Tamás Gergely

Cognitive Reasoning Framework: Possibilities, Problems, Prospects

The paper discusses a general scheme of constructing different systems of artificial intelligence and data mining. This scheme interprets various intelligent technologies as kinds of reasoning. All of these kinds of reasoning aim to cognition and formation of domain models. We assume that reasoning has a referential character, i.e. reasoning can use semantic arguments as well as syntactic rules of deduction. We use some non-classical logics to formalize cognitive reasoning.

Basic System of Concepts

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.

Perfect Modification Calculi (PMC)

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.

Advanced JSM Theories

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.

JSM Theories for Complex Structures

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).

Simple JSM Theories

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

Set-Admitting Structures

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.

First-Order Logics

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.

Iterative Representation of Structure Generators

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 = Iτ(L).I-structures represent the history of the cognitive process. The cognitive process itself is simulated by an inference in a modification calculus.

Towards the Realisation

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.