Canonical Proof nets for Classical Logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In [23], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK\ast in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of [23]), we give a full proof of (c) for expansion nets with respect to LK\ast, and in addition give a cut-elimination procedure internal to expansion nets - this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.Comment: Accepted for publication in APAL (Special issue, Classical Logic and Computation

Conversion Calls for Confrontation: Facing the Old to Become New in the Work of James Baldwin

Book Summary: The recognition and study of African American (AA) artists and public intellectuals often include Martin Luther King, Jr., and occasionally Booker T. Washington, W.E.B.DuBois, and Malcolm X. The literary canon also adds Ralph Ellison, Richard White, Langston Hughes, and others such as female writers Zora Neale Hurston, MayaAngelou, and Alice Walker. Yet, the acknowledgement of AA artists and public intellectuals tends to skew the voices and works of those included toward normalized portrayals that fit well within foundational aspects of the American myths reflected in and perpetuated by traditional schooling. Further, while many AA artists and public intellectuals are distorted by mainstream media, public and political characterizations, and the curriculum, several powerful AA voices are simply omitted, ignored, including James Baldwin. This edited volume gathers a collection of essays from a wide range of perspectives that confront Baldwin’s impressive and challenging canon as well as his role as a public intellectual. Contributors also explore Baldwin as a confrontational voice during his life and as an enduring call for justice. [From the Publisher] Chapter Summary: This discussion examines Baldwin\u27s novel, Go Tell It on the Mountain (1953), and his essay collection, No Name in the Street (1972). Baldwin revisits the traditional biblical conversion narrative by challenging how the converted must learn to reconcile with their past, rather than simply turning away from it

Inflation-Targeting in Sub-Saharan Africa: Why Now? Why at All?

Sub-Saharan Africa, Inflation

Why Have Tax Reforms Hampered MDG Financing?

Tax; Reforms; MDGs; Financing; Poverty