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Top1. Introduction
Cognitive Informatics is a multidisciplinary research area that investigates the internal information processing mechanisms of the brain and natural intelligence shared by almost all science and engineering disciplines (Wang, 2007). Cognitive Computing is an emerging paradigm of Artificial Intelligence (AI) based on Cognitive Informatics, that implements computational intelligence by autonomous inferences and perceptions mimicking the mechanisms of the brain and natural intelligence (Wang et al., 2010).
Metacognition in Cognitive Computing refers to the capability of Intelligent Systems (IS) to monitor and control their own learning and reasoning processes. Reasoning and learning processes are two higher level cognitive functions of natural intelligence. Metacognition allows IS to gain awareness of knowledge about cognition and control of cognition.
Now a days increasingly complex IS that make decisions based on multiple variables are being developed. The complexity increases the probability that reasoning failures occur in an IS (Conitzer & Sandholm, 2003; Cox, 2005; Schmid, Ragni, Gonzalez, & Funke, 2011). A reasoning failure is defined as an outcome other than what is expected or a lack of some outcome or appropriate expectation (Cox, 1997). Reasoning failures are generated mainly by unfinished tasks or unexpected results in the performance of a task. Metacognition provides introspective monitoring and meta-level control mechanisms for an IS to detect and correct its own reasoning failures.
Diverse formal models of the brain and mind have been developed in the field of Cognitive Informatics. The layered reference model of the brain (LRMB) (Wang, Wang, Patel, & Patel, 2006) presents a formal and rigorous explanation of the functional mechanisms and cognitive processes of natural intelligence. In LRMB, metacognitive processes are formally described and are arranged in an upper layer of the model. However, the model does not explicitly describe the inherent mechanisms to solve reasoning failures using metacognitive control. Wang describes in (Wang, 2008) formal models for a set of metacognitive processes of the brain using two denotational mathematics, real-time process algebra (RTPA) and concept algebra. Although the metacognitive processes are rigorously formalized, in this work the mechanisms of introspective monitoring and meta-level control applied to the solution of reasoning failures are not described.
Moreover, several models of metacognition focused on solving reasoning failures have been described in the literature. In (Cox, 1997) a formal representation of reasoning failures is presented, but without formally describing the meta-reasoning rules that allow the system to respond to reasoning failures.
Other studies describe different approaches to modeling reasoning failures in intelligent systems. Some works such as (Josyula et al., 2010; Schmill et al., 2007) present models based on ontologies. Case-based Reasoning has been used by (Mehta & Onta, 2009; Soh & Blank, 2008) to represent metacognitive models that respond to reasoning failures. However, none of the models described has approached the description of processes associated with the metacognitive reasoning from a formal perspective. More recent works as (Erdem, Aker, & Patoglu, 2012) describe formalisms for robots responding to failures. However the robot is not able to solve the failure itself but rather seeks help from other robots.
In the context described, the main objective of this paper is to introduce a formal Metacognitive Model for monitoring and control of reasoning failures in intelligent systems. The proposed model is named fM2 and has support for introspective monitoring and meta-level control. fM2 uses predicate logic to represent the basic rules of metacognitive reasoning. fM2 was implemented in an Intelligent Tutorial System (ITS) using SWI-Prolog. The results of validation test indicate that the implementation of fM2 was able to reduce the number of failures of reasoning in IS.