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Quantified multimodal logics in simple type theory
, 2009
"... We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higherorder theorem provers, to demonstr ..."
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Cited by 27 (16 self)
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We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple experiments, using existing higherorder theorem provers, to demonstrate that the embedding allows automated proofs of statements in these logics, as well as meta properties of them.
Terminating tableau systems for hybrid logic with difference and converse
, 2009
"... This paper contributes to the principled construction of tableaubased decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For conversefree formulas we present a terminating control that does not rely on the usu ..."
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Cited by 14 (4 self)
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This paper contributes to the principled construction of tableaubased decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For conversefree formulas we present a terminating control that does not rely on the usual chainbased blocking scheme. Our tableau systems are based on a new model existence theorem.
Multimodal and Intuitionistic Logics in Simple Type Theory
"... We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational inve ..."
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Cited by 14 (12 self)
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We study straightforward embeddings of propositional normal multimodal logic and propositional intuitionistic logic in simple type theory. The correctness of these embeddings is easily shown. We give examples to demonstrate that these embeddings provide an effective framework for computational investigations of various nonclassical logics. We report some experiments using the higherorder automated theorem prover LEOII.
Automating access control logics in simple type theory with LEOII
 FB Informatik, U. des Saarlandes
, 2008
"... Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrate ..."
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Cited by 13 (11 self)
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Abstract Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory and we have demonstrated that the higherorder theorem prover LEOII can automate reasoning in and about them. In this paper we combine these results and describe a sound (and complete) embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEOII can be applied to automate reasoning in and about prominent access control logics. 1
Terminating Tableaux for Graded Hybrid Logic with Global Modalities and Role Hierarchies
"... Abstract. We present a terminating tableau calculus for graded hybrid logic with global modalities, reflexivity, transitivity and role hierarchies. Termination of the system is achieved through patternbased blocking. Previous approaches to related logics all rely on chainbased blocking. Besides be ..."
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Cited by 8 (1 self)
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Abstract. We present a terminating tableau calculus for graded hybrid logic with global modalities, reflexivity, transitivity and role hierarchies. Termination of the system is achieved through patternbased blocking. Previous approaches to related logics all rely on chainbased blocking. Besides being conceptually simple and suitable for efficient implementation, the patternbased approach gives us a NExpTime complexity bound for the decision procedure.
An Efficient Approach to Nominal Equalities in Hybrid Logic Tableaux
"... This is a draft version of a paper published on the Journal of Applied NonClassical Logics. It should not be cited, quoted or reproduced. Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the socalled satis ..."
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Cited by 5 (4 self)
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This is a draft version of a paper published on the Journal of Applied NonClassical Logics. It should not be cited, quoted or reproduced. Basic hybrid logic extends modal logic with the possibility of naming worlds by means of a distinguished class of atoms (called nominals) and the socalled satisfaction operator, that allows one to state that a given formula holds at the world named a, for some nominal a. Hence, in particular, hybrid formulae include “equality ” assertions, stating that two nominals are distinct names for the same world. The treatment of such nominal equalities in proof systems for hybrid logics may induce many redundancies. This paper introduces an internalized tableau system for basic hybrid logic, significantly reducing such redundancies. The calculus enjoys a strong termination property: tableau construction terminates without relying on any specific rule application strategy, and no loopchecking is needed. The treatment of nominal equalities specific of the proposed calculus is briefly compared to other approaches. Its practical advantages are demonstrated by empirical results obtained by use of implemented systems. Finally, it is briefly shown how to extend the calculus to include the global and converse modalities. 1
Two tableau provers for basic hybrid logic
, 2009
"... loopchecking and with any rule application strategy. The two systems were independently proposed, respectively, by Bolander and Blackburn [1] and Cerrito and Cialdea Mayer [2]. The comparison is carried out both from the theoretical point of view and on the practical side. The two calculi bear stro ..."
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Cited by 4 (3 self)
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loopchecking and with any rule application strategy. The two systems were independently proposed, respectively, by Bolander and Blackburn [1] and Cerrito and Cialdea Mayer [2]. The comparison is carried out both from the theoretical point of view and on the practical side. The two calculi bear strong similarities that are highlighted in the paper. They do differ, however, in the treatment of nominal equalities, which in [1] is elegant and simple, while in [2] is more technically involved, using, in fact, explicit substitution and nominal deletion. As a matter of fact, nominal deletion is the crucial difference with the treatment of equalities in the tableau system for hybrid logic previously proposed by van Eijck [10]. In order to evaluate the impact of the different approaches to nominal equalities of the considered calculi, they have been implemented and their performances compared. This work describes the implementations and the results of the empirical evaluation, which shows that substitution and nominal deletion, although unelegant from the theoretical point of view, has meaningful practical advantages. 2 1
Terminating Tableau Systems for Modal Logic with Equality
, 2008
"... The paper presents two terminating tableau systems for hybrid logic with the difference modality. Both systems are based on an abstract treatment of equality. They expand formulas with respect to a congruence closure that is not represented explicitly. The first system employs patternbased blocking ..."
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The paper presents two terminating tableau systems for hybrid logic with the difference modality. Both systems are based on an abstract treatment of equality. They expand formulas with respect to a congruence closure that is not represented explicitly. The first system employs patternbased blocking. The second system employs chainbased blocking and covers converse modalities. Both systems can handle transitive relations. 1Introduction There are two established ways to arrive at modal logic with equality [5, 10, 1]. One approach employs the difference modality D, defined such that a property Ds holds for a state x if there exists a different state y such that s holds for y. The other approach, known as hybrid logic, employs nominals, which are primitive properties holding for exactly one state x. Without further extensions, the difference modality is more powerful than nominals. Once nominals are accompanied by the global modality E (Es holds for x if there exists a y for which s holds), both approaches have the same expressivity [13].
Hybrid Logic with the Difference Modality for Generalisations of Graphs
"... We discuss recent work generalising the basic hybrid logic with the difference modality to any reasonable notion of transition. This applies equally to both subrelational transitions such as monotone neighbourhood frames or selection function models as well as those with more structure such as Marko ..."
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We discuss recent work generalising the basic hybrid logic with the difference modality to any reasonable notion of transition. This applies equally to both subrelational transitions such as monotone neighbourhood frames or selection function models as well as those with more structure such as Markov chains and alternating temporal frames. We provide a generic canonical cutfree sequent system and a terminating proofsearch strategy for the fragment without the difference modality but including the global modality. Keywords: Global Modality, Difference Modality, Coalgebraic Semantics, Cutfree Sequent System
AGS 2004 This SEKI Report was internally reviewed by:
, 901
"... Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory (which is also known as highero ..."
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Garg and Abadi recently proved that prominent access control logics can be translated in a sound and complete way into modal logic S4. We have previously outlined how normal multimodal logics, including monomodal logics K and S4, can be embedded in simple type theory (which is also known as higherorder logic) and we have demonstrated that the higherorder theorem prover LEOII can automate reasoning in and about them. In this paper we combine these results and describe a sound and complete embedding of different access control logics in simple type theory. Employing this framework we show that the off the shelf theorem prover LEOII can be applied to automate reasoning in prominent access control logics. 1