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189
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 59 (20 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
Rules of definitional reflection
 In Symposium on Logic and Computer Science
, 1993
"... This paper discusses two rules of definitional reflection: The “logical ” version of definitional reflection as used in the extended logic programming language GCLA and the “ω”version of definitional reflection as proposed by Eriksson and Girard. The logical version is a Leftintroduction rule comp ..."
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Cited by 56 (8 self)
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This paper discusses two rules of definitional reflection: The “logical ” version of definitional reflection as used in the extended logic programming language GCLA and the “ω”version of definitional reflection as proposed by Eriksson and Girard. The logical version is a Leftintroduction rule completely analogous to the Leftintroduction rules for logical operators in Gentzenstyle sequent systems, whereas the ωversion extends the logical version by a principle related to the ωrule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection. 1
The Taming of the Cut. Classical Refutations with Analytic Cut
 JOURNAL OF LOGIC AND COMPUTATION
, 1994
"... The method of analytic tableaux is a direct descendant of Gentzen's cutfree sequent calculus and is regarded as a paradigm of the notion of analytic deduction in classical logic. However, cutfree systems are anomalous from the prooftheoretical, the semantical and the computational point of view. F ..."
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Cited by 52 (1 self)
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The method of analytic tableaux is a direct descendant of Gentzen's cutfree sequent calculus and is regarded as a paradigm of the notion of analytic deduction in classical logic. However, cutfree systems are anomalous from the prooftheoretical, the semantical and the computational point of view. Firstly, they cannot represent the use of auxiliary lemmas in proofs. Secondly, they cannot express the bivalence of classical logic. Thirdly, they are extremely inefficient, as is emphasized by the "computational scandal" that such systems cannot polynomially simulate the truthtables. None of these anomalies occurs if the cut rule is allowed. This raises the problem of formulating a proof system which incorporates a cut rule and yet can provide a suitable model of classical analytic deduction. For this purpose we present an alternative refutation system for classical logic, that we call KE. This system, though being "close" to Smullyan's tableau method, is not cutfree but includes a class...
Reasoning Theories  Towards an Architecture for Open Mechanized Reasoning Systems
, 1994
"... : Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be ..."
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Cited by 47 (11 self)
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: Our ultimate goal is to provide a framework and a methodology which will allow users, and not only system developers, to construct complex reasoning systems by composing existing modules, or to add new modules to existing systems, in a "plug and play" manner. These modules and systems might be based on different logics; have different domain models; use different vocabularies and data structures; use different reasoning strategies; and have different interaction capabilities. This paper makes two main contributions towards our goal. First, it proposes a general architecture for a class of reasoning systems called Open Mechanized Reasoning Systems (OMRSs). An OMRS has three components: a reasoning theory component which is the counterpart of the logical notion of formal system, a control component which consists of a set of inference strategies, and an interaction component which provides an OMRS with the capability of interacting with other systems, including OMRSs and hum...
A natural extension of natural deduction
 Journal of Symbolic Logic
, 1984
"... One of the main ideas of calculi of natural deduction, as introduced by Jaskowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions whi ..."
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Cited by 45 (5 self)
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One of the main ideas of calculi of natural deduction, as introduced by Jaskowski and Gentzen, is that assumptions may be discharged in the course of a derivation. As regards sentential logic, this conception will be extended in so far as not only formulas but also rules may serve as assumptions which can be discharged. The resulting calculi and derivations with rules of any finite level are informally introduced in?1, while??2 and 3 state formal definitions of the concepts involved and basic lemmata. Within this framework, a standard form for introduction and elimination rules for arbitrary nary sentential operators is motivated in?4, understood as a contribution to the theory of meaning for logical signs.?5 proves that the set {&, v, D, A} of standard intuitionistic connectives is complete, i.e. &, v a and A suffice to express each nary sentential operator having rules of the standard form given in?4.?6 makes some remarks on related approaches. For an extension of the conception presented here to quantifier logic, see [1 1].?1. Derivations with rules of higher levelsinformal exposition. Assumptions in sentential calculi technically work like additional axioms. A formula a is derivable from formulas,, f38 in a calculus 1 ' if a is derivable in the calculus @ ' resulting from W by adding fi1,..., An as axioms. But whereas "genuine " axioms belong to the chosen framework and are usually assumed to be valid in some sense, assumptions bear an ad hoc character: they are considered only within the context of certain derivations. When deriving ac from Ale..., f we do not want to change our framework and to extend the calculus 1'; we are interested in the derivability relation between I3,.. & Bn and ac with respect to W'. This ad hoc character of assumptions, as compared with axioms, is made obvious in natural deduction systems: some of their inference rules allow one to discharge assumptions used in the derivations of the premisesthat means, such assumptions are used only in specific subderivations for the purpose of establishing a certain formula in the superior derivation. Whereas inference rules of a Hilberttype system may be written as (1) a
A Method for Automatic Cryptographic Protocol Verification
, 2000
"... . We present an automatic, terminating method for verifying confidentiality properties, and to a lesser extent freshness properties of cryptographic protocols. It is based on a safe abstract interpretation of cryptographic protocols using a specific extension of tree automata, parameterized tree ..."
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Cited by 38 (4 self)
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. We present an automatic, terminating method for verifying confidentiality properties, and to a lesser extent freshness properties of cryptographic protocols. It is based on a safe abstract interpretation of cryptographic protocols using a specific extension of tree automata, parameterized tree automata, which mix automatatheoretic techniques with deductive features. Contrary to most modelchecking approaches, this method offers actual security guarantees. It owes much to D. Bolignano's ways of modeling cryptographic protocols and to D. Monniaux' seminal idea of using tree automata to verify cryptographic protocols by abstract interpretation. It extends the latter by adding new deductive abilities, and by offering the possibility of analyzing protocols in the presence of parallel multisession principals, following some ideas by M. Debbabi, M. Mejri, N. Tawbi, and I. Yahmadi. 1 Introduction When secrets are to be preserved, or authenticity of messages is to be establish...
Authentication Tests and the Structure of Bundles
 Theoretical Computer Science
, 2002
"... Suppose a principal in a cryptographic protocol creates and transmits a message containing a new value v, later receiving v back in a different cryptographic context. It can conclude that some principal possessing the relevant key has received and transformed the message in which v was emitted. In s ..."
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Cited by 35 (13 self)
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Suppose a principal in a cryptographic protocol creates and transmits a message containing a new value v, later receiving v back in a different cryptographic context. It can conclude that some principal possessing the relevant key has received and transformed the message in which v was emitted. In some circumstances, this principal must be a regular participant of the protocol, not the penetrator. An inference of this kind is an authentication test. We introduce two main kinds of authentication test. An outgoing test is one in which the new value v is transmitted in encrypted form, and only a regular participant can extract it from that form. An incoming test is one in which v is received back in encrypted form, and only a regular participant can put it in that form. We combine these two tests with a supplementary idea, the unsolicited test, and a related method for checking that keys remain secret. Together, these techniques determine what authentication properties are achieved by a wide range of cryptographic protocols. In this paper we introduce authentication tests and prove their soundness. We illustrate their power by giving new and straightforward proofs of security goals for several protocols. We also illustrate how to use the authentication tests as a heuristic for finding attacks against incorrect protocols. Finally, we suggest a protocol design process. We express these ideas in the strand space formalism [Thayer, Herzog, and Guttman (1999b, Journal of Computer Security, 7, 191230)], which provides a convenient context to prove them correct.
Labelled Propositional Modal Logics: Theory and Practice
, 1996
"... We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and wellknown class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base lo ..."
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Cited by 34 (8 self)
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We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and wellknown class of propositional modal logics (including K, D, T , B, S4, S4:2, KD45, S5). Our approach is modular and based on a separation between a base logic and a labelling algebra, which interact through a fixed interface. While the base logic stays fixed, different modal logics are generated by plugging in appropriate algebras. This leads to a hierarchical structuring of modal logics with inheritance of theorems. Moreover, it allows modular correctness proofs, both with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. We also investigate the tradeoffs in possible labelled presentations: We show that a narrow interface between the base logic and the labelling algebra supports modularity and provides an attractive prooftheory (in comparision to, e.g., semantic embedding) but limits th...
Minimal Classical Logic and Control Operators
 In ICALP: Annual International Colloquium on Automata, Languages and Programming, volume 2719 of LNCS
, 2003
"... We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce's law without enforcing Ex Falso Quodlibet. We show that a \natural" implementation of this logic is Parigot's classical natural deduction. ..."
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Cited by 30 (5 self)
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We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce's law without enforcing Ex Falso Quodlibet. We show that a \natural" implementation of this logic is Parigot's classical natural deduction.