The Conditional Logical Framework LFK is a variant of the Harper-Honsell-Plotkin’s Edinburgh Logical Framemork LF. It features a generalized form of λ-abstraction where β-reductions fire under the condition that the argument satisfies a logical predicate. The key idea is that the type system memorizes under what conditions and where reductions have yet to fire. Different notions of β-reductions corresponding to different predicates can be combined in LFK . The framework LFK subsumes, by simple instantiation, LF (in fact, it is also a subsystem of LF!), as well as a large class of new generalized conditional λ-calculi. These are appropriate to deal smoothly with the side-conditions of both Hilbert and Natural Deduction presentations of Modal Logics. We investigate and characterize the metatheoretical properties of the calculus underpinning LFK, such as subject reduction, confluence, strong normalization.
A Conditional Logical Framework
HONSELL, Furio;LENISA, Marina;SCAGNETTO, Ivan
2008-01-01
Abstract
The Conditional Logical Framework LFK is a variant of the Harper-Honsell-Plotkin’s Edinburgh Logical Framemork LF. It features a generalized form of λ-abstraction where β-reductions fire under the condition that the argument satisfies a logical predicate. The key idea is that the type system memorizes under what conditions and where reductions have yet to fire. Different notions of β-reductions corresponding to different predicates can be combined in LFK . The framework LFK subsumes, by simple instantiation, LF (in fact, it is also a subsystem of LF!), as well as a large class of new generalized conditional λ-calculi. These are appropriate to deal smoothly with the side-conditions of both Hilbert and Natural Deduction presentations of Modal Logics. We investigate and characterize the metatheoretical properties of the calculus underpinning LFK, such as subject reduction, confluence, strong normalization.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
