Introduction to Part II

Abstract

Just as the propositional assumptions in a sequent may be structured as bunches, supporting the distinction between additive and multiplicative connectives, so the collection of (first-order) variables over which such a sequent is formed may be structured as bunches of variables. With variables structured as bunches, each connective may be formulated either with additive maintenance of variables or with multiplicative maintenance of variables. So, just as explicit control of the structural rules at the propositional level decomposes conjunction and implication into additive and multiplicative parts, so explicit control of the structural rules in the formation of terms further decomposes each predicate connective into additive and multiplicative parts. We describe this idea here using a single-sorted version of predicate BI. We suppress the details of function symbols and the formation of terms. For simplicity in this introduction, we work with bunches of variables without types.

Some of the content of Part II has appeared in [O’Hearn and Pym, 1999, Pym, 1999, Ishtiaq and Pym, 1998, Ishtiaq and Pym, 1999, Ishtiaq and Pym, 2000, Ishtiaq and Pym, 2001, ArmelIn and Pym, 2001]. References are given in the text as appropriate.

—DJP