Objective knowledge: an evolutionary approach

Logic for Mathematicians By Prof. J. Barkley Rosser. (International Series in Pure and Applied Mathematics.) Pp. xiv + 530. (London: McGraw-Hill Publishing Co., 1953.) 85s.

Logic for Mathematicians

Nomological Statements and Admissible Operation. By Hans Reichenbach. Pp. 140. 27s. 1954. (North–Holland Publishing Company, Amsterdam)

In this article we consider the set of M-predicates used for the formalization of J.S. Mill's inductive methods of agreement, of difference, of agreement and difference, of residue, of concomitant variations, and of their strengthenings by the ban on counterexamples. Two partial orders on this set are considered using relations of logical deducibility and inclusion of sets of hypotheses generated. It is established that these partially ordered sets of M-predicates form distributive lattices. Products of these distributive lattices form the set of possible strategies of plausible JSM-reasoning (they represent rules of unductive inference).

Distributive lattices of inductive JSM procedures

This article consists of two parts. Part I considers the so-called problem of induction, viz., the history of its genesis and elaboration, and formulates the main principles and logical tools of the JSM method for automatic hypothesis generation, including JSM reasoning. JSM reasoning is demonstrated to be a synthesis of three cognitive procedures: induction, analogy, and abduction. Two possible kinds of abduction are considered. Part I focuses on formal tools to be used for the solution of the natural-scientific problem of induction. Part II formulates the procedural semantics for predicates that are used to formalize JSM reasoning, considers quasi-axiomatic (open) theories used to represent knowledge in intelligent systems, determines the means for assessing the quality of JSM-reasoning results, and, finally, suggests a solution of the naturalscientific problem of induction for intelligent systems. Part I was published in the journal Nauchno-Tekhnicheskaya Informatsiya, ser. 2, 2013, no. 9, pp. 1---29. Part II was published in the journal Nauchno-Tekhnicheskaya Informatsiya, ser. 2, 2013, no. 12, pp. 1---26.

Epistemological foundations of the JSM method for automatic hypothesis generation

The heuristics of the detection of empirical regularities by the JSM method of automated support of scientific research is considered. This heuristic consists of applying the JSM reasoning for JSM research, which consist of recognizing the preservation of hypotheses about the causes and hypotheses about predictions that form empirical dependencies for embedded database sequences. Mechanisms for detecting empirical regularities are causal forcing (CF), through which the necessity modalities (for empirical laws), the possibility modality (for empirical tendencies) and the modality of weak possibilities (for suspicious tendencies) are determined. The means of approximate detection of empirical regularities are determined and the results of their application for detecting the possibility of diabetes mellitus in patients with chronic pancreatitis are presented.

The Heuristics of Detection of Empirical Regularities by JSM Reasoning

The logical means of detecting empirical regularities using the JSM method of automated research support are considered. Generators of hypotheses about the causes and hypotheses about predictions that are stored in sequences of expandable fact bases are determined. Many “histories of possible worlds” are considered, where “world” refers to an expandable fact base. This set is used to determine empirical regularities, that is, empirical laws, tendencies, and weak tendencies. Empirical regularities are used to determine empirical modalities of necessity (for empirical laws), possibilities (for empirical tendencies), and weak possibilities (for weak empirical tendencies). The Propositional calculi of the class ERA are proposed, that is, modal logics with two empirical modalities of necessity and possibility such that they imitate abductive inference through the axioms of abduction (◻(p → q) & Tq) → ◻p), (◇(p → q) & Tq) → ◇p), where ◻, ◇, T are operators of necessity, possibility, and truth (“it is true that…”). A series of definitions related to the characterization of data mining using heuristics of the JSM method of automated research support is given.

On the Heuristics of JSM Research (Additions to Articles)

The previously introduced definition of empirical regularities (ERs) is considered using JSM reasoning. These definitions used functionals of the inconsistency degree for expandable sets of generated hypotheses. New ER definitions (of empirical laws and empirical trends) are formulated by the predicates of preserving truth-value types (factual truth, factual falsity, factual contradiction, and uncertainty). It is shown that the previously introduced definitions are the consequence of the new definitions. A set of possible ER definition options is considered using various JSM-reasoning strategies (inductive inference rules), which form a distributive lattice. It is proposed to use the projection of the set of JSM strategies on the set of empirical regularities and the inverse mapping of the ER set into the set of JSM strategies. The ER definition is used to amplify K.R. Popper's demarcation criterion, which characterizes a study that uses empirical data as a completed research work.

Detecting empirical regularities in bases of facts using JSM reasoning

This paper describes an intelligent system that performs the JSM automated research support method, which is designed to diagnose pancreatic diseases, that is, chronic pancreatitis and pancreatic cancer. A preliminary study is presented; further trends for the development of the system are listed.

V. K. Finn

Papers

Epistemological foundations of the JSM method for automatic hypothesis generation

The Heuristics of Detection of Empirical Regularities by JSM Reasoning

On the Heuristics of JSM Research (Additions to Articles)

Detecting empirical regularities in bases of facts using JSM reasoning

An Intelligent System for Diagnostics of Pancreatic Diseases