28 found
Order:
  1.  5
    Unification in Modal and Description Logics.Franz Baader & Silvio Ghilardi - 2011 - Logic Journal of the IGPL 19 (6):705-730.
    Unification was originally introduced in automated deduction and term rewriting, but has recently also found applications in other fields. In this article, we give a survey of the results on unification obtained in two closely related, yet different, application areas of unification: description logics and modal logics.
    Direct download  
     
    Export citation  
     
    Bookmark   17 citations  
  2.  46
    Unification in Intuitionistic Logic.Silvio Ghilardi - 1999 - Journal of Symbolic Logic 64 (2):859-880.
    We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   39 citations  
  3.  3
    Best Solving Modal Equations.Silvio Ghilardi - 2000 - Annals of Pure and Applied Logic 102 (3):183-198.
    We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   34 citations  
  4.  12
    The Bounded Proof Property Via Step Algebras and Step Frames.Nick Bezhanishvili & Silvio Ghilardi - 2014 - Annals of Pure and Applied Logic 165 (12):1832-1863.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  5.  20
    Unification, Finite Duality and Projectivity in Varieties of Heyting Algebras.Silvio Ghilardi - 2004 - Annals of Pure and Applied Logic 127 (1-3):99-115.
    We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  6.  18
    An Algebraic Approach to Subframe Logics. Modal Case.Guram Bezhanishvili, Silvio Ghilardi & Mamuka Jibladze - 2011 - Notre Dame Journal of Formal Logic 52 (2):187-202.
    We prove that if a modal formula is refuted on a wK4-algebra ( B ,□), then it is refuted on a finite wK4-algebra which is isomorphic to a subalgebra of a relativization of ( B ,□). As an immediate consequence, we obtain that each subframe and cofinal subframe logic over wK4 has the finite model property. On the one hand, this provides a purely algebraic proof of the results of Fine and Zakharyaschev for K4 . On the other hand, it (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  7.  8
    An Algebraic Approach to Subframe Logics. Intuitionistic Case.Guram Bezhanishvili & Silvio Ghilardi - 2007 - Annals of Pure and Applied Logic 147 (1):84-100.
    We develop duality between nuclei on Heyting algebras and certain binary relations on Heyting spaces. We show that these binary relations are in 1–1 correspondence with subframes of Heyting spaces. We introduce the notions of nuclear and dense nuclear varieties of Heyting algebras, and prove that a variety of Heyting algebras is nuclear iff it is a subframe variety, and that it is dense nuclear iff it is a cofinal subframe variety. We give an alternative proof that every subframe variety (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  8.  42
    Incompleteness Results in Kripke Semantics.Silvio Ghilardi - 1991 - Journal of Symbolic Logic 56 (2):517-538.
    By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   15 citations  
  9.  8
    Continuity, Freeness, and Filtrations.Silvio Ghilardi - 2010 - Journal of Applied Non-Classical Logics 20 (3):193-217.
    The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in incremental constructions of finitely generated free.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  10.  7
    Constructive Canonicity in Non-Classical Logics.Silvio Ghilardi & Giancarlo Meloni - 1997 - Annals of Pure and Applied Logic 86 (1):1-32.
    Sufficient syntactic conditions for canonicity in intermediate and intuitionistic modal logics are given. We present a new technique which does not require semantic first-order reduction and which is constructive in the sense that it works in an intuitionistic metatheory through a model without points which is classically isomorphic to the usual canonical model.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  11.  21
    Filtering Unification and Most General Unifiers in Modal Logic.Silvio Ghilardi & Lorenzo Sacchetti - 2004 - Journal of Symbolic Logic 69 (3):879-906.
    We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  12.  3
    An Algebraic Theory of Normal Forms.Silvio Ghilardi - 1995 - Annals of Pure and Applied Logic 71 (3):189-245.
    In this paper we present a general theory of normal forms, based on a categorial result for the free monoid construction. We shall use the theory mainly for proposictional modal logic, although it seems to have a wider range of applications. We shall formally represent normal forms as combinatorial objects, basically labelled trees and forests. This geometric conceptualization is implicit in and our approach will extend it to other cases and make it more direct: operations of a purely geometric and (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  13.  28
    A Sheaf Representation and Duality for Finitely Presented Heyting Algebras.Silvio Ghilardi & Marek Zawadowski - 1995 - Journal of Symbolic Logic 60 (3):911-939.
    A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  14.  31
    Undefinability of Propositional Quantifiers in the Modal System S.Silvio Ghilardi & Marek Zawadowski - 1995 - Studia Logica 55 (2):259 - 271.
    We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  15.  9
    Presheaf Semantics and Independence Results for Some Non-Classical First-Order Logics.Silvio Ghilardi - 1989 - Archive for Mathematical Logic 29 (2):125-136.
    The logicD-J of the weak exluded middle with constant domains is proved to be incomplete with respect to Kripke semantics, by introducing models in presheaves on an arbitrary category. Additional incompleteness results are obtained for the modal systems with nested domains extendingQ-S4.1.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  16.  18
    Directed Frames.Giovanna Corsi & Silvio Ghilardi - 1989 - Archive for Mathematical Logic 29 (1):53-67.
    Predicate extensions of the intermediate logic of the weak excluded middle and of the modal logic S4.2 are introduced and investigated. In particular it is shown that some of them are characterized by subclasses of the class of directed frames with either constant or nested domains.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  17.  5
    Multiple-Conclusion Rules, Hypersequents Syntax and Step Frames.Nick Bezhanishvili & Silvio Ghilardi - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 54-73.
    No categories
    Direct download  
     
    Export citation  
     
    Bookmark   1 citation  
  18.  15
    Quantified Extensions of Canonical Propositional Intermediate Logics.Silvio Ghilardi - 1992 - Studia Logica 51 (2):195 - 214.
    The quantified extension of a canonical prepositional intermediate logic is complete with respect to the generalization of Kripke semantics taking into consideration set-valued functors defined on a category.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  19.  17
    Connecting Many-Sorted Theories.Franz Baader & Silvio Ghilardi - 2007 - Journal of Symbolic Logic 72 (2):535 - 583.
    Basically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called E-connection approach for combining modal logics to an (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  20.  19
    Model Completions and R-Heyting Categories.Silvio Ghilardi & Marek Zawadowski - 1997 - Annals of Pure and Applied Logic 88 (1):27-46.
    Under some assumptions on an equational theory S , we give a necessary and sufficient condition so that S admits a model completion. These assumptions are often met by the equational theories arising from logic. They say that the dual of the category of finitely presented S-algebras has some categorical stucture. The results of this paper combined with those of [7] show that all the 8 theories of amalgamable varieties of Heyting algebras [12] admit a model completion. Further applications to (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  21.  10
    Modularity Results for Interpolation, Amalgamation and Superamalgamation.Silvio Ghilardi & Alessandro Gianola - 2018 - Annals of Pure and Applied Logic 169 (8):731-754.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  22.  24
    On Canonicity and Strong Completeness Conditions in Intermediate Propositional Logics.Silvio Ghilardi & Pierangelo Miglioli - 1999 - Studia Logica 63 (3):353-385.
    By using algebraic-categorical tools, we establish four criteria in order to disprove canonicity, strong completeness, w-canonicity and strong w-completeness, respectively, of an intermediate propositional logic. We then apply the second criterion in order to get the following result: all the logics defined by extra-intuitionistic one-variable schemata, except four of them, are not strongly complete. We also apply the fourth criterion in order to prove that the Gabbay-de Jongh logic D1 is not strongly w-complete.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  23.  12
    A Model-Theoretic Characterization of Monadic Second Order Logic on Infinite Words.Silvio Ghilardi & Samuel J. van Gool - 2017 - Journal of Symbolic Logic 82 (1):62-76.
    Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary predicate symbols.Monadic second order logic over infinite words can alternatively be described as a first-order logic interpreted in${\cal P}\left$, the power set Boolean algebra of the natural numbers, equipped with modal operators for ‘initial’, ‘next’, and ‘future’ states. We prove that the first-order theory (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  24.  22
    Foreword.Silvio Ghilardi & Daniele Mundici - 2003 - Studia Logica 73 (1):1-1.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  25.  6
    Admissible Bases Via Stable Canonical Rules.Nick Bezhanishvili, David Gabelaia, Silvio Ghilardi & Mamuka Jibladze - 2016 - Studia Logica 104 (2):317-341.
    We establish the dichotomy property for stable canonical multi-conclusion rules for IPC, K4, and S4. This yields an alternative proof of existence of explicit bases of admissible rules for these logics.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  26.  13
    Relational and Partial Variable Sets and Basic Predicate Logic.Silvio Ghilardi & Giancarlo Meloni - 1996 - Journal of Symbolic Logic 61 (3):843-872.
    In this paper we study the logic of relational and partial variable sets, seen as a generalization of set-valued presheaves, allowing transition functions to be arbitrary relations or arbitrary partial functions. We find that such a logic is the usual intuitionistic and co-intuitionistic first order logic without Beck and Frobenius conditions relative to quantifiers along arbitrary terms. The important case of partial variable sets is axiomatizable by means of the substitutivity schema for equality. Furthermore, completeness, incompleteness and independence results are (...)
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  27. Advances in Modal Logic 9.Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.) - 2012 - College Publications.
     
    Export citation  
     
    Bookmark  
  28. Existentially Closed Brouwerian Semilattices.Luca Carai & Silvio Ghilardi - forthcoming - Journal of Symbolic Logic:1-29.
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark