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73
A Judgmental Reconstruction of Modal Logic
 Mathematical Structures in Computer Science
, 1999
"... this paper we reconsider the foundations of modal logic, following MartinL of's methodology of distinguishing judgments from propositions [ML85]. We give constructive meaning explanations for necessity (2) and possibility (3). This exercise yields a simple and uniform system of natural deductio ..."
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Cited by 183 (42 self)
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deduction for intuitionistic modal logic which does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic [FM97] and find that it is already contained in modal logic, using the decomposition of the lax modality fl A as
Propositional Lax Logic
, 1997
"... We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware verificat ..."
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Cited by 66 (8 self)
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We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal verification of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints  a central notion in hardware
Lax Logical Relations
 In 27th Intl. Colloq. on Automata, Languages and Programming, volume 1853 of LNCS
, 2000
"... Lax logical relations are a categorical generalisation of logical relations; though they preserve product types, they need not preserve exponential types. But, like logical relations, they are preserved by the meanings of all lambdacalculus terms. We show that lax logical relations coincide with th ..."
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Cited by 18 (2 self)
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Lax logical relations are a categorical generalisation of logical relations; though they preserve product types, they need not preserve exponential types. But, like logical relations, they are preserved by the meanings of all lambdacalculus terms. We show that lax logical relations coincide
Proof Search in Lax Logic
, 2000
"... This paper describes two new sequent calculi for Lax Logic. One calculus is for proof enumeration for quanti ed Lax Logic, the other calculus is for theorem proving in propositional Lax Logic ..."
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Cited by 4 (1 self)
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This paper describes two new sequent calculi for Lax Logic. One calculus is for proof enumeration for quanti ed Lax Logic, the other calculus is for theorem proving in propositional Lax Logic
Quantified Lax Logic
, 1997
"... Lax Logic is an intuitionistic modal logic which has so far been investigated at the propositional level. It has shown itself to have applications in the formal verification of hardwarea logical modality is used to capture and express the correctness of specifications `up to' behavioural con ..."
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Cited by 3 (1 self)
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Lax Logic is an intuitionistic modal logic which has so far been investigated at the propositional level. It has shown itself to have applications in the formal verification of hardwarea logical modality is used to capture and express the correctness of specifications `up to' behavioural
Monadic reflection in Lax Logic
"... • Revisit “Representing monads ” [Filinski, 1994] from a logical standpoint. • Goal: understand the logical meaning of shift/reset in the restricted framework of a major application, i.e. implementing monadic reflection. • Through the formulasastypes interpretation, a monad ♦ ⊔ corresponds ..."
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• Revisit “Representing monads ” [Filinski, 1994] from a logical standpoint. • Goal: understand the logical meaning of shift/reset in the restricted framework of a major application, i.e. implementing monadic reflection. • Through the formulasastypes interpretation, a monad ♦ ⊔ corresponds
Reasoning About Staged Computation (Abstract for Invited Talk)
"... Abstract. We report on recent progress in the design of modal dependent type theories that integrate specications into languages for expressing staged computation. Recently, type systems based on constructive modal logic have been proposed as an expressive basis for runtime code generation [DP96,W ..."
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foundation for propositional modal logic [PD00], providing new insights into constructive S4, lax logic [FM97] and the monadic metalanguage [Mog91]. The discipline of the approach brings a number of issues into sharp focus. For example, the choice between intensional and extensional interpretations of modal
Cover semantics for quantified lax logic
 Journal of Logic and Computation
"... Lax modalities occur in intuitionistic logics concerned with hardware verification, the computational lambda calculus, and access control in secure systems. They also encapsulate the logic of LawvereTierneyGrothendieck topologies on topoi. This paper provides a complete semantics for quantified la ..."
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Cited by 1 (0 self)
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Lax modalities occur in intuitionistic logics concerned with hardware verification, the computational lambda calculus, and access control in secure systems. They also encapsulate the logic of LawvereTierneyGrothendieck topologies on topoi. This paper provides a complete semantics for quantified
Lax Extensions of Coalgebra Functors and Their Logic
"... Abstract We discuss the use of relation lifting in the theory of setbased coalgebra and coalgebraic logic. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavioral equivalence. On the other ..."
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bisimilarity captures behavioral equivalence. We also show that a finitary T admits such an extension iff it has a separating set of finitary monotone predicate liftings. Finally, we present the coalgebraic logic, based on a cover modality, for an arbitrary lax extension.
Results 1  10
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