Cognitive Reasoning | springerprofessional.de

Springer Professional

nach oben

2010 | Buch

Kapitel lesen Erstes Kapitel lesen

Cognitive Reasoning

A Formal Approach

verfasst von: Tamás Gergely, Oleg M. Anshakov

Verlag: Springer Berlin Heidelberg

Buchreihe : Cognitive Technologies

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten

Über dieses Buch

Dealing with uncertainty, moving from ignorance to knowledge, is the focus of cognitive processes. Understanding these processes and modelling, designing, and building artificial cognitive systems have long been challenging research problems.

This book describes the theory and methodology of a new, scientifically well-founded general approach, and its realization in the form of intelligent systems applicable in disciplines ranging from social sciences, such as cognitive science and sociology, through natural sciences, such as life sciences and chemistry, to applied sciences, such as medicine, education, and engineering.

The main subject developed in the book is cognitive reasoning investigated at three levels of abstraction: conceptual, formal, and realizational. The authors offer a model of a cognizing agent for the conceptual theory of cognitive reasoning, and they also present a logically well-founded formal cognitive reasoning framework to handle the various plausible reasoning methods. They conclude with an object model of a cognitive engine.

The book is suitable for researchers, scientists, and graduate students working in the areas of artificial intelligence, mathematical logic, and philosophy.

Anzeige

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract

Recently the creation of artificial cognitive systems has been one of the main challenges in the field of information and communication technology. Despite the many alternative approaches a complete and convincing artificial cognitive system has not yet been developed and, even further, it has not been known how to design and build artificial cognitive systems. This is why understanding cognition and modelling, designing and building artificial cognitive systems are challenging but long-term research problems. In this book we wish to take a step towards a better understanding of cognition and its modelling by providing a well-founded integrated theory together with methods and tools for designing and building artificial cognitive systems.

Oleg M. Anshakov, Tamás Gergely

Conceptual Theory of Cognitive Reasoning

Frontmatter

Chapter 2. Introductory Explanation

Abstract

In this chapter we develop the first constituent of the proposed formal approach, namely the conceptual theory of cognitive reasoning. In the course of this discussion, the key topics included in this book emerge at the conceptual level. We will describe the main processes and their cognitive reasoning constituents which permit going beyond the readily available information. We will develop a model which represents the processes occurring as common forms of reasoning in the case of insufficient and incomplete information. In order to characterise and model cognitive reasoning processes we will describe the systems where these processes take place. Thus we will model cognitive reasoning with respect to a general cognitive system able to interact with its environment to obtain data, facts and information, and to process these in order to extract new information and relationships. These will be used to augment the system’s knowledge about the environment or about a problem domain. The model of cognitive reasoning will be developed with respect to a model of the cognizing agent.

Oleg M. Anshakov, Tamás Gergely

Chapter 3. Basic System of Concepts

Abstract

The objective of the present chapter is the informal introduction of the main notions that will serve as the basis of our approach for modelling cognitive reasoning. Most of these notions should be well known to readers. However we aim not to give them a formal definition but to provide an explanation of how these notions will be understood and applied by our approach in the forthcoming sections.

Oleg M. Anshakov, Tamás Gergely

Chapter 4. Constructing a Model of a Cognizing Agent

Abstract

In this chapter we describe the structure, processes, techniques and methods at the conceptual level, which according to our approach will be necessary (i) to understand (e.g. human) cognition and (ii) to support its modelling. This structure, together with all the constituents forms, we call a “cognitive architecture”. This architecture will be developed w.r.t. a cognizing agent, which is the main actor in our approach. A cognizing agent means either a living entity (particularly a human being), or a group of them or a technical system, which can adapt to the changing conditions of the external environment.

Oleg M. Anshakov, Tamás Gergely

Chapter 5. Cognitive Reasoning Framework

Abstract

In this chapter we aim to provide a conceptual theory of cognitive reasoning processes, i.e. processes that permit a cognizing agent to gain new knowledge.

According to our approach the conceptual model should provide the preparatory stage for the development of the formal theory of cognitive reasoning. Therefore the main constituents of the formal theory should be prepared on the conceptual level. Our conceptual theory should meet the following main requirements.

Oleg M. Anshakov, Tamás Gergely

Logic Foundation

Frontmatter

Chapter 6. Introductory Explanation

Abstract

In this part we are going to develop the logic foundation of our approach which is to provide an appropriate formalism to represent, simulate and generate the cognitive reasoning processes of cognizing agents. Thus, in our view, the foundation should be appropriate for the representation of the process from ignorance to knowledge, that is, the learning and knowledge acquisition processes.

Oleg M. Anshakov, Tamás Gergely

Chapter 7. Propositional Logic

Abstract

The main purpose of this chapter is to introduce some classes of many-valued logics, namely the class of pure J logic (PJ logics) and two its subclasses: the class of finite pure J logics (FPJ logics) and the class of iterative versions of finite PJ logics.

Oleg M. Anshakov, Tamás Gergely

Chapter 8. First-Order Logics

Abstract

In this chapter we introduce the first-order logics that correspond to the propositional ones discussed in the previous section. We will consider many-sorted firstorder logics where many-sortedness is significant for the applications further to be discussed.

Oleg M. Anshakov, Tamás Gergely

Formal CR Framework

Frontmatter

Chapter 9. Introductory Explanation

Abstract

Our objective in the present part is the development of the main instrument of our formal approach, which will provide appropriate formalism for the representation, simulation and generation of the cognitive reasoning processes of cognizing agents, i.e. the processes that allow cognizing subjects to gain new knowledge.

Oleg M. Anshakov, Tamás Gergely

Chapter 10. Modification Calculi

Abstract

We introduce a formalism that has a dual semantical–syntactical character. Modification calculi contain a collection of statements, practically playing the role of axioms, which identically define a certain canonical model.The representation of this model implicitly affects certain inference rules. Note that, besides some usual inference rules of first-order calculus (modus ponens and generalisation), we will also use the plausible inference rules, i.e. the modification rules. Application of these rules is interpreted as a move from uncertainty to definiteness, i.e. from ignorance to knowing. Application of these rules creates a new knowledge state.

Oleg M. Anshakov, Tamás Gergely

Chapter 11. Derivability in Modification Calculi and L 1

Abstract

Here we introduce the cut of arbitrary strings and we discuss a few basic properties of the cuts. In this case we are not interested in the nature of the elements of a string. Obviously we will use the tools introduced above for working with the record strings.

Oleg M. Anshakov, Tamás Gergely

Chapter 12. Semantics

Abstract

In the present chapter appropriate semantics will be developed for the modification calculi as a special type of inference. This semantics will correspond to the intuitive meaning of discrete cognitive processes, sectioned into stages and modules.

Oleg M. Anshakov, Tamás Gergely

Chapter 13. Iterative Representation of Structure Generators

Abstract

In this chapter we establish a relationship between validities in L-structures and I-structures, where L is an FPJ logic and I is its iterative version w.r.t. some value τ ∈ 𝓥 (L, |),i.e.I = I^τ(L).I-structures represent the history of the cognitive process. The cognitive process itself is simulated by an inference in a modification calculus.

Oleg M. Anshakov, Tamás Gergely

Chapter 14. Modification Theories

Abstract

Now we investigate the connection between derivability in modification calculi and validity in L-structures, where L is an FPJ logic. With few exceptions, in this section we will consider only pure inferences in modification calculi, i.e. inferences from own state descriptions of modification calculi.

Oleg M. Anshakov, Tamás Gergely

Chapter 15. Conformability

Abstract

The imitation of cognitive reasoning will be based on the technique of modification calculi. In this section two classes of modification calculi will be introduced differing in special syntactical restrictions. We will study the calculi of these classes and show that any calculus of these classes is conformable and, consequently, correct and complete w.r.t. the semantics defined in the previous section.

Oleg M. Anshakov, Tamás Gergely

Handling Complex Structures

Frontmatter

Chapter 16. Introductory Explanation

Abstract

In the previous chapter the first results connecting syntactic and semantic constructs were obtained under the assumption that the modification calculi possess the property of conformability. This property means that there exists a generating rule system which corresponds to the modification rule system of a modification calculus in a special, strictly defined meaning. To define the iterative image of the modification theory we need to assume the same condition. Similarly to modification rules, generating rules are syntactic constructs but they are used in a semantic context.

Oleg M. Anshakov, Tamás Gergely

Chapter 17. Set-Admitting Structures

Abstract

In this section we study the so-called set sorts. As mentioned above, objects of set sorts are regarded as sets. This is related to a certain number of restrictions, some of which will be considered below. Note that we will first investigate those sets of conditions that are technically simple and transparent. Later on our technique will be much more sophisticated and complex.

Oleg M. Anshakov, Tamás Gergely

Chapter 18. Set Sorts in Modification Calculi

Abstract

In the present section we introduce the tools used to represent the sets of properties in the modification calculi. First of all we define the definition method for modification rules. Then we define the transformation of modification rules into generator rules. There will be a wider class of modification calculi defined than the class of atomic modification calculi.

Oleg M. Anshakov, Tamás Gergely

Chapter 19. Perfect Modification Calculi (PMC)

Abstract

The notion of perfect modification calculi may seem unexpected and abstract, but it is introduced because of the needs arising from practical applications. Below we provide a fairly simple artificial example for the rule that allows the analysis of property sets.

Oleg M. Anshakov, Tamás Gergely

JSM Theories

Frontmatter

Chapter 20. Introductory Explanation

Abstract

In the present part we will consider a set of examples of modification theories related to one of the methods of logical data analysis and knowledge acqusition, the socalled JSM method of automatic hypothesis generation. This method was proposed by V. K. Finn at the beginning of the 1980s.

Oleg M. Anshakov, Tamás Gergely

Chapter 21. Simple JSM Theories

Abstract

Pure J logics are the logical basis for the JSM method. Both the modification and the iterative theories built over the St or It logics, respectively, can be suggested for the mathematical representation of various versions of the JSM method

Oleg M. Anshakov, Tamás Gergely

Chapter 22. Advanced JSM Theories

Abstract

The generalised JSM method was proposed as a method that provides finer data analysis than that provided by the simple JSM method. The main supposition of the generalised JSM method is: each possible cause may be associated with a set of its own inhibitors, which interfere with the appearence of effects even if the cause exists. Therefore, we can conclude that an object possesses a certain property (according to the generalised JSM method) only if this object contains the cause of this property and contains none of the inhibitors of this cause.

Oleg M. Anshakov, Tamás Gergely

Chapter 23. Similarity Representation

Abstract

Let σ be a basic JSM signature and 𝔍; be an L-structure of signature σ, where L is a PJ logic.Then 𝔍; is called a basic JSM-structure (BJSMstructure), if it is a model of the axioms (S1)—(S4) and (SA) of the basic JSM theory.

Oleg M. Anshakov, Tamás Gergely

Chapter 24. JSM Theories for Complex Structures

Abstract

Suppose that we have a situation where the properties themselves are sets, i.e. the elements of the sort 𝖯 are sets. If we attempt to represent this situation in some versions of the JSM theories then this yields significant changes and complications in the selected theories. The advantage may be a potential decrease of the computational complexity of the corresponding algorithms caused by the interdependency of the properties (sets of properties).

Oleg M. Anshakov, Tamás Gergely

Looking Back and Ahead

Frontmatter

Chapter 25. Introductory Overview

Abstract

Understanding cognition and particularly cognitive reasoning and developing artificial cognizing agents are challenging and long-term research problems. In this book we wish to take a step towards a better understanding of cognitive reasoning processes by developing a scientifically well-founded general approach that provides methods and tools for modelling, designing and generating information processing responsible for the cognitive processes of artificial cognizing agents. Our aim is that the required general approach should support the study at three levels of abstraction: conceptual, formal, and realisational.

Oleg M. Anshakov, Tamás Gergely

Chapter 26. Towards the Realisation

Abstract

In this chapter we discuss the level of realisation of the proposed CR formalism. We introduce the general scheme (the object model) of an application program for data analysis by means of the formalised reasonings provided by the formal CR framework.

Oleg M. Anshakov, Tamás Gergely

Chapter 27. CR Framework

Abstract

At the conceptual level of abstraction the proposed approach provides the conceptual CR framework. In order to characterise and model the cognitive reasoning processes this framework defines the main actor of cognition, which is the cognizing agent. The structure together with all the constituents and functioning of cognizing agents is represented in the form of a cognitive architecture. This framework has modelled cognitive reasoning with respect to this architecture that interacts with its environment in order to obtain data, facts and information, and it processes these in order to extract new information and regularities. The extracted information is used to augment the agent’s knowledge about the environment and/or about the corresponding subject domain.

Oleg M. Anshakov, Tamás Gergely

Chapter 28. Open Problems

Abstract

Here we discuss some open problems connected with the further development of the mathematical theory of the formal CR framework developed in the present book. We present the problems in thematically grouped form.

Oleg M. Anshakov, Tamás Gergely

Chapter 29. Philosophical–Methodological Implications of the Proposed CR Framework

Abstract

As mentioned, the proposed approach integrates all three types of methodology of investigation: the philosophical–methodological, the logical–mathematical and the engineering–computational ones. At the formal level of abstraction the approach basically provides methods and tools in the logical–mathematical spirit. However, at the same time the formal CR framework has philosophical–methodological implications which differ from the issues described at the conceptual level of abstraction. Here we discuss some of these.

Oleg M. Anshakov, Tamás Gergely

Backmatter

Titel: Cognitive Reasoning
verfasst von: Tamás Gergely
Oleg M. Anshakov
Copyright-Jahr: 2010
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-540-68875-4
Print ISBN: 978-3-540-43058-2
DOI: https://doi.org/10.1007/978-3-540-68875-4

Premium Partner