Argument-based inductive logics, with coverage of compromised perception

Abstract

Formal deductive logic, used to express and reason over declarative, axiomatizable content, captures, we now know, essentially all of what is known in mathematics and physics, and captures as well the details of the proofs by which such knowledge has been secured. This is certainly impressive, but deductive logic alone cannot enable rational adjudication of arguments that are at variance (however much additional information is added). After affirming a fundamental directive, according to which argumentation should be the basis for human-centric AI, we introduce and employ both a deductive and—crucially—an inductive cognitive calculus. The former cognitive calculus, (Formula presented.), is the deductive one and is used with our automated deductive reasoner ShadowProver; the latter, (Formula presented.), is inductive, is used with the automated inductive reasoner ShadowAdjudicator, and is based on human-used concepts of likelihood (and in some dialects of (Formula presented.), probability). We explain that ShadowAdjudicator centers around the concept of competing and nuanced arguments adjudicated non-monotonically through time. We make things clearer and more concrete by way of three case studies, in which our two automated reasoners are employed. Case Study 1 involves the famous Monty Hall Problem. Case Study 2 makes vivid the efficacy of our calculi and automated reasoners in simulations that involve a cognitive robot (PERI.2). In Case Study 3, as we explain, the simulation employs the cognitive architecture ARCADIA, which is designed to computationally model human-level cognition in ways that take perception and attention seriously. We also discuss a type of argument rarely analyzed in logic-based AI; arguments intended to persuade by leveraging human deficiencies. We end by sharing thoughts about the future of research and associated engineering of the type that we have displayed.