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Automatic Documentation and Mathematical Linguistics

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01.04.2022 | INTELLIGENT SYSTEMS

JSM Reasoning and Knowledge Discovery: Ampliative Reasoning, Causality Recognition, and Three Kinds of Completeness^#

verfasst von: V. K. Finn

Erschienen in: Automatic Documentation and Mathematical Linguistics | Ausgabe 2/2022

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Abstract

Inductive inferences and inferences, by analogy with JSM reasoning, are characterized as ampliative inferences generating new knowledge. New predicates for inductive inference rules and their ordering are considered. The case of a single-element effect for the predicate “X has effect Y” is also investigated.

Vorheriger Artikel Loss of Scientific Knowledge As a Consequence of Publication Requirements

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The fifth level of acceptance of the generated hypotheses is an M-sequence of modal operators of rank r, where r > 1, representing empirical regularities that are obtained by applying JSM reasoning r-fold to sequences of extensible fact bases [1, p. 22].

Thus, the empirical patterns are a formalization of the idea of the knowledge-discovery process formulated in [2].

To understand the definition of knowledge in a computer system, one should become familiarized with its definition in [5, p. 31].

FB(0), FB(1), …, FB(s) is the sequence of expandable fact bases: FB(0) ⊂ FB(1) ⊂ … ⊂ FB(s).

Note that the degree of plausibility of a fact is 0 and that of a hypothesis is greater than 0, since it represents the number of steps of a plausible inference.

Since the truth values of JL formulas have the form \(\bar {v} = \left\langle {v,n} \right\rangle \), where \(v \in \left\{ {1, - 1,0,\tau } \right\}\), and \(n \in N\), the logic is infinite-valued.

In the case |Y| =1, \({{J}_{{\left\langle {1,1} \right\rangle }}}\left( {{{V}_{i}} \Rightarrow _{2}^{{(P)}}{{Y}_{i}}} \right)\) and \({{J}_{{\left\langle {1,0} \right\rangle }}}\left( {X \Rightarrow _{1}^{{(P)}}Y} \right)\) are used.

That is, similarities for (+)-examples and (–)-examples.

For convenience of notation, we will represent finite sets {A, B, ..., P} as words AB...P; for example, we will represent {A, B, C} as АВС.

Therefore, the relation \( \Rightarrow _{2}^{*}\) is not functional.

The premises of p.i.r.-1 are the corresponding elements of the diagram for \({{\Re }_{1}}\), and the premises of p.i.r.-2 are the corresponding elements of the diagram for \({{\bar {\Re }}_{1}}\).

In IS–JSM intelligent systems that implement the ARS JSM method [4, 19], D_1,0(p) form a fact base.

If CCA^(σ) are true, then the admissible JSM reasoning is strong [5].

This condition can be generalized to all Str_x, _y from [7]. The same holds true for the sufficient condition (**).

Obviously, for strong admissible JSM reasoning ρ^σ(s) = 1, where σ = +,–.

In Section 4 of this paper, possible strengthenings will be considered.

Since \(X{{ \Rightarrow }_{1}}Y\) and \(V{{ \Rightarrow }_{2}}Y\) are defined with respect to relational systems and their corresponding D_0,1(P), these primitive predicates depend on the parameter Р.

In [8], J.S. Mill used the term agreement–difference. In the ARS JSM, the term similarity–difference is preferred.

The elements of M have a superscript σ, where σ = +, –, which, for the sake of notation, will sometimes be omitted.

Definitions of operations and are contained in the Appendix.

φ is obtained in the Appendix.

Indices (P) and (x, y) will sometimes be omitted for convenience of notation.

In the Appendix, the relational system \({{\bar {\Re }}_{f}}\) is considered such that the predicates \(M_{{{{a}_{{12}}}fg,0}}^{\sigma }\left( {V,Y} \right)\) are satisfiable in it.

Part II of this article will deal with the cases when |Y| > 1 and there is ¬α.

The content of this section assumes familiarity with papers [1, 5].

They are empirical nomological statements [1, 26].

This means strengthened realization of the scientific research demarcation criterion [27].

This definition is formulated for computer systems that implement the ARS JSM method.

We intend to consider the Boolean function F₂() for the case |Y | > 1 in the second part of this article.

The sets \(\overline {Str} \times A_{E}^{\sigma }\) are partially ordered with the largest and smallest element for σ = +, –, respectively.

Recall that \(A_{\chi }^{\sigma }\) is an element of the intension of the concept of empirical regularity and \(A_{\chi }^{\sigma }(C{\kern 1pt} ',\,\,Q)\) is an extension element of this concept.

Situational JSM reasoning is obviously in demand for the analysis of sociological data. Note also that there are cases when V = Ø or S = Ø.

We intend to consider this problem in the second part of this article.

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Titel: JSM Reasoning and Knowledge Discovery: Ampliative Reasoning, Causality Recognition, and Three Kinds of Completeness#
verfasst von: V. K. Finn
Publikationsdatum: 01.04.2022
Verlag: Pleiades Publishing
Erschienen in: Automatic Documentation and Mathematical Linguistics / Ausgabe 2/2022
Print ISSN: 0005-1055
Elektronische ISSN: 1934-8371
DOI: https://doi.org/10.3103/S0005105522020066

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JSM Reasoning and Knowledge Discovery: Ampliative Reasoning, Causality Recognition, and Three Kinds of Completeness^#

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