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

Results found: 5

first rewind previous Page / 1 next fast forward last

Search results

Search:
in the keywords:  three-valued logic
help Sort By:

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

Natural Deduction for Three-Valued Regular Logics

100%
Petrukhin Y.
Logic and Logical Philosophy
|
2017
|
vol. 26
|
issue 2
197–206
EN
In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermediate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction systems are built only for strong Kleene’s logic both with one (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values.
2
Publication available in full text mode
Content available

Number three as a law of science. In praise of number three

100%
Maciuk A., Smoluk A.
Didactics of Mathematics
|
2016
|
issue 13(17)
25-34
EN
Comprehension of nature, in the simplest and quickest fashion, boils down to the differentiation of three states. This is probably related to the psychological fact that the human mind grasps only natural numbers from zero to three and the other numbers it calculates. We live in a divalent world created by Aristotle. However not everything can be reduced to two categories: “yes” and “no”, because Nature is abundant. The principle of continuity which facilitates understanding is in natural conflict with the binary description of the world. Ever since the times of Aristotle it has been normal to use in science a description of the world that is reduced to two states: “true” and “false”. In nature it is more obvious to distinguish three states: low-medium-high or negative-neutral-positive, etc. Man embraces at a single glance sets of three elements at most, and more numerous sets are divided into parts. Binary logic may have a negative impact on the process of teaching and examinations, especially if the tests are used.
3

The Theory of Form Logic

88%
Freitag W., Zinke A.
Logic and Logical Philosophy
|
2012
|
vol. 21
|
issue 4
363-389
EN
We investigate a construction schema for first-order logical sys- tems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Du- alism is replaced by a pluralism of terms of different “logical forms”. Indi- vidual form-logical systems are generated by the determination of a range of logical forms and of the formbased syntax rules for combining terms into formulas. We develop a generic syntax and semantics for such systems and provide a completeness proof for them. To illustrate the idea of form logic, and the possibilities it facilitates, we discuss three particular systems, one of which is the form-logical reconstruction of standard first-order predicate logic.
4
Content available remote

Automated Proof-searching for Strong Kleene Logic and its Binary Extensions via Correspondence Analysis

75%
Petrukhin Y., Shangin V.
Logic and Logical Philosophy
|
2019
|
vol. 28
|
issue 2
223–257
EN
Using the method of correspondence analysis, Tamminga obtains sound and complete natural deduction systems for all the unary and binary truth-functional extensions of Kleene’s strong three-valued logic K3 . In this paper, we extend Tamminga’s result by presenting an original finite, sound and complete proof-searching technique for all the truth-functional binary extensions of K3.
5
Content available remote

Partial and paraconsistent three-valued logics

63%
Degauquier V.
Logic and Logical Philosophy
|
2016
|
vol. 25
|
issue 2
143–171
EN
On the sidelines of classical logic, many partial and paraconsistent three-valued logics have been developed. Most of them differ in the notion of logical consequence or in the definition of logical connectives. This article aims, firstly, to provide both a model-theoretic and a proof-theoretic unified framework for these logics and, secondly, to apply these general frameworks to several well-known three-valued logics. The proof-theoretic approach to which we give preference is sequent calculus. In this perspective, several results concerning the properties of functional completeness, cut redundancy, and proof-search procedure are shown. We also provide a general proof for the soundness and the completeness of the three sequent calculi discussed.
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.