Catálogo de publicaciones - libros

Cognitive science has emerged as a new discipline of knowledge that deals with the mental aspects of the human beings. The chapter attempts to explain the psychological processes involved in human reasoning, learning, understanding, and planning. It elucidated various models of human memory and representation of imagery and cognitive maps on memory. The mechanism of understanding a complex problem is also presented here with special reference to the focus of attention in the problem.

Human beings usually perform a complex task by activating various distributed modules of their brain. The chapter takes a preparatory attempt to model distributed processes involved in human reasoning, learning, planning, etc. by a specialized distributed model similar with Petri nets. It ends with a discussion on the elementary properties of classical Petri nets and suggests the necessary extensions as required to model the brain processes.

It is demonstrated how a dependently typed lambda calculus (a logical framework) can be formalised inside a language with inductive-recursive families. The formalisation does not use raw terms; the well-typed terms are defined directly. It is hence impossible to create ill-typed terms.

As an example of programming with strong invariants, and to show that the formalisation is usable, normalisation is proved. Moreover, this proof seems to be the first formal account of normalisation by evaluation for a dependently typed language.

This chapter presented principles of fuzzy reasoning by various models of fuzzy Petri nets. Broadly speaking, the models are of two basic types: forward reasoning models and backward reasoning models. The forward reasoning models are usually employed to determine the membership distribution of the concluding propositions in a fuzzy Petri net. The backward reasoning model, on the other hand, first identifies the selected axioms in the Petri net, which only can influence the membership of the goal proposition. This is implemented by back-tracing the network from the available goal (concluding) proposition until the axioms are reached. The places thus traced in the FPN are sufficient to determine the membership of the given goal proposition. The chapter also introduces the possible scheme of machine learning on a fuzzy Petri net. Because of the inherent feature of approximate reasoning, FPNs used for machine learning have a promising feature in fuzzy pattern recognition from noisy training instances.

This chapter introduced the models of belief propagation and belief revision for approximate reasoning in acyclic and cyclic networks respectively. The analysis of deadlock freedom of the belief propagation algorithm ensures that the algorithm does not terminate pre-maturely. The belief revision algorithm on the other hand may undergo limit cyclic behaviors. The principles of the limit cycle elimination technique may then be undertaken to keep the reasoning free from getting stuck into limit cycles. Possible sources of entry of nonmonotonicity into the reasoning space and their elimination by a special voting arrangement has also been undertaken.

Unlike the existing methodology of reasoning on FPN, the most important aspect of the chapter lies in the representation of the belief updating policy by a single vector-matrix equation. Thus, if the belief revision does not get trapped into limit cycles and nonmonotonicity, the steady state solution of the reasoning system can be obtained by recurrently updating the belief vector until the vector converges to a stable state.

This chapter presented a new learning model of neural nets capable of representing the semantics of high-level knowledge. The unconditional convergence of the error states to the origin in error space has been proved and is an added advantage of the proposed learning model. The model has successfully been applied to a practical problem in fuzzy pattern recognition. The generic scheme of the model will find applications in both many-to-many fuzzy semantic function realization as well as recognition of objects from their fuzzy feature space.

This chapter presented various models of fuzzy cognitive maps and their learning behavior. Most of these models employ unsupervised learning. Kosko’s model and its extension by Pal and Konar include Hebbian-type encoding. The model by Zhang et al. is of completely different type and is used for reasoning using a specialized algebra, well known as NPN algebra. All the models introduced in the chapter provide scope for fusion of knowledge of multiple experts. The principle of knowledge fusion has been illustrated in exercise 2.

It is demonstrated how a dependently typed lambda calculus (a logical framework) can be formalised inside a language with inductive-recursive families. The formalisation does not use raw terms; the well-typed terms are defined directly. It is hence impossible to create ill-typed terms.

As an example of programming with strong invariants, and to show that the formalisation is usable, normalisation is proved. Moreover, this proof seems to be the first formal account of normalisation by evaluation for a dependently typed language.

This chapter presented a new learning model of neural nets capable of representing the semantics of high-level knowledge. The unconditional convergence of the error states to the origin in error space has been proved and is an added advantage of the proposed learning model. The model has successfully been applied to a practical problem in fuzzy pattern recognition. The generic scheme of the model will find applications in both many-to-many fuzzy semantic function realization as well as recognition of objects from their fuzzy feature space.

This chapter introduced the models of belief propagation and belief revision for approximate reasoning in acyclic and cyclic networks respectively. The analysis of deadlock freedom of the belief propagation algorithm ensures that the algorithm does not terminate pre-maturely. The belief revision algorithm on the other hand may undergo limit cyclic behaviors. The principles of the limit cycle elimination technique may then be undertaken to keep the reasoning free from getting stuck into limit cycles. Possible sources of entry of nonmonotonicity into the reasoning space and their elimination by a special voting arrangement has also been undertaken.

Unlike the existing methodology of reasoning on FPN, the most important aspect of the chapter lies in the representation of the belief updating policy by a single vector-matrix equation. Thus, if the belief revision does not get trapped into limit cycles and nonmonotonicity, the steady state solution of the reasoning system can be obtained by recurrently updating the belief vector until the vector converges to a stable state.

It is demonstrated how a dependently typed lambda calculus (a logical framework) can be formalised inside a language with inductive-recursive families. The formalisation does not use raw terms; the well-typed terms are defined directly. It is hence impossible to create ill-typed terms.

As an example of programming with strong invariants, and to show that the formalisation is usable, normalisation is proved. Moreover, this proof seems to be the first formal account of normalisation by evaluation for a dependently typed language.