Reasoning and learning with context logic

Abstract

Context logic (CL), a logical language similar in style to description logics but with a more cognitive motivation as a logical language of cognition, was developed since 2007 to provide a new approach to the symbol grounding problem, a key problem for reliable intelligent environments and other intelligent sensory systems. CL is a three-layered integrated hierarchy of languages: a relational base layer with the expressiveness of propositional logic (CLA), a quantifier-free decidable language (CL0), and an expressive language with full quantification (CL1). As was shown in 2018, the core CLA reasoning can be implemented on a variant of Kanerva’s Vector Symbolic Architecture, the activation bit vector machine (ABVM), shedding new light on the fundamental cognitive faculties of symbol grounding and imagery, but the system raised two questions: first, the core reasoning algorithm was a classical EXPTIME reasoner; second, fundamental aspects for a learning algorithm were sketched but not presented with a full algorithm. This paper addresses those two questions. We present a probabilistic linear time algorithm for reasoning over conjunctive normal form (CNF) CLA formulae together with a dual probabilistic linear time algorithm for learning CLA statements by collecting experienced snapshots in a disjunctive normal form (DNF).