The Cognitive Processes of Formal Inferences

The Cognitive Processes of Formal Inferences

Yingxu Wang (University of Calgary, Canada)
Copyright: © 2009 |Pages: 14
DOI: 10.4018/978-1-60566-170-4.ch006
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Theoretical research is predominately an inductive process, while applied research is mainly a deductive process. Both inference processes are based on the cognitive process and means of abstraction. This chapter describes the cognitive processes of formal inferences such as deduction, induction, abduction, and analogy. Conventional propositional arguments adopt static causal inference. This chapter introduces more rigorous and dynamic inference methodologies, which are modeled and described as a set of cognitive processes encompassing a series of basic inference steps. A set of mathematical models of formal inference methodologies is developed. Formal descriptions of the 4 forms of cognitive processes of inferences are presented using Real-Time Process Algebra (RTPA). The cognitive processes and mental mechanisms of inferences are systematically explored and rigorously modeled. Applications of abstraction and formal inferences in both the revilement of the fundamental mechanisms of the brain and the investigation of next generation cognitive computers are explored.
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Inferences are a formalized cognitive process that reasons a possible causal conclusion from given premises based on known causal relations between a pair of cause and effect proven true by empirical observations, theoretical inferences, and/or statistical regulations (Bender, 1996; Wilson and Keil, 2001; Wang, 2007a). Formal logic inferences may be classified as causal argument, deductive inference, inductive inference, abductive inference, and analogical inference (Schoning, 1989; Sperschneider and Antoniou, 1991; Hurley, 1997; Tomassi, 1999; Smith, 2001; Wilson and Keil, 2001; Wang et al., 2006).

Theoretical research is predominately an inductive process; while applied research is mainly a deductive process. Abstraction is a powerful means of philosophy and mathematics. It is also a preeminent trait of the human brain identified in cognitive informatics studies (Wang, 2005, 2007c; Wang et al., 2006). All formal logical inferences and reasonings can only be carried out on the basis of abstract properties shared by a given set of objects under study.

  • Definition 1.Abstraction is a process to elicit a subset of objects that shares a common property from a given set of objects and to use the property to identify and distinguish the subset from the whole in order to facilitate reasoning.

Abstraction is a gifted capability of human beings. Abstraction is a basic cognitive process of the brain at the meta cognitive layer according to the Layered Reference Model of the Brain (LRMB) (Wang, 2003a, 2007c; Wang et al., 2003, 2006). Only by abstraction can important theorems and laws about the objects under study be elicited and discovered from a great variety of phenomena and empirical observations in an area of inquiry.

  • Definition 2.Inferences are a formal cognitive process that reasons a possible causality from given premises based on known causal relations between a pair of cause and effect proven true by empirical arguments, theoretical inferences, or statistical regulations.

Mathematical logic, such as propositional and predicate logic, provide a powerful means for logical reasoning and inference on truth and falsity (Schoning, 1989; Sperschneider and Antoniou, 1991; Hurley, 1997; van Heijenoort, 1997).

  • Definition 3. An argument Α is an assertion that yields (□) a proposition Q called the conclusion from a given finite set of propositions known as the premises P1, P2, …, Pn, i.e.:

ΑBL Α (P1BL ∧ P2BL ∧ … ∧ PnBL □ QBL)BL (1)where the argument and all propositions are in type Boolean (BL). Hence, ΑBL = T called a valid argument, otherwise it is a fallacy, i.e. ΑBL = F.

Equation 1 can also be denoted in the following inference structure:

  • Example 1. The following expressions are concrete arguments:

    • a.

      A concrete deductive argument


    • b.

      A concrete inductive argument


  • Example 2. The following expressions are abstract arguments:

    • a.

      Abstract deductive arguments



where N represents the type of natural numbers.
  • b.

    Abstract inductive arguments



where N represents the type of natural numbers.

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Table of Contents
Yingxu Wang
Chapter 1
Yingxu Wang
Cognitive Informatics (CI) is a transdisciplinary enquiry of the internal information processing mechanisms and processes of the brain and natural... Sample PDF
The Theoretical Framework of Cognitive Informatics
Chapter 2
Withold Kinsner
This chapter provides a review of Shannon and other entropy measures in evaluating the quality of materials used in perception, cognition, and... Sample PDF
Is Entropy Suitable to Characterize Data and Signals for Cognitive Informatics?
Chapter 3
Ismael Rodríguez, Manuel Núñez, Fernando Rubio
Finite State Machines (FSM) are formalisms that have been used for decades to describe the behavior of systems. They can also provide an intelligent... Sample PDF
Cognitive Processes by using Finite State Machines
Chapter 4
Yingxu Wang
An interactive motivation-attitude theory is developed based on the Layered Reference Model of the Brain (LRMB) and the Object-Attribute-Relation... Sample PDF
On the Cognitive Processes of Human Perception with Emotions, Motivations, and Attitudes
Chapter 5
Qingyong Li, Zhiping Shi, Zhongzhi Shi
Sparse coding theory demonstrates that the neurons in the primary visual cortex form a sparse representation of natural scenes in the viewpoint of... Sample PDF
A Selective Sparse Coding Model with Embedded Attention Mechanism
Chapter 6
Yingxu Wang
Theoretical research is predominately an inductive process, while applied research is mainly a deductive process. Both inference processes are based... Sample PDF
The Cognitive Processes of Formal Inferences
Chapter 7
Douglas Griffith, Frank L. Greitzer
The purpose of this article is to re-address the vision of human-computer symbiosis as originally expressed by J.C.R. Licklider nearly a... Sample PDF
Neo-Symbiosis: The Next Stage in the Evolution of Human Information Interaction
Chapter 8
Ray E. Jennings
Although linguistics may treat languages as a syntactic and/or semantic entity that regulates both language production and comprehension, this... Sample PDF
Language, Logic, and the Brain
Chapter 9
Yingxu Wang, Guenther Ruhe
Decision making is one of the basic cognitive processes of human behaviors by which a preferred option or a course of actions is chosen from among a... Sample PDF
The Cognitive Process of Decision Making
Chapter 10
Tiansi Dong
This chapter proposes a commonsense understanding of distance and orientation knowledge between extended objects, and presents a formal... Sample PDF
A Commonsense Approach to Representing Spatial Knowledge Between Extended Objects
Chapter 11
Natalia López, Manuel Núñez, Fernando L. Pelayo
In this chapter we present the formal language, stochastic process algebra (STOPA), to specify cognitive systems. In addition to the usual... Sample PDF
A Formal Specification of the Memorization Process
Chapter 12
Yingxu Wang
Autonomic computing (AC) is an intelligent computing approach that autonomously carries out robotic and interactive applications based on goal- and... Sample PDF
Theoretical Foundations of Autonomic Computing
Chapter 13
Witold Kinsner
Numerous attempts are being made to develop machines that could act not only autonomously, but also in an increasingly intelligent and cognitive... Sample PDF
Towards Cognitive Machines: Multiscale Measures and Analysis
Chapter 14
Amar Ramdane-Cherif
Cognitive approach through the neural network (NN) paradigm is a critical discipline that will help bring about autonomic computing (AC). NN-related... Sample PDF
Towards Autonomic Computing: Adaptive Neural Network for Trajectory Planning
Chapter 15
Lee Flax
We give an approach to cognitive modelling, which allows for richer expression than the one based simply on the firing of sets of neurons. The... Sample PDF
Cognitive Modelling Applied to Aspects of Schizophrenia and Autonomic Computing
Chapter 16
Yan Zhao, Yiyu Yao
Classification is one of the main tasks in machine learning, data mining, and pattern recognition. Compared with the extensively studied automation... Sample PDF
Interactive Classification Using a Granule Network
Chapter 17
Mehdi Najjar, André Mayers
Encouraging results of last years in the field of knowledge representation within virtual learning environments confirms that artificial... Sample PDF
A Cognitive Computational Knowledge Representation Theory
Chapter 18
Du Zhang
A crucial component of an intelligent system is its knowledge base that contains knowledge about a problem domain. Knowledge base development... Sample PDF
A Fixpoint Semantics for Rule-Base Anomalies
Chapter 19
Christine W. Chan
This chapter presents a method for ontology construction and its application in developing ontology in the domain of natural gas pipeline... Sample PDF
Development of an Ontology for an Industrial Domain
Chapter 20
Václav Rajlich, Shaochun Xu
This article explores the non-monotonic nature of the programmer learning that takes place during incremental program development. It uses a... Sample PDF
Constructivist Learning During Software Development
Chapter 21
Witold Kinsner
Many scientific chapters treat the diversity of fractal dimensions as mere variations on either the same theme or a single definition. There is a... Sample PDF
A Unified Approach to Fractal Dimensions
Chapter 22
Du Zhang, Witold Kinsner, Jeffrey Tsai, Yingxu Wang, Philip Sheu, Taehyung Wang
The 2005 IEEE International Conference on Cognitive Informatics (ICCI’05) was held during August 8th to 10th 2005 on the campus of University of... Sample PDF
Cognitive Informatics: Four Years in Practice
Chapter 23
Yiyu Yao, Zhongzhi Shi, Yingxu Wang, Witold Kinsner, Yixin Zhong, Guoyin Wang
Cognitive informatics (CI) is a cutting-edge and multidisciplinary research area that tackles the fundamental problems shared by modern informatics... Sample PDF
Toward Cognitive Informatics and Cognitive Computers: A Report on IEEE ICCI'06
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