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Reports on Mathematical Logic

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No. 32 (1998)

Francesco PAOLI:

Simplified Affine Phase Structures
A b s t r a c t.
Phase models for affine linear logic were independently devised
by Lafont [10] and Piazza [15], although foreshadowed by Ono [14].
However, the existing semantics either contain no explicit directions for
the construction of models in the general case, or else are forced to
resort to additional conditions extending Girard's semantics (preordering
of the monoids, the condition that the set of antiphases be an ideal). We
dispense with these extra postulates - at least for the subexponential
fragment of this logic - considering structures where the set of
antiphases is concretely constructed. Moreover, we show the equivalence of
our phase models and the algebraic models of affine linear logic by means
of a representation theorem.

*Due to an unfortunate printing error (inconsistency of the fonts) the
paper contains many errors. We print the corrected version of the article
in
RML 33*

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