Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

Refine search results

Journals help

  1. 1 Logic and Logical Philosophy

Years help

  1. 1 2014

Authors help

  1. 1 Łukowski P.

Results found: 1

first rewind previous Page / 1 next fast forward last

Search results

Search:
in the keywords:  admissible valuations
help Sort By:

help Limit search:
first rewind previous Page / 1 next fast forward last
1

Logical problems with nonmonotonicity

100%
Łukowski P.
Logic and Logical Philosophy
|
2014
|
vol. 23
|
issue 2
171–188
EN
A few years ago, believing that human thinking is nonmonotonic, I tried to reconstruct a nonmonotonic reasoning by application of two monotonic procedures. I called them “step forward” and “step backward” (see [4]). The first procedure is just a consequence operation responsible for an extension of the set of beliefs. The second one, defined on the base of the logic of falsehood reconstructed for the given logic of truthfulness, is responsible for a reduction of the set of beliefs. Both procedures taken together were successfully verified by using so-called AGM (see [5]), postulates for expansion, contraction and revision formulated by Alchourrón, Gärdenfors and Makinson (e.g. [1]). Reasoning composed of the mutual application of both procedures seemed to be quite natural for modeling our thinking. At that time, I supposed that it should be nonmonotonic but I was wrong. It turned out impossible to satisfy a definition of the nonmonotonic inference by reasoning composed both steps. To understand why this is impossible, I began to analyze how nonmonotonicity is obtainable in some well-known cases in the literature. I analyzed the problem from two points of view: (1) non-formal examples for nonmonotonicity and (2) formal constructions of nonmonotonic operations/relations. The result of those investigations was astonishing: none of the considered by me cases of nonmonotonicity belonging to point (1) and almost none belonging to (2) satisfies the definition of nonmonotonic inference. Arguments against the nonmonotonic character of well-known examples for nonmonotonicity of human thinking are more precisely presented in [6]. I present them below an abbreviated version of them.
first rewind previous Page / 1 next fast forward last
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.