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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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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
Semantic Labelled Tableaux for Propositional BI
 Journal of Logic and Computation
, 2003
"... In this paper, we study semantic labelled tableaux for the propositional Bunched Implications logic (BI) that freely combines intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL). ..."
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In this paper, we study semantic labelled tableaux for the propositional Bunched Implications logic (BI) that freely combines intuitionistic logic (IL) and multiplicative intuitionistic linear logic (MILL).
www.elsevier.com/locate/tcs The universe of propositional approximations
"... The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249–310] as a way of modelling the reasoning of an agent with limited resources. In that framework, a family of logics, parameterised by a set of proposition ..."
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The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249–310] as a way of modelling the reasoning of an agent with limited resources. In that framework, a family of logics, parameterised by a set of propositional letters, approximates classical logic as the size of the set increases. The original proposal dealt onlywith formulas in clausal form, but in Finger andWassermann [Approximate and limited reasoning: semantics, proof theory, expressivity and control, J. Logic Comput. 14(2) (2004) 179–204], one of the approximate systems was extended to deal with full propositional logic, giving the new system semantics, an axiomatisation, and a sound and complete proof method based on tableaux. In this paper, we extend another approximate system by Schaerf and Cadoli, presented in a subsequent work [M. Cadoli, M. Schaerf, The complexity of entailment in propositional multivalued logics, Ann. Math. Artif. Intell. 18(1) (1996) 29–50] and then take the idea further, presenting a more general approximation framework of which the previous ones are particular cases, and show how it can be used to formalise heuristics used in theorem proving.
A Tableau Compiled Labelled Deductive System for Hybrid Logic
"... Compiled Labelled Deductive Systems (CLDS) provide a uniform logical framework where families of different logics can be given a uniform proof system and semantics. A variety of applications of this framework have been proposed so far ranging from extensions of classical logics (e.g. normal modal lo ..."
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Compiled Labelled Deductive Systems (CLDS) provide a uniform logical framework where families of different logics can be given a uniform proof system and semantics. A variety of applications of this framework have been proposed so far ranging from extensions of classical logics (e.g. normal modal logics and multimodal logics) to nonclassical logics such as resource and substructural loogics. Labelled natural deduction proof systems have been developed and proved to be a generalization of existing proof systems for each of these logics. This extended abstract gives a brief presentation of the CLDS framework and outlines how it can be applied to develop a labeled tableau system for Hybrid Logic. 1
Compiled Labelled Deductive Systems for Access Control
"... abstract. This paper proposes a Compiled Labelled Deductive System, called ACCLDS, for reasoning about rolebased access control in distributed systems, which builds upon Massacci’s tableau system for rolebased access control. The ACCLDS system overcomes some of the limitations of Massaci’s approac ..."
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abstract. This paper proposes a Compiled Labelled Deductive System, called ACCLDS, for reasoning about rolebased access control in distributed systems, which builds upon Massacci’s tableau system for rolebased access control. The ACCLDS system overcomes some of the limitations of Massaci’s approach by combining its multimodal propositional language with a labelling algebra that allows reasoning explicitly about dynamic properties of the accessibility relations. This combined feature, which is typical of the Compiled Labelled Deductive framework, facilitates a sound and complete, and more natural ACCLDS reasoning mechanism than Massacci’s sound and only partially complete tableau system. Limitations of the usefulness of Massacci’s multimodal logic in formalising access control systems are also discussed, showing that they relate to the initial formulation of Abadi’s calculus for access control. Solutions for overcoming these limitations are briefly proposed within the context of the ACCLDS system. 1