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Logics of Formal Inconsistency
 Handbook of Philosophical Logic
"... 1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory ..."
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Cited by 69 (24 self)
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1.1 Contradictoriness and inconsistency, consistency and noncontradictoriness In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory
Fibring: Completeness Preservation
 Journal of Symbolic Logic
, 2000
"... 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 bring logics with congruence provided that congruence is retained in the resulting logic. The class of logics ..."
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Cited by 50 (24 self)
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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 bring logics with congruence provided that congruence is retained in the resulting logic. The class of logics with equivalence is shown to be closed under bring and to be included in the class of logics with congruence. Thus, completeness is shown to be preserved by bring logics with equivalence and general semantics. An example is provided showing that completeness is not always preserved by bring logics endowed with standard (non general) semantics. A categorial characterization of bring is provided using coproducts and cocartesian liftings. 1 Introduction Much attention has been recently given to the problems of combining logics and obtaining transference results. Besides leading to very interesting applications whenever it is necessary to work with dierent logics at the same time, ...
Fibring NonTruthFunctional Logics: Completeness Preservation
 Journal of Logic, Language and Information
, 2000
"... Fibring has been shown to be useful for combining logics endowed with truthfunctional semantics. One wonders if bring can be extended in order to cope with logics endowed with nontruthfunctional semantics as, for example, paraconsistent logics. The rst main contribution of the paper is a po ..."
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Cited by 30 (20 self)
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Fibring has been shown to be useful for combining logics endowed with truthfunctional semantics. One wonders if bring can be extended in order to cope with logics endowed with nontruthfunctional semantics as, for example, paraconsistent logics. The rst main contribution of the paper is a positive answer to this question. Furthermore, it is shown that this extended notion of bring preserves completeness under certain reasonable conditions. This completeness transfer result, the second main contribution of the paper, generalizes the one established by Zanardo et al. and is obtained using a new technique exploiting the properties of the metalogic where the (possibly nontruthfunctional) valuations are de ned. The modal paraconsistent logic of da Costa and Carnielli is obtained by bring and its completeness is so established.
Modulated Fibring and the Collapsing Problem
, 2001
"... 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 ..."
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Cited by 26 (13 self)
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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. Main properties like soundness and completeness are shown to be preserved, comparison with bring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem. 1
The UniForM Workbench, a Universal Development Environment for Formal Methods
 FM'99
, 1999
"... The UniForM Workbench supports combination of Formal Methods (on a solid logical foundation), provides tools for the development of hybrid, realtime or reactive systems, transformation, verification, validation and testing. Moreover, it... ..."
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Cited by 20 (3 self)
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The UniForM Workbench supports combination of Formal Methods (on a solid logical foundation), provides tools for the development of hybrid, realtime or reactive systems, transformation, verification, validation and testing. Moreover, it...
Fibring Labelled Deduction Systems
 Journal of Logic and Computation
, 2002
"... We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial ..."
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Cited by 16 (9 self)
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We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial characterization of fibring of models. Based on this, we establish the conditions under which our systems are sound and complete with respect to the general semantics for the corresponding logics, and establish requirements on logics and systems so that completeness is preserved by both forms of fibring.
Specifying Communication in Distributed Information Systems
 Acta Informatica
, 1998
"... . In this paper, we present two logics that allow for specifying distributed information systems, emphasizing communication among sites. The lowlevel logic D 0 offers features that are easy to implement but awkward to use for specification, while the highlevel logic D 1 offers convenient specifica ..."
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Cited by 16 (8 self)
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. In this paper, we present two logics that allow for specifying distributed information systems, emphasizing communication among sites. The lowlevel logic D 0 offers features that are easy to implement but awkward to use for specification, while the highlevel logic D 1 offers convenient specification features that are not easy to implement. We show that D 1 specifications may be automatically translated to D 0 in a sound and complete way. In order to prove soundness and completeness, we define our translation as a simple map of institutions. Our result may be useful for making implementation platforms like Corba easier accessible by providing highlevel planning and specification methods for communication. 1 Introduction Two logics are presented that allow for specifying distributed information systems, emphasizing communication among sites. The lowlevel logic D 0 offers features that are easy to implement but awkward to use for specification, while the highlevel logic D 1 offers...
Fibring Logics with Topos Semantics
, 2002
"... The concept of fibring is extended to higherorder logics with arbitrary modalities and binding operators. A general completeness theorem is established for such logics including HOL and with the metatheorem of deduction. As a corollary, completeness is shown to be preserved when fibring such rich ..."
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Cited by 14 (6 self)
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The concept of fibring is extended to higherorder logics with arbitrary modalities and binding operators. A general completeness theorem is established for such logics including HOL and with the metatheorem of deduction. As a corollary, completeness is shown to be preserved when fibring such rich logics. This result is extended to weaker logics in the cases where fibring preserves conservativeness of HOLenrichments. Soundness is shown to be preserved by fibring without any further assumptions.
Categorial Fibring of Logics with Terms and Binding Operators
 FRONTIERS OF COMBINING SYSTEMS 2, STUDIES IN LOGIC AND COMPUTATION
, 1998
"... Categorial characterizations are given of both unconstrained and constrained fibring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison wi ..."
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Cited by 14 (11 self)
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Categorial characterizations are given of both unconstrained and constrained fibring of Hibert calculi and interpretation systems for languages with variables, terms, variable binding operators and modal like operators. Some preliminary transference results are established. A brief comparison with model theoretic parchments is included.
Fibring Modal FirstOrder Logics: Completeness Preservation
 Logic Journal of the IGPL
, 2002
"... Fibring is de ned as a mechanism for combining logics with a rstorder 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 i ..."
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Cited by 13 (5 self)
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Fibring is de ned as a mechanism for combining logics with a rstorder 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 bring logics in that class. A modal rstorder logic is obtained as a bring where neither the Barcan formula nor its converse hold.