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  1.  32
    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).
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  2.  26
    Kripke-style semantics for many-valued logics.Franco Montagna & Lorenzo Sacchetti - 2003 - Mathematical Logic Quarterly 49 (6):629.
    This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important many-valued logics (...)
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    Corrigendum to "Kripke-style semantics for many-valued logics".Franco Montagna & Lorenzo Sacchetti - 2004 - Mathematical Logic Quarterly 50 (1):104.
    This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect.
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  4.  31
    The Fixed Point Property in Modal Logic.Lorenzo Sacchetti - 2001 - Notre Dame Journal of Formal Logic 42 (2):65-86.
    This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every has the explicit fixed point property. Our main result states that every complete modal logic L having the Craig's interpolation property and such that , where and are suitable modal formulas, has the explicit fixed point property.
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  5.  19
    Incompleteness and Fixed Points.Lorenzo Sacchetti - 2002 - Mathematical Logic Quarterly 48 (1):15-28.
    Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.
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