Declarative/Logic-Based Computational Cognitive Modeling∗

This chapter is an esemplastic systematization of declarative computational cognitive modeling, a field that cuts across cognitive modeling based on cognitive architectures (such as ACT-R, Soar, and Clarion), human-level artificial intelligence (AI), logic itself, and psychology of reasoning (especially of the computational kind). The hallmarks of declarative computational cognitive modeling are the following two intertwined constraints: (1) The central units of information used in the approach are (at least in significant part) declarative in nature, and the central process carried out over these units is inference. (2) The approach to modeling the mind is top-down, rather than bottom-up. (These two points are interconnected because once one commits to (1), (2) becomes quite unavoidable, since bottom-up processing in the brain, as reflected in relevant formalisms (e.g., artificial neural networks), is based on units of information that are numerical, not declarative.) The systematization of declarative computational cognitive modeling is achieved by using formal logic, and hence declarative computational cognitive modeling, from the formal perspective, becomes logic-based computational cognitive modeling (LCCM). The chapter covers some prior research that falls under LCCM; this research has been carried out by such thinkers as Johnson-Laird, Langley, Rips, Simon, and Sun. The material that follows is introductory in nature, and self-contained; it assumes only a modicum of previous exposure to discrete mathematics and computability theory. The key formal elements of LCCM are (a) a generalization of the concept of a logical system, central to mathematical logic, and (b) computing in such systems in the declarative programming paradigm, via logic-based computer programs, which are generalized versions of logic programs from mathematical logic and computer science. In LCCM, a (logic-based) computational cognitive model of some (or all) human cognition amounts to the execution of a logic-based computer program PL in the context of a logical system selected from a family F of such systems. LCCM is designed to meet a number of challenges facing those wishing to devise computational simulations of human cognition. Three such challenges are discussed in the present chapter: the need to model and simulate sophisticated human reasoning (of the three, the one emphasized herein); the need to formulate a transparently unified theory of cognition; and the apparent need to achieve significant rigor in the computational simulation of human cognition — rigor which, in LCCM, emerges naturally from providing a formal syntax and semantics that precisely determines the structure and meaning of a logical system used to represent some part of human cognition, and determines as well the meaning of a computational cognitive model, or simulation, on the strength of the fact that the meaning of a logic-based computer program is easily made precise. The gain in precision offered by LCCM enables this field to be, like physics, mathematics, logic, and computer science, theorem-guided. Many regard such guidance to be desirable. ∗Special thanks are due to my friend and colleague Konstantine Arkoudas for myriad suggestions, and for implemented systems that help make declarative computational cognitive modeling a concrete, rigorous reality.