Permutative Conversions in Generalised Multiary -calculus Jos e - - PowerPoint PPT Presentation

Permutative Conversions in Generalised Multiary

• calculus

Jos´ e Esp´ ırito Santo and Lu´ ıs Pinto

jes,luis

@math.uminho.pt. Departamento de Matem´ atica, Universidade do Minho Braga, Portugal

First APPSEM-II Workshop (26-28 March 2003, Nottingham) – p.1/8

• ✄

: the generalised multiary

• calculus

gm-application

Ax

Lft

Axiom

Right

gm-Elim

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Subsystems of

• ✄

gm-application

g-application

Abbreviation:

m-application

Abbreviation:

application

Abbreviation:

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Elimination rules for the subsystems of

• ✄

gm-Elim

g-Elim

m-Elim

Elim

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Reduction rules for

• ✄

• normal forms:

• normal forms: as above, with proviso

if

,

must occur either in

,

• r

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Permutative conversions

if

where

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Main results

Permutability Thms.

iff

,

.

iff

,

.

iff

,

. Representation Thms.

,

.

,

.

,

.

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Conclusion

Permutability study on a multiary sequent calculus with cuts

Defined the calculus

and the notion of generalised multiary application

Computational interpretation for fragments of sequent calculus obtained via their correspondence to extended

• calculi (

,

,

,

)

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