Results in Classical Logic

 

A Textbook on Logic 

For the present, you can see the cover of the textbook only. In the future, I will show some pages as well. The content follows the educational programme of the Ministry of Education, Youth and Science. Respectively, the textbook has been approved by a Commission at the Ministry. Special chapters are devoted to the classical propositional and predicate calculi. In accordance with the programme, some philosophical and ethical topics are exposed, too. All matter is illustrated with numerous pictures, cartoons, verses, aphorisms, stories, and many other edifying examples connected with logic. Some of the illustrations have been used for the Logical Show in this site. Each lesson is accompanied also with problems together with their solutions. Even a logical "machine" is enclosed enable to check syllogisms! 

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Edited 2002 by Publishing House "Veles", ISBN 954-302-001-9, price 8 BG lev (€ 4).


Maybe C. S. Pierce was the first to observe 130 years ago that implication involves many properties of negation if any subformula of the form X → s (with s a distinguished propositional letter) is interpreted as ~X. In this sense some kind of a non-classical negation is “hidden” in the classical logic. Another non-classical connective is the necessity "hidden" in the conjunction and defined by X&s. The two operations so introduced are axiomatized and it is shown that they belong to the 4-valued logic of Łukasiewicz. A 2-point Kripke semantics is built leading directly to the 4-valued logical tables. The paper is published in the Special Issue of the Journal of Applied Non-Classical Logics dedicated to the 70th anniversary of my colleague and friend Prof. Dimiter Vakarelov (v. 18, no. 2-3/2008, pp. 309-324):

Non-Classical Operations Hidden in Classical Logic