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Fibring of logics as a categorial construction
 Journal of Logic and Computation
, 1999
"... Much attention has been given recently to the mechanism of fibring of logics, allowing free mixing of the connectives and using proof rules from both logics. Fibring seems to be a rather useful and general form of combination of logics that deserves detailed study. It is now well understood at the p ..."
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Cited by 51 (31 self)
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Much attention has been given recently to the mechanism of fibring of logics, allowing free mixing of the connectives and using proof rules from both logics. Fibring seems to be a rather useful and general form of combination of logics that deserves detailed study. It is now well understood at the prooftheoretic level. However, the semantics of fibring is still insufficiently understood. Herein we provide a categorial definition of both prooftheoretic and modeltheoretic fibring for logics without terms. To this end, we introduce the categories of Hilbert calculi, interpretation systems and logic system presentations. By choosing appropriate notions of morphism it is possible to obtain pure fibring as a coproduct. Fibring with shared symbols is then easily obtained by cocartesian lifting from the category of signatures. Soundness is shown to be preserved by these constructions. We illustrate the constructions within propositional modal logic.
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 45 (23 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, ...
Temporal Development Methods for AgentBased Systems
 J. Autonomous Agents and MultiAgent Systems
"... Abstract. In this paper we overview one specific approach to the formal development of multiagent systems. This approach is based on the use of temporal logics to represent both the behaviour of individual agents, and the macrolevel behaviour of multiagent systems. We describe how formal specific ..."
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Cited by 28 (4 self)
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Abstract. In this paper we overview one specific approach to the formal development of multiagent systems. This approach is based on the use of temporal logics to represent both the behaviour of individual agents, and the macrolevel behaviour of multiagent systems. We describe how formal specification, verification and refinement can all be developed using this temporal basis, and how implementation can be achieved by directly executing these formal representations. We also show how the basic framework can be extended in various ways to handle the representation and implementation of agents capable of more complex deliberation and reasoning.
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 20 (12 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
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 (10 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.
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 13 (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...
Combining Valuations with Society Semantics
, 2003
"... Society Semantics, introduced in [5] by W. Carnielli and M. LimaMarques, is a method for obtaining new logics from the combination of agents (valuations) of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to manyvalued ..."
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Cited by 11 (7 self)
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Society Semantics, introduced in [5] by W. Carnielli and M. LimaMarques, is a method for obtaining new logics from the combination of agents (valuations) of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to manyvalued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called P n (for n 2 N) and a hierarchy of paracomplete logics I n (for n 2 N). We also propose three increasing generalizations, obtaining Society Semantics for several manyvalued logics, including a hierarchy of logics called I n P k which are both paraconsistent and paracomplete. Keywords: society semantics, paraconsistent logics, paracomplete logics, manyvalued logics, combinations of logics, agents.
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 11 (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.
Parameterisation of Logics
 Recent trends in algebraic development techniques Selected papers
, 1999
"... . Combined logics have recently deserved much attention. In this paper we develop a detailed study of a form of combination that generalises the temporalisation construction proposed in [9]. It consists of replacing an atomic part (formal parameter) of one (parameterised) logic by another (actual pa ..."
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Cited by 10 (6 self)
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. Combined logics have recently deserved much attention. In this paper we develop a detailed study of a form of combination that generalises the temporalisation construction proposed in [9]. It consists of replacing an atomic part (formal parameter) of one (parameterised) logic by another (actual parameter) logic. We provide a categorial characterisation of parameterisation and illustrate it with an example. Under reasonable assumptions, we show that the result logic is a conservative extension of both the parameterised and parameter logics and also that soundness, completeness and decidability are transferred. 1 Introduction We need to work with evermore complex systems. The challenge is to identify abstractions that may lead to a modular and integrated management of this complexity. One such approach is the combination of logics. In practice, it is geared by the need for integrating heterogeneous platforms and tools. Theoretically, the study of logics for combined structures has bee...
Synchronization of Logics with Mixed Rules: Completeness Preservation
 In Algebraic Methodology and Software Technology  AMAST'97
, 1997
"... . Several mechanisms for combining logics have appeared in the literature. Synchronization is one of the simplest: the language of the combined logic is the disjoint union of the given languages, but the class of models of the resulting logic is a subset of the cartesian product of the given classes ..."
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Cited by 9 (5 self)
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. Several mechanisms for combining logics have appeared in the literature. Synchronization is one of the simplest: the language of the combined logic is the disjoint union of the given languages, but the class of models of the resulting logic is a subset of the cartesian product of the given classes of models (the interaction between the two logics is imposed by constraining the class of pairs of models). Herein, we give both a modeltheoretic and a prooftheoretic account of synchronization as a categorial construction (using coproducts and cocartesian liftings) . We also prove that soundness is preserved by possibly constrained synchronization and state sufficient conditions for preservation of model existence and strong completeness. We provide an application to the combination of dynamic logic and linear temporal logic. Keywords: combination of logics, synchronization of logics, model existence, completeness, dynamic logic, temporal logic. 1 Introduction There has been a recent g...