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Total Equivalence Systems for Classes of 3-valued Projection Logic whose Projections Equal to the Class of Linear Boolean Functions
Ch. 23. P. 82-86.
Olga Gerasimova, Makarov I.
We give a complete description of total equivalence systems (TES) for formulas based on closed classes of functions from the projection logic P3,2 with the property that the restrictions of its functions to the set {0,1} constitute a closed class of linear Boolean functions. For each such class, we find a total equivalence system, providing an algorithm for a transformation of an arbitrary formula to its canonical form.
In book
Samos Island : University of Aegean, 2015
Ilya Makarov, Olga Gerasimova, Logica Universalis 2017
We describe a method of finding the canonical types of formulas based on three-valued projection logic functions. The method focuses on a separation of all tuples of values for variables into disjoint sets and write indicators of these sets using only functions from the closed class under consideration. We obtain the required canonical type combining ...
Added: September 25, 2015
Existence of Finite Total Equivalence Systems for Certain Closed Classes of 3-Valued Logic Functions
Makarov I., Logica Universalis 2015 Vol. 9 No. 1 P. 1-26
The article deals with finding finite total equivalence systems for formulas based on an arbitrary closed class of functions of several variables defined on the set \{0, 1, 2\} and taking values in the set \{0,1\} with the property that the restrictions of its functions to the set \{0, 1\} constitutes a closed class of ...
Added: February 28, 2015
Mikhailovich A., В кн. : Материалы X молодежной научной школы по дискретной математике и ее приложениям. : М. : Издательство ИПМ РАН, 2015. С. 51-55.
Closed classes of three-valued logic functions generated by quazi-symmetric functions that take values from the set {0,1} are considered. Criteria of basis existence and finite basis existence have been obtained. ...
Added: April 8, 2016
Mikhailovich A., Вестник Нижегородского университета им. Н.И. Лобачевского 2013 № 1 С. 208-212
Closed classes are considered of three-valued logic functions generated by symmetric functions taking values in the set {0, 1}. Criteria for existence of bases and for existence of finite generating systems are obtained for some classes generated by elementary periodic symmetric functions. ...
Added: April 11, 2013
Olga Gerasimova, Makarov I., , in : Handbook of the 5th World Congress and School on Universal Logic. : Istanbul : University of Istanbul, 2015. P. 372-373.
We present a new method of nding the canonical types of formulas based on three-valued projection logic functions. The method is focused on separation of all tuples of values for variables into disjoint sets. For every such set we take its own simple canonical type that identies this set. Combining the results for each set ...
Added: September 19, 2015
Mikhailovich A., В кн. : Труды IX Международной конференции "Дискретные модели в теории управляющих систем". : М. : МАКС Пресс, 2015. С. 163-166.
Closed classes of multi-valued logic are observed. Families of closed classes generated by function with special properties are considered. Criteria for basis existence have been obtained for these classes. ...
Added: March 28, 2015
L. Beklemishev, Flaminio T., Studia Logica 2016 Vol. 104 No. 1 P. 1-46
Franco Montagna, a prominent logician and one of the leaders of the Italian school on Mathematical Logic, passed away on February 18, 2015. We survey some of his results and ideas in the two disciplines he greatly contributed along his career: provability logic and many-valued logic. ...
Added: March 13, 2016
Mikhailovich A., / Cornell University. Series math "arxiv.org". 2015.
Closed classes of three-valued logic generated by symmetric funtions that equal 1 in almost all tuples from {1,2}n and equal 0 on the rest tuples are considered. Criteria for bases existence for these classes is obtained. ...
Added: March 28, 2015
Mikhailovich A., В кн. : Проблемы теоретической кибернетики. Материалы XVII международной конференции. : Каз. : Отечество, 2014. С. 204-206.
Closed classes of three-valued logic functions whose generating systems consist of symmetric functions taking all values in the set {0, 1, 2} and taking values 1 and 2 on tuples from {1, 2}^n are consideder. Criteria of existence of a basis and existence of finite basis are obtained for these classes. ...
Added: March 12, 2015
Mikhailovich A., Прикладная дискретная математика 2015 № 1 С. 17-26
Closed classes of three-valued logic functions whose generating systems consist of symmetric functions taking values in the set {0, 1} and taking value 1 on bounded number of layers from {1, 2}^n are consideder. Criteria of existence of a basis and existence of finite basis are obtained for these classes. There shown how existence of ...
Added: March 11, 2015
Mikhailovich A., В кн. : Материалы IX молодежной научной школы по дискретной математике и ее приложениям (Москва, 16-21 сентября 2013 г.). : М. : Издательство ИПМ РАН, 2013. С. 80-85.
Closed classes of functions of three-valued logic whose generating systems include nonmonotone symmetric functions taking values in the set {0,1} and taking value 1 on restricted number of layers are studied. Cryteria of existence of basis and existence of finite basis has been obtained. ...
Added: October 24, 2013
Mikhailovich A., В кн. : Материалы XII Международного семинара "Дискретная математика и её приложения" имени академика О.Б. Лупанова (Москва, МГУ, 20-25 июня 2016г.). : М. : Изд-во механико-математического факультета МГУ, 2016. С. 209-212.
Closed classes of three-valued logic, generated by periodical functions taking values from the set {0,1} are considered. Criteria of basis exitstence and finite basis existence for classes generated by periodical functions with period of the form p^k (p is fixed prime number, k is arbitrary natural number) are obtained. ...
Added: September 1, 2016
Mikhailovich A., В кн. : Математические вопросы кибернетики. Вып. 18.: М. : Физматлит, 2013. С. 123-212.
Closed classes of functions of many-valued logic are studied. Problem on the basis existence is considered for some families of closed sets. Functions from generating systems are symmetric functions taking the values from the set {0,1} and equal to zero on the unit collection and collections containing at least one zero. Furthermore, closure of any ...
Added: March 25, 2014
Mikhailovich A., В кн. : Материалы 5-й Российской школы-семинара "Синтаксис и семантика логических систем". : Улан-Удэ : Издательство Бурятского госуниверситета, 2017. С. 91-95.
Lattice of all closed classes from closure of all functions from Janov and Muchnik examples has been described. ...
Added: September 22, 2017
Mikhailovich A., / Cornell University. Series math "arxiv.org". 2016.
Closed classes of three-valued logic generated by periodic symmetric funtions that equal $1$ in tuples from $\{1,2\}^n$ and equal $0$ on the rest tuples are considered. Criteria for bases existence and finite bases existence for these classes is obtained. ...
Added: April 15, 2016
Mikhailovich A., Moscow University Mathematics Bulletin 2012 Vol. 67 No. 1 P. 41-45
Closed classes of functions of three-valued logic whose generating systems include nonmonotone symmetric functions taking values in the set {0,1} are studied. It is shown that in some cases the problems of existence of a basis and existence of a finite basis can be reduced to a similar problem for reduced generated systems. ...
Added: October 30, 2012
Schang F., Journal of Indian Council of Philosophical Research 2011 Vol. 27 No. 1 P. 47-76
A rational interpretation is proposed for two ancient Indian logics: the Jaina saptabhangi, and the Madhyamika catuskoti. It is argued that the irrationality currently imputed to these logics relies upon some philosophical preconceptions inherited from Aristotelian metaphysics. This misunderstanding can be corrected in two steps: by recalling their assumptions about truth; by reconstructing their ensuing ...
Added: November 4, 2014
Schang F., International Journal of Jaina Studies 2013 Vol. 9 No. 1 P. 1-25
The Jain saptabhaṅgī is well-known for its general stance of non-one-sidedness. After a number of debates about the occurrence of contradictory sentences inside the so-called "Jain logic", three main theses are presented in the following: the saptabhaṅgī is a theory of judgment giving an exhaustive list of possible statements; it is not a "logic" in the modern sense of ...
Added: October 30, 2014
Schang F., , in : New Directions in Paraconsistent Logic. : Springer, 2015. P. 529-552.
Added: June 14, 2016
Dagaev D., Moscow University Mathematics Bulletin 2012 Vol. 67 No. 4 P. 182-184
Added: March 21, 2016
Mikhailovich A., Вестник Московского университета. Серия 1: Математика. Механика 2012 № 1 С. 58-62
Изучаются замкнутые классы функций трехзначной логики, порождающие системы которых содержат симметрические функции, принимающие значения из множества {0, 1}. Показано, что в некоторых случаях задачи о базируемости и конечной порожденности для таких классов сводятся к аналогичным задачам для классов, порождающие системы которых являются подмножествами порождающих систем исходных множеств. ...
Added: October 30, 2012
Mikhailovich A., В кн. : Материалы VIII молодежной научной школы по дискретной математике и ее приложениям (Москва, 24–29 октября 2011 г.). Ч. II.: М. : Механико-математический факультет МГУ, 2011. С. 16-19.
Рассматривается некоторое семейство замкнутых классов функций трехзначной логики, порожденных монотонными симметрическими функциями. Для этих классов получены критерии базируемости и конечной порожденности. ...
Added: November 23, 2012
Makarov I., / Logica Universalis. Series " ". 2015.
The article deals with finding finite total equivalence systems (FTES) for formulas based on an arbitrary closed class of functions of several variables defined on the set {0, 1, 2} and taking values in the set {0,1} with the property that the restrictions of its functions to the set {0, 1} constitutes a closed class ...
Added: October 17, 2013
О замкнутых классах функций трехзначной логики, порожденных периодическими симметрическими функциями
Mikhailovich A., В кн. : Проблемы теоретической кибернетики. Материалы XVI Международной конференции (Нижний Новгород, 20–25 июня 2011 г.). : Н. Новгород : Нижегородского госуниверситета, 2011. С. 319-322.
В работе изучается семейство замкнутых классов, порожденных периодическими симметрическими функциями с ограниченным периодом. Показано, что такой класс имеет базис тогда и только тогда, когда порождающая система содержит конечное число функций. ...
Added: November 22, 2012