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13
Distributed First Order Logics
, 1998
"... ist and Wiksell, Stockholm, 1965. [ Serafini and Ghidini, 1997 ] L. Serafini and C. Ghidini. Context Based Semantics for Federated Databases. In Proceedings of the 1st International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT97), pages 3345, Rio de Jeneiro, Brazil, 199 ..."
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Cited by 69 (21 self)
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ist and Wiksell, Stockholm, 1965. [ Serafini and Ghidini, 1997 ] L. Serafini and C. Ghidini. Context Based Semantics for Federated Databases. In Proceedings of the 1st International and Interdisciplinary Conference on Modeling and Using Context (CONTEXT97), pages 3345, Rio de Jeneiro, Brazil, 1997. Also IRSTTechnical Report 960902, IRST, Trento, Italy. [ Subrahmanian, 1994 ] V.S. Subrahmanian. Amalgamating Knowledge Bases. ACM Trans. Database Syst., 19(2):291331, 1994. [ Wiederhold, 1992 ] G. Wiederhold. Mediators in the architecture of future information systems. IEEE Computer, 25(3):3849, 1992. and complete calculus for DFOL based on ML systems. Finally we have compared our formalism with other formalisms for the representation and integration of distributed knowledge and reasoning systems. Acknowledgments. We thank all the people of the Mechanized Reasoning Group of IRST and DISA for useful discussions and feedb
Substructural Logics on Display
, 1998
"... Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek ca ..."
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Cited by 50 (16 self)
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Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen's sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek calculus, which contains these multiple connectives, and obtain numerous logics like: exponentialfree linear logic, relevant logic, BCK logic, and intuitionistic logic, in an incremental way. Each of these logics also has a classical counterpart, and some also have a "cyclic" counterpart. These logics have been studied extensively and are quite well understood. Generalising further, one can start with intuitionistic BiLambek logic, which contains the dual of every connective from the Lambek calculus. The addition of the structural rules then gives Bilinear, Birelevant, BiBCK and Biintuitionistic logic, again in an incremental way. Each of these logics also has a classical counterpart, and som...
A Computational Interpretation of Modal Proofs
 Proof Theory of Modal Logics
, 1994
"... The usual (e.g. Prawitz's) treatment of natural deduction for modal logics involves a complicated rule for the introduction of the necessity, since the naive one does not allow normalization. We propose natural deduction systems for the positive fragments of the modal logics K, K4, KT, and S4, ..."
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Cited by 31 (2 self)
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The usual (e.g. Prawitz's) treatment of natural deduction for modal logics involves a complicated rule for the introduction of the necessity, since the naive one does not allow normalization. We propose natural deduction systems for the positive fragments of the modal logics K, K4, KT, and S4, extending previous work by Masini on a twodimensional generalization of Gentzen's sequents (2sequents). The modal rules closely match the standard rules for an universal quantifier and different logics are obtained with simple conditions on the elimination rule for 2. We give an explicit term calculus corresponding to proofs in these systems and, after defining a notion of reduction on terms, we prove its confluence and strong normalization. 1. Introduction Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent impossibility to obtain elegant, natural systems for intensional operators (with the excellent ex...
On the Fine Structure of the Exponential Rule
 Advances in Linear Logic
, 1993
"... We present natural deduction systems for fragments of intuitionistic linear logic obtained by dropping weakening and contractions also on !prefixed formulas. The systems are based on a twodimensional generalization of the notion of sequent, which accounts for a clean formulation of the introduction ..."
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Cited by 14 (4 self)
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We present natural deduction systems for fragments of intuitionistic linear logic obtained by dropping weakening and contractions also on !prefixed formulas. The systems are based on a twodimensional generalization of the notion of sequent, which accounts for a clean formulation of the introduction/elimination rules of the modality. Moreover, the different subsystems are obtained in a modular way, by simple conditions on the elimination rule for !. For the proposed systems we introduce a notion of reduction and we prove a normalization theorem. 1. Introduction Proof theory of modalities is a delicate subject. The shape of the rules governing the different modalities in the overpopulated world of modal logics is often an example of what a good rule should not be. In the context of sequent calculus, if we want cut elimination, we are often forced to accept rules which are neither left nor right rules, and which completely destroy the deep symmetries the calculus is based upon. In the c...
Natural Deduction for NonClassical Logics
, 1996
"... We present a framework for machine implementation of families of nonclassical logics with Kripkestyle semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke m ..."
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Cited by 13 (3 self)
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We present a framework for machine implementation of families of nonclassical logics with Kripkestyle semantics. We decompose a logic into two interacting parts, each a natural deduction system: a base logic of labelled formulae, and a theory of labels characterizing the properties of the Kripke models. By appropriate combinations we capture both partial and complete fragments of large families of nonclassical logics such as modal, relevance, and intuitionistic logics. Our approach is modular and supports uniform proofs of correctness and proof normalization. We have implemented our work in the Isabelle Logical Framework.
ML systems: A Proof Theory for Contexts
, 2001
"... In the last decade the concept of context has been extensively exploited in many research areas, e.g., distributed artificial intelligence, multi agent systems, distributed databases, information integration, cognitive science, and epistemology. Three alternative approaches to the formalization of t ..."
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Cited by 12 (5 self)
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In the last decade the concept of context has been extensively exploited in many research areas, e.g., distributed artificial intelligence, multi agent systems, distributed databases, information integration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion of context have been proposed: Giunchiglia and Serafini's Multi Language Systems (ML systems), McCarthy's modal logics of contexts, and Gabbay's Labelled Deductive Systems. Previous papers have argued in favor of ML systems with respect to the other approaches. Our aim in this paper is to support these arguments from a theoretical perspective. We provide a very general definition of ML systems, which covers all the ML systems used in the literature, and we develop a proof theory for an important subclass of them: the MR systems. We prove various important results; among other things, we prove a normal form theorem, the subformula property, and the decidability of an important instance of the class of the MR systems. The paper concludes with a detailed comparison among the alternative approaches.
Linear Logic by Levels and Bounded Time Complexity
, 2009
"... This work deals with the characterization of elementary and deterministic polynomial time computation in linear logic through the proofsasprograms correspondence. Girard’s seminal results, concerning elementary and light linear logic, use a principle called stratification to ensure the complexity b ..."
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Cited by 10 (1 self)
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This work deals with the characterization of elementary and deterministic polynomial time computation in linear logic through the proofsasprograms correspondence. Girard’s seminal results, concerning elementary and light linear logic, use a principle called stratification to ensure the complexity bound on the cutelimination procedure. Here, we propose a more flexible control principle, that of indexing, which allows us to extend Girard’s systems while keeping the same complexity properties. A consequence of the higher flexibility of indexing with respect to stratification is the absence of boxes for handling the § modality. We finally propose a variant of our polytime system in which the § modality is only allowed on atoms, and which may thus serve as a basis for developing λcalculus type assignment systems with more efficient typing algorithms than existing ones.
Modal Sequent Calculi Labelled with Truth Values: Completeness, Duality and Analyticity
 LOGIC JOURNAL OF THE IGPL
, 2003
"... 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 accessi ..."
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Cited by 8 (5 self)
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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 twosorted algebraic semantics. As a corollary, strong completeness is also obtained over general Kripke semantics. A duality result
Labelled modal sequents
 In Areces and de Rijke [AdR99]. Use Your Logic 7
"... Abstract. In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more “liberal ” modal language which allows inferential steps where different formulas refer to different labels without moving to a particular world and there computing if the consequen ..."
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Cited by 2 (0 self)
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Abstract. In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more “liberal ” modal language which allows inferential steps where different formulas refer to different labels without moving to a particular world and there computing if the consequence holds. Worldpaths can be composed, decomposed and manipulated through unification algorithms and formulas in different worlds can be compared even if they are subformulas which do not depend directly on the main connective. Accordingly, such a sequent system can provide a general definition of modal consequence relation. Finally, we briefly sketch a proof of the soundness and completeness results. 1
A Contextbased Logic for Distributed Knowledge Representation and Reasoning
 Modelling and Using Context
, 1999
"... This paper is concerned with providing a logic, called Distributed First Order Logic (DFOL), for the formalization of distributed knowledge representation and reasoning systems. In such systems knowledge is contained in a set of heterogeneous subsystems. Each subsystem represents, using a possibly d ..."
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Cited by 2 (0 self)
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This paper is concerned with providing a logic, called Distributed First Order Logic (DFOL), for the formalization of distributed knowledge representation and reasoning systems. In such systems knowledge is contained in a set of heterogeneous subsystems. Each subsystem represents, using a possibly different language, partial knowledge about a subset of the whole domain, it is able to reason about such a knowledge, and it is able to exchange knowledge with other subsystems via query answering. Our approach is to represent each subsystem as a context, each context having its own language, a set of basic facts describing what is "explicitly known" by the subsystem, and a set of inference rules representing the reasoning capabilities of the subsystem. Knowledge exchange is represented by two different relations on contexts: the former on the languages (query mapping) and the latter on the domains (answer mapping) of different contexts. DFOL is based on a semantics for contextua...