6 found
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  1. Fibring: Completeness Preservation.Alberto Zanardo, Amilcar Sernadas & Cristina Sernadas - 2001 - Journal of Symbolic Logic 66 (1):414-439.
    A completeness theorem is established for logics with congruence endowed with general semantics. As a corollary, completeness is shown to be preserved by fibring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under fibring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by fibring logics with equivalence and general semantics. An example is provided showing that (...)
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  2.  18
    Importing Logics.João Rasga, Amílcar Sernadas & Cristina Sernadas - 2012 - Studia Logica 100 (3):545-581.
    The novel notion of importing logics is introduced, subsuming as special cases several kinds of asymmetric combination mechanisms, like temporalization [8, 9], modalization [7] and exogenous enrichment [13, 5, 12, 4, 1]. The graph-theoretic approach proposed in [15] is used, but formulas are identified with irreducible paths in the signature multi-graph instead of equivalence classes of such paths, facilitating proofs involving inductions on formulas. Importing is proved to be strongly conservative. Conservative results follow as corollaries for temporalization, modalization and exogenous (...)
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  3.  38
    Synchronization of Logics.Amílcar Sernadas, Cristina Sernadas & Carlos Caleiro - 1997 - Studia Logica 59 (2):217-247.
    Motivated by applications in software engineering, we propose two forms of combination of logics: synchronization on formulae and synchronization on models. We start by reviewing satisfaction systems, consequence systems, one-step derivation systems and theory spaces, as well as their functorial relationships. We define the synchronization on formulae of two consequence systems and provide a categorial characterization of the construction. For illustration we consider the synchronization of linear temporal logic and equational logic. We define the synchronization on models of two satisfaction (...)
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  4.  38
    Fibring Logics, Dov M. Gabbay.Amílcar Sernadas - 2000 - Journal of Logic, Language and Information 9 (4):511-513.
  5.  16
    Truth-Values as Labels: A General Recipe for Labelled Deduction.Cristina Sernadas, Luca Viganò, João Rasga & Amílcar Sernadas - 2003 - Journal of Applied Non-Classical Logics 13 (3-4):277-315.
    We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The “truth-values as (...)
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    Fibring Modal First-Order Logics: Completeness Preservation.Amilcar Sernadas, Cristina Sernadas & Alberto Zanardo - 2002 - Logic Journal of the IGPL 10 (4):413-451.
    Fibring is defined as a mechanism for combining logics with a first-order base, at both the semantic and deductive levels. A completeness theorem is established for a wide class of such logics, using a variation of the Henkin method that takes advantage of the presence of equality and inequality in the logic. As a corollary, completeness is shown to be preserved when fibring logics in that class. A modal first-order logic is obtained as a fibring where neither the Barcan formula (...)
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