19 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 (in the style of general frames). 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. (...)
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  2.  97
    Modulated fibring and the collapsing problem.Cristina Sernadas, João Rasga & Walter A. Carnielli - 2002 - Journal of Symbolic Logic 67 (4):1541-1569.
    Fibring is recognized as one of the main mechanisms in combining logics, with great signicance in the theory and applications of mathematical logic. However, an open challenge to bring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that bring imposes unwanted interconnections between the given logics. Modulated bring allows a ner control of the combination, solving the collapsing problem both at the semantic and deductive levels. (...)
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  3.  19
    Reduction Techniques for Proving Decidability in Logics and Their Meet–Combination.João Rasga, Cristina Sernadas & Walter Carnielli - 2021 - Bulletin of Symbolic Logic 27 (1):39-66.
    Satisfaction systems and reductions between them are presented as an appropriate context for analyzing the satisfiability and the validity problems. The notion of reduction is generalized in order to cope with the meet-combination of logics. Reductions between satisfaction systems induce reductions between the respective satisfiability problems and (under mild conditions) also between their validity problems. Sufficient conditions are provided for relating satisfiability problems to validity problems. Reflection results for decidability in the presence of reductions are established. The validity problem in (...)
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  4.  15
    Preservation of admissible rules when combining logics.João Rasga, Cristina Sernadas & Amílcar Sernadas - 2016 - Review of Symbolic Logic 9 (4):641-663.
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  5.  30
    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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  6.  48
    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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  7.  23
    Heterogeneous Fibring of Deductive Systems Via Abstract Proof Systems.Luis Cruz-Filipe, Amílcar Sernadas & Cristina Sernadas - 2008 - Logic Journal of the IGPL 16 (2):121-153.
    Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way . Heterogeneous fibring, allowing the original logics to have different presentations , has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus (...)
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  8.  34
    Interpolation via translations.João Rasga, Walter Carnielli & Cristina Sernadas - 2009 - Mathematical Logic Quarterly 55 (5):515-534.
    A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear logic, a Kolmogorov-Gentzen-Gödel style translation, and a new translation between (...)
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  9.  9
    Modal Sequent Calculi Labelled with Truth Values: Cut Elimination.Paulo Mateus, João Rasga & Cristina Sernadas - 2005 - Logic Journal of the IGPL 13 (2):173-199.
    Cut elimination is shown, in a constructive way, to hold in sequent calculi labelled with truth values for a wide class of normal modal logics, supporting global and local reasoning and allowing a general frame semantics. The complexity of cut elimination is studied in terms of the increase of logical depth of the derivations. A hyperexponential worst case bound is established. The subformula property and a similar property for the label terms are shown to be satisfied by that class of (...)
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  10.  17
    Modal Sequent Calculi Labelled with Truth Values: Completeness, Duality and Analyticity.Paulo Mateus, Amílcar Sernadas, Cristina Sernadas & Luca Viganò - 2004 - Logic Journal of the IGPL 12 (3):227-274.
    Labelled sequent calculi are provided for a wide class of normal modal systems using truth values as labels. The rules for formula constructors are common to all modal systems. For each modal system, specific rules for truth values are provided that reflect the envisaged properties of the accessibility relation. Both local and global reasoning are supported. Strong completeness is proved for a natural two-sorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result (...)
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  11.  29
    Craig Interpolation in the Presence of Unreliable Connectives.João Rasga, Cristina Sernadas & Amlcar Sernadas - 2014 - Logica Universalis 8 (3-4):423-446.
    Arrow and turnstile interpolations are investigated in UCL [introduced by Sernadas et al. ], a logic that is a complete extension of classical propositional logic for reasoning about connectives that only behave as expected with a given probability. Arrow interpolation is shown to hold in general and turnstile interpolation is established under some provisos.
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  12.  16
    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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  13. Abductive Reasoning over Temporal Specifications of Objects.Paula Gouveia & Cristina Sernadas - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 293-318.
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  14. Abductive Reasoning over Temporal Specifications of Objects.Paula Gouveia & Cristina Sernadas - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 293-318.
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  15.  24
    Essential Structure of Proofs as a Measure of Complexity.Jaime Ramos, João Rasga & Cristina Sernadas - 2020 - Logica Universalis 14 (2):209-242.
    The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...)
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  16.  35
    Completeness and interpolation of almost‐everywhere quantification over finitely additive measures.João Rasga, Wafik Boulos Lotfallah & Cristina Sernadas - 2013 - Mathematical Logic Quarterly 59 (4-5):286-302.
    We give an axiomatization of first‐order logic enriched with the almost‐everywhere quantifier over finitely additive measures. Using an adapted version of the consistency property adequate for dealing with this generalized quantifier, we show that such a logic is both strongly complete and enjoys Craig interpolation, relying on a (countable) model existence theorem. We also discuss possible extensions of these results to the almost‐everywhere quantifier over countably additive measures.
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  17.  15
    Fusion of sequent modal logic systems labelled with truth values.João Rasga, Karina Roggia & Cristina Sernadas - 2010 - Logic Journal of the IGPL 18 (6):893-920.
    Fusion is a well-known form of combining normal modal logics endowed with a Hilbert calculi and a Kripke semantics. Herein, fusion is studied over logic systems using sequent calculi labelled with truth values and with a semantics based on a two-sorted algebra allowing, in particular, the representation of general Kripke structures. A wide variety of logics, including non-classical logics like, for instance, modal logics and intuitionistic logic can be presented by logic systems of this kind. A categorical approach of fusion (...)
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  18.  17
    Time-stamped claim logic.João Rasga, Cristina Sernadas, Erisa Karafili & Luca Viganò - 2021 - Logic Journal of the IGPL 29 (3):303-332.
    The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. (...)
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  19.  24
    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):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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