Depth-Bounded Logic for Realistic Agents

In this paper we survey the “informational view” of classical propositional logic that has been outlined in (D’Agostino & Floridi, 2009; D’Agostino, 2010, 2013; D’Agostino et al., 2013). This view is based on a kind of “informational semantics” for the logical operators and on a non-standard proof-theory. The latter is a system of classical natural deduction (Mondadori, 1989; D’Agostino, 2005) that, unlike Gentzen’s and Prawitz’s systems, provides natural means for measuring the “depth” of inferences in terms of the minimum number of nested applications of a single (non-eliminable) structural rule, which is an informational version of the Principle of Bivalence and is closely related to classical (analytic) cut. This leads to defining, in a natural way, hierarchies of tractable depth- bounded logical systems that indefinitely approximate Boolean logic. We argue that this approach may be apt to provide more realistic prescriptive models of resource-bounded logical agents and, at the same time, solve the most disturbing anomalies that affect the received view in classical semantics and proof-theory. We also suggest that this informational view of classical logic can partially vindicate the old Kantian idea of synthetic a priori knowledge.