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Extra info for 1998 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '98

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In order to have a viable system. e.. has no ';'. It turns out that this system in which modalized formulas have no more properties than "plain" formulas is a natural object. as proved by the straightforward phase semantics design (see the full extent of this paper [l]). It is of course sound and complete with respect to phase spaces, and enjoys cut 1998 ASSOCIATION FOR SYMBOLIC LOGIC EUROPEAN SUMMER MEETING 105 elimination. [I] AKIMDEMAILLE, Yet another mixed linear logic, Technical Report 98 ZNF 001, &ole Nationale Superieure des Telecommunications.

T] = x: and m, ( ~ x=) Tm, ( x ) Then m, is a bijection: m, is its own inverse: [(x t ) We now employ m, to Induce a new Boolean structure on the set B. e.. to construct the Boolean algebra 13, = (B. L,,n. u . where 7 ) x L J : u m,(x) 5 m,(y): x n J := m, (m, ( x ) A m, (J )): x u y := m,(m,(x) V m t ( y ) ) . 98 1998 ASSOCIATION FOR SYMBOLIC LOGIC EIJROPEAN SUMMER MEETING (Thecomplement operation of BI is the same as that of B,since m, ( ~ m( x, ) ) = mi (m,( l x ) ) = l x . ) Then m, is an isomorphism: ml : B % Br.

E-mail: baazOlogic . at. Institut fiir Computersprachen, University of Vienna, Resselgasse 3, 1040 Vienna, Austria. Statman and Orevkov independently proved that cut-elimination is of non-elementary complexity even for Horn theories. By restricting the logical operators to {A, V, 3,V) we obtain the type of monotone formulas. We show that the elimination of monotone cuts can be of non-elementary complexity (here generalized disjunctions in the antecedents of sequents play a central r6le). On the other hand we define a large class of problems (including all Horn theories) where elimination of monotone cuts is only exponential and show that this bound is tight.

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