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Additional resources for 1998 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '98

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Fields Institute for Research in Mathematical Science, University of Toronto, Toronto M5S 1A4, Canada. ca. A ramified arithmetic 27: is defined whose provable functions are exactly the polynomialtime computable functions. Remarkably, 2;is defined without any reference to polynomial bounds, and using only a small set of initial functions. The system also admits induction over formulas containing arbitrarily many alternations of unbounded quantifiers-these quantifiers range over "tier 0" values, being binary strings not accompanied by any comprehension of the strings.

Syr . edu. Department of Mathematics. Rand Afrikaans University, Box 524. Auckland Park 2006, Johannesburg. South Africa. rau . za. For the branching-time temporal logic based on an Ockhamist semantics (where the truth of a formula is evaluated relative to possible future branches. or equivalently. at pairs (moment, history through that moment), and the temporal operators are relativized to the actual history of the evaluation) we explore a temporal language extended with two additional syntactic tools.

The data-modulated relation S t is nonmonotonic in the following two ways: (1) X L, Y does not imply Z L t Y when Z k X , and (2) X L,, Y does not imply X Liz Y when t z k tl. In the relationship between the orders B and B, the group structure of the Abelian group (B. -, T) plays an interesting role. MARTIN BUNDER AND SACHIO HIROKAWA, Classical formulas as types of Ivcalculus. Department of Mathematics, University of Wollongong, Box 1144,Wollongong, NSW 2500, Australia. E-mail: Mart in-BunderQuuo.

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