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33
The RussellPrawitz Modality
, 1999
"... this paper are to highlight the notion of a lax modality, :: being the paradigm example, to generalise the double negation interpretation to any lax modality and to characterize the RussellPrawitz reinterpretation of intuitionistic logic as a variant of this generalisation for a lax modality P that ..."
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Cited by 15 (1 self)
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this paper are to highlight the notion of a lax modality, :: being the paradigm example, to generalise the double negation interpretation to any lax modality and to characterize the RussellPrawitz reinterpretation of intuitionistic logic as a variant of this generalisation for a lax modality P
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
Tschantz. From indexed lax logic to intuitionistic logic
, 2008
"... We present translations from a logic with indexed lax modalities to firstorder intuitionistic logic and intuitionistic linear logic. These translations rely on a continuation passing style encoding for the lax modalities. We show that our translations preserve provability of formulas. 1 ..."
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Cited by 1 (0 self)
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We present translations from a logic with indexed lax modalities to firstorder intuitionistic logic and intuitionistic linear logic. These translations rely on a continuation passing style encoding for the lax modalities. We show that our translations preserve provability of formulas. 1
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
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
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
A pragmatic framework for intuitionistic modalities: Classical logic and Lax logic.
"... Summary. We reconsider Dalla Pozza and Garola pragmatic interpretation of intuitionistic logic [13] where sentences and proofs formalize assertions and their justifications and revise it so that the costruction is done within an intuitionistic metatheory. We reconsider also the extension of Dalla Po ..."
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is justified and of expectation, an assertion that a hypothesis is justified we obtain pragmatic counterparts of the modalities of classical S4, but also a framework for different interpretations of intuitionistic modalities necessity and possibility. We consider two applications: one is typing Parigot’s λµ
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.
Under consideration for publication in Math. Struct. in Comp. Science A Judgmental Reconstruction of Modal Logic
, 2000
"... We reconsider the foundations of modal logic, following MartinLöf’s methodology of distinguishing judgments from propositions. We give constructive meaning explanations for necessity and possibility which yields a simple and uniform system of natural deduction for intuitionistic modal logic which ..."
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does not exhibit anomalies found in other proposals. We also give a new presentation of lax logic and nd that the lax modality is already expressible using possibility and necessity. Through a computational interpretation of proofs in modal logic we further obtain a new formulation of Moggi’s monadic
Almost duplicationfree tableau calculi for propositional Lax logics
 In TABLEAUX'96
, 1996
"... In this paper we provide tableau calculi for the intuitionistic modal logics PLL and PLL 1 , where the calculus for PLL 1 is duplicationfree while among the rules for PLL there is just one rule that allows duplication of formulas. These logics have been investigated by Fairtlough and Mendler in re ..."
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Cited by 4 (0 self)
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In this paper we provide tableau calculi for the intuitionistic modal logics PLL and PLL 1 , where the calculus for PLL 1 is duplicationfree while among the rules for PLL there is just one rule that allows duplication of formulas. These logics have been investigated by Fairtlough and Mendler
Results 1  10
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