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Pierluigi Minari
Università degli Studi di Firenze
  1.  43
    On the Extension of Intuitionistic Propositional Logic with Kreisel-Putnam's and Scott's Schemes.Pierluigi Minari - 1986 - Studia Logica 45 (1):55-68.
    LetSKP be the intermediate prepositional logic obtained by adding toI (intuitionistic p.l.) the axiom schemes:S = (( ) ) (Scott), andKP = ()()() (Kreisel-Putnam). Using Kripke's semantics, we prove:1) SKP has the finite model property; 2) SKP has the disjunction property. In the last section of the paper we give some results about Scott's logic S = I+S.
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  2.  25
    Labeled Sequent Calculi for Modal Logics and Implicit Contractions.Pierluigi Minari - 2013 - Archive for Mathematical Logic 52 (7-8):881-907.
    The paper settles an open question concerning Negri-style labeled sequent calculi for modal logics and also, indirectly, other proof systems which make (more or less) explicit use of semantic parameters in the syntax and are thus subsumed by labeled calculi, like Brünnler’s deep sequent calculi, Poggiolesi’s tree-hypersequent calculi and Fitting’s prefixed tableau systems. Specifically, the main result we prove (through a semantic argument) is that labeled calculi for the modal logics K and D remain complete w.r.t. valid sequents whose relational (...)
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  3.  32
    On the Semantics of Comparative Logic.Pierluigi Minari - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (5):433-448.
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  4.  25
    Analytic Combinatory Calculi and the Elimination of Transitivity.Pierluigi Minari - 2004 - Archive for Mathematical Logic 43 (2):159-191.
    We introduce, in a general setting, an ‘‘analytic’’ version of standard equational calculi of combinatory logic. Analyticity lies on the one side in the fact that these calculi are characterized by the presence of combinatory introduction rules in place of combinatory axioms, and on the other side in that the transitivity rule proves to be eliminable. Apart from consistency, which follows immediately, we discuss other almost direct consequences of analyticity and the main transitivity elimination theorem; in particular the Church−Rosser and (...)
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  5. Intermediate Predicate Logics Determined by Ordinals.Pierluigi Minari, Mitio Takano & Hiroakira Ono - 1990 - Journal of Symbolic Logic 55 (3):1099-1124.
    For each ordinal $\alpha > 0, L(\alpha)$ is the intermediate predicate logic characterized by the class of all Kripke frames with the poset α and with constant domain. This paper will be devoted to a study of logics of the form L(α). It will be shown that for each uncountable ordinal of the form α + η with a finite or a countable $\eta (> 0)$ , there exists a countable ordinal of the form β + η such that L(α (...)
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  6.  39
    Uniform Inseparability in Explicit Mathematics.Andrea Cantini & Pierluigi Minari - 1999 - Journal of Symbolic Logic 64 (1):313-326.
    We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW + . Next, we show that POW + can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.
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  7.  45
    A Solution to Curry and Hindley’s Problem on Combinatory Strong Reduction.Pierluigi Minari - 2009 - Archive for Mathematical Logic 48 (2):159-184.
    It has often been remarked that the metatheory of strong reduction $\succ$ , the combinatory analogue of βη-reduction ${\twoheadrightarrow_{\beta\eta}}$ in λ-calculus, is rather complicated. In particular, although the confluence of $\succ$ is an easy consequence of ${\twoheadrightarrow_{\beta\eta}}$ being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of $\succ$ , one which makes no detour through λ-calculus. We answer positively to this question, by extending (...)
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  8.  28
    Analytic Proof Systems for Λ-Calculus: The Elimination of Transitivity, and Why It Matters. [REVIEW]Pierluigi Minari - 2007 - Archive for Mathematical Logic 46 (5-6):385-424.
    We introduce new proof systems G[β] and G ext[β], which are equivalent to the standard equational calculi of λβ- and λβη- conversion, and which may be qualified as ‘analytic’ because it is possible to establish, by purely proof-theoretical methods, that in both of them the transitivity rule admits effective elimination. This key feature, besides its intrinsic conceptual significance, turns out to provide a common logical background to new and comparatively simple demonstrations—rooted in nice proof-theoretical properties of transitivity-free derivations—of a number (...)
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  9. Logic and Foundations of Mathematics: Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995.Andrea Cantini, Ettore Casari & Pierluigi Minari (eds.) - 1999 - Dordrecht, Netherland: Springer.
    The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of (...)
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  10. Husserl and Schröder.Pierluigi Minari & Stefania Centrone - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    We aim at clarifying to what extent the work of the German mathematician Ernst Schröder on the algebra of logic is taken into consideration and rehashed in the work of the early Husserl, focusing on Husserl’s 1891 Review of the first volume of Schröder’s monumental Vorlesungen über die Algebra der Logik and on Husserl’s text Der Folgerungskalkül und die Inhaltslogik written in the same year. We will try to show how and why Husserl, while praising Schröder’s calculus, strongly criticizes Schröder’s (...)
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  11.  27
    Quasilinear Posets and Some Subsystems Of Dummett's LC.Pierluigi Minari - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (3):257-266.
  12.  37
    Infinitary Modal Logic and Generalized Kripke Semantics.Pierluigi Minari - 2011 - Annali Del Dipartimento di Filosofia 17:135-166.
    This paper deals with the infinitary modal propositional logic Kω1, featuring countable disjunctions and conjunc- tions. It is known that the natural infinitary extension LK.
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  13.  20
    A Note on a Subsystem Of Intuitionistic Logic with Constant Domains.Pierluigi Minari - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (5):385-387.
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  14. Selected Contributed Papers of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence, August 1995.Andrea Cantini, Etiore Casari & Pierluigi Minari (eds.) - 1999 - Springer-Science+Business Media.
  15.  2
    Husserl and Boole.Pierluigi Minari & Stefania Centrone - 2017 - In Stefania Centrone (ed.), Essays on Husserl’s Logic and Philosophy of Mathematics. Springer Verlag.
    We aim at clarifying to what extent the work of the English mathematician George Boole on the algebra of logic is taken into consideration and discussed in the work of early Husserl, focusing in particular on Husserl’s lecture “Über die neueren Forschungen zur deduktiven Logik” of 1895, in which an entire section is devoted to Boole. We confront Husserl’s representation of the problem-solving processes with the analysis of “symbolic reasoning” proposed by George Boole in the Laws of Thought and try (...)
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  16.  30
    Theories of Types and Names with Positive Stratified Comprehension.Pierluigi Minari - 1999 - Studia Logica 62 (2):215-242.
    We introduce a certain extension of -calculus, and show that it has the Church-Rosser property. The associated open-term extensional combinatory algebra is used as a basis to construct models for theories of Explict Mathematics (formulated in the language of "types and names") with positive stratified comprehension. In such models, types are interpreted as collections of solutions (of terms) w.r. to a set of numerals. Exploiting extensionality, we prove some consistency results for special ontological axioms which are refutable under elementary comprehension.
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  17.  25
    Completeness Theorems for Some Intermediate Predicate Calculi.Pierluigi Minari - 1983 - Studia Logica 42 (4):431 - 441.
    We give completeness results — with respect to Kripke's semantic — for the negation-free intermediate predicate calculi.
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  18.  6
    Uniform Inseparability in Explicit Mathematics.Andrea Cantini & Pierluigi Minari - 1999 - Journal of Symbolic Logic 64 (1):313-326.
    We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jager's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW$^+$. Next, we show that POW$^+$ can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.
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