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Deep isomorphism of modal derivations and -terms
 

Summary: Deep isomorphism of modal derivations
and -terms
Sergei N. Artemov 
June, 1999
Abstract
The traditional Curry-Howard isomorphism given a derivation of F
from assumptions in intuitionistic modal logic constructs the -term
t(~x) such that the sequent ~x : ) t(~x) : F is derivable in the corresponding
calculus of typed modal -terms. Technically speaking this isomorphism
is a realization by -terms of the outermost modalities in some (not all)
derivable modal sequents 2 ) 2F .
In this talk we describe a system of -terms (in the combinatory terms
form) LPi suĂcient for a uniform realization of all modalities (not just the
outermost ones) in any derivable modal sequent. The expressive power of
LPi surpasses the one of the usual modal -calculus. LPi also extends
the natural provability semantics of Curry-Howard terms under which t : F
can be interpreted as \t is a proof of F in a given suĂciently rich system,
e.g. Heyting Arithmetic HA".
1 Introduction
The traditional Curry-Howard isomorphism given a derivation ) F constructs

  

Source: Artemov, Sergei N. - Faculty of Mechanics and Mathematics, Moscow State University

 

Collections: Computer Technologies and Information Sciences