73 citations · 149 across the 21 of their papers we have counts for
8 papers · 1 filter
Admissibility of -Inference Rules: interpolation, model completion, and contact algebras
Nick Bezhanishvili, Luca Carai, Silvio Ghilardi +1
We devise three strategies for recognizing admissibility of non-standard inference rules via interpolation, uniform interpolation, and model completions. We apply our machinery to…
Diego's Theorem for nuclear implicative semilattices
Guram Bezhanishvili, Nick Bezhanishvili, Luca Carai +3
We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego's Theorem. The key ingredients of our proof include the coloring technique…
Free Heyting Algebra Endomorphisms: Ruitenburg's Theorem and Beyond
Silvio Ghilardi, Luigi Santocanale
Ruitenburg's Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ultimately periodic if f fixes all the generators but one. More precisely, there…
Ruitenburg's Theorem via Duality and Bounded Bisimulations
Luigi Santocanale, Silvio Ghilardi
For a given intuitionistic propositional formula A and a propositional variable x occurring in it, define the infinite sequence of formulae { A \_i | i1} by letting A\_1 be A…
Fixed-point elimination in the Intuitionistic Propositional Calculus (extended version)
Silvio Ghilardi, Maria Joao Gouveia, Luigi Santocanale
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the alge- braic models of the Intuitionistic Pr…
Existentially Closed Brouwerian Semilattices
Luca Carai, Silvio Ghilardi
The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results due to W. H. Wheeler, it has a model completion (whose models are the existent…
Monadic second order logic as the model companion of temporal logic
Silvio Ghilardi, Samuel J. van Gool
The main focus of this paper is on bisimulation-invariant MSO, and more particularly on giving a novel model-theoretic approach to it. In model theory, a model companion of a theor…
A model-theoretic characterization of monadic second order logic on infinite words
Silvio Ghilardi, Samuel J. van Gool
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 natura…