application of this result it is shown that some intermediate predicate logics satisfy Harrop disjunction property. Download Export citation Bookmark
Preface. In memoriam Pierangelo Miglioli (1946–1999).Mario Ornaghi - 2003 - Studia Logica 73 (1):5-19.details Download Export citation Bookmark
A method to single out maximal propositional logics with the disjunction property I.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (1):1-46.details This is the first part of a paper concerning intermediate propositional logics with the disjunction property which cannot be properly extended into logics of the same kind, and are therefore called maximal. To deal with these logics, we use a method based on the search of suitable nonstandard logics, which has an heuristic content and has allowed us to discover a wide family of logics, as well as to get their maximality proofs in a uniform way. The present part illustrates (...) Download Export citation Bookmark 3 citations
A method to single out maximal propositional logics with the disjunction property II.Mauro Ferrari & Pierangelo Miglioli - 1995 - Annals of Pure and Applied Logic 76 (2):117-168.details This is the second part of a paper devoted to the study of the maximal intermediate propositional logics with the disjunction property , whose first part has appeared in this journal with the title “A method to single out maximal propositional logics with the disjunction property I”. In the first part we have explained the general results upon which a method to single out maximal constructive logics is based and have illustrated such a method by exhibiting the Kripke semantics of (...) Download Export citation Bookmark 5 citations

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