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  1. A Tableau Calculus for Propositional Intuitionistic Logic with a Refined Treatment of Nested Implications.Mauro Ferrari, Camillo Fiorentini & Guido Fiorino - 2009 - Journal of Applied Non-Classical Logics 19 (2):149-166.
    Since 1993, when Hudelmaier developed an O-space decision procedure for propositional Intuitionistic Logic, a lot of work has been done to improve the efficiency of the related proof-search algorithms. In this paper a tableau calculus using the signs T, F and F c with a new set of rules to treat signed formulas of the kind T → C) is provided. The main feature of the calculus is the reduction of both the non-determinism in proof-search and the width of proofs (...)
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  2. A Proof-Theoretical Analysis of Semiconstructive Intermediate Theories.Mauro Ferrari & Camillo Fiorentini - 2003 - Studia Logica 73 (1):21 - 49.
    In the 80's Pierangelo Miglioli, starting from motivations in the framework of Abstract Data Types and Program Synthesis, introduced semiconstructive theories, a family of large subsystems of classical theories that guarantee the computability of functions and predicates represented by suitable formulas. In general, the above computability results are guaranteed by algorithms based on a recursive enumeration of the theorems of the whole system. In this paper we present a family of semiconstructive systems, we call uniformly semiconstructive, that provide computational procedures (...)
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  3. On Maximal Intermediate Predicate Constructive Logics.Alessandro Avellone, Camillo Fiorentini, Paolo Mantovani & Pierangelo Miglioli - 1996 - Studia Logica 57 (2-3):373 - 408.
    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.
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  4. A Secondary Semantics for Second Order Intuitionistic Propositional Logic.Mauro Ferrari, Camillo Fiorentini & Guido Fiorino - 2004 - Mathematical Logic Quarterly 50 (2):202-210.
    In this paper we propose a Kripke-style semantics for second order intuitionistic propositional logic and we provide a semantical proof of the disjunction and the explicit definability property. Moreover, we provide a tableau calculus which is sound and complete with respect to such a semantics.
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  5.  98
    All Intermediate Logics with Extra Axioms in One Variable, Except Eight, Are Not Strongly Ω-Complete.Camillo Fiorentini - 2000 - Journal of Symbolic Logic 65 (4):1576-1604.
    In [8] it is proved that all the intermediate logics axiomatizable by formulas in one variable, except four of them, are not strongly complete. We considerably improve this result by showing that all the intermediate logics axiomatizable by formulas in one variable, except eight of them, are not strongly ω-complete. Thus, a definitive classification of such logics with respect to the notions of canonicity, strong completeness, ω-canonicity and strong ω-completeness is given.
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