Finitely many-valued paraconsistent systems

In the paper n-valued paraconsistent matrices are defined by an adaptation of the well-known Łukasiewicz’s matrices. An appropriate set of axioms is presented and the 3-valued case is examined

Joseph E. Brenner, "Logic in Reality", Springer, 2008

Book Reviews: Joseph E. Brenner, "Logic in Reality", Springer, 2008, ISBN 978-1-4020-8374-

Formal logic and natural ways of reasoning

In the paper I ask the question about the relation between formal logic and the natural logic of human mind. By a natural logic I mean the ways of thinking of a person that is intelligent but untrained in formal logic. As it turns out that the laws, rules or properties of formal logic in some cases diverge from the natural ways of reasoning, I explain the causes of this divergence. Since the majority of research in this area has been carried out from the standpoint of psychology, as a logician I suggest a slight change of the angle from which we look at the problem. I argue that certain narrowing of an interdisciplinary research would be helpful in getting a better picture of natural logic, and might provide a new stimulus for formal investigations.In the paper I ask the question about the relation between formal logic and the natural logic of human mind. By a natural logic I mean the ways of thinking of a person that is intelligent but untrained in formal logic. As it turns out that the laws, rules or properties of formal logic in some cases diverge from the natural ways of reasoning, I explain the causes of this divergence. Since the majority of research in this area has been carried out from the standpoint of psychology, as a logician I suggest a slight change of the angle from which we look at the problem. I argue that certain narrowing of an interdisciplinary research would be helpful in getting a better picture of natural logic, and might provide a new stimulus for formal investigations

Z punktu widzenia logiki

From a logical viewpointIn this paper we sketch out the general picture of the science of contemporary logic. We discuss the possibilities of gaining back the logic’s position among other sciences. Especially promising seem the possibilities of applying formal logic to A.I., computer or cognitive science.From a logical viewpointIn this paper we sketch out the general picture of the science of contemporary logic. We discuss the possibilities of gaining back the logic’s position among other sciences. Especially promising seem the possibilities of applying formal logic to A.I., computer or cognitive science

Maksymalne logiki tolerujące sprzeczność

Maximal paraconsistent logicsAs we know there is an infinite number of various paraconsistent logics i.e. logics that, unlike classical logic, allow reasoning within inconsistent but non-trivial theories. It seems that certain natural assumptions about them could reduce the number of systems to those that are especially important. One of the main assumptions about paraconsistent logics is that they should be as rich as possible. In formal terms this may mean that paraconsistent logics should be maximal. In this paper we provide an overview of the main maximality results obtained: first by D. Batens, then by T. Skura, and R. Tuziak, and finally by O. Arieli, A. Avron, and A. Zamansky. We compare the approaches to the problem and examine the very notion of maximality. We argue that maximal calculi are worth examining and especially interesting as formal systems that can be successfully applied to inconsistent databases.Maximal paraconsistent logicsAs we know there is an infinite number of various paraconsistent logics i.e. logics that, unlike classical logic, allow reasoning within inconsistent but non-trivial theories. It seems that certain natural assumptions about them could reduce the number of systems to those that are especially important. One of the main assumptions about paraconsistent logics is that they should be as rich as possible. In formal terms this may mean that paraconsistent logics should be maximal. In this paper we provide an overview of the main maximality results obtained: first by D. Batens, then by T. Skura, and R. Tuziak, and finally by O. Arieli, A. Avron, and A. Zamansky. We compare the approaches to the problem and examine the very notion of maximality. We argue that maximal calculi are worth examining and especially interesting as formal systems that can be successfully applied to inconsistent databases

BOOK REVIEWS

Aleksander Stępkowski, Zasada proporcjonalności w europejskiej kulturze prawnej. Sądowa kontrola władzy dyskrecjonalnej w nowoczesnej Europie, Warszawa 2010 (rec. Maria Z m i e r c z a k), s. 223-227; Anetta Breczko, Podmiotowość prawna człowieka w warunkach postępu biotechnomedycznego, Białystok 2011 (rec. Roman T o k a r c z y k), s. 227-231; Czas w prawie administracyjnym, pod red. Jana Zimmermanna, Warszawa 2011 (rec. Eugeniusz O c h e n d o w s k i), s. 231-236; Andrzej Piekara, Jakość administracji w Polsce. Zarys współczesnej problematyki, Warszawa 2010 (rec. Bożena T u z i a k), s. 236-239; Wiesława Przybylska-Kapuścińska, Marek Mozalewski, Kapitał wysokiego ryzyka, Warszawa 2011 (rec. Jerzy W ę c ł a w s k i), s. 239-241; Badania kapitału społecznego w Wielkopolsce. Diagnoza stanu i perspektywy wzrostu, pod red. Eulalii Skawińskiej, Poznań 2011 (rec. Felicjan B y l o k), s. 241-245; Marcin Wiśniewski, Ocena zdolności kredytowej gminy (rec. Teresa L u b i ń s k a), s. 245-24

BOOK REVIEWS

Aleksander Stępkowski, Zasada proporcjonalności w europejskiej kulturze prawnej. Sądowa kontrola władzy dyskrecjonalnej w nowoczesnej Europie, Warszawa 2010 (rec. Maria Z m i e r c z a k), s. 223-227; Anetta Breczko, Podmiotowość prawna człowieka w warunkach postępu biotechnomedycznego, Białystok 2011 (rec. Roman T o k a r c z y k), s. 227-231; Czas w prawie administracyjnym, pod red. Jana Zimmermanna, Warszawa 2011 (rec. Eugeniusz O c h e n d o w s k i), s. 231-236; Andrzej Piekara, Jakość administracji w Polsce. Zarys współczesnej problematyki, Warszawa 2010 (rec. Bożena T u z i a k), s. 236-239; Wiesława Przybylska-Kapuścińska, Marek Mozalewski, Kapitał wysokiego ryzyka, Warszawa 2011 (rec. Jerzy W ę c ł a w s k i), s. 239-241; Badania kapitału społecznego w Wielkopolsce. Diagnoza stanu i perspektywy wzrostu, pod red. Eulalii Skawińskiej, Poznań 2011 (rec. Felicjan B y l o k), s. 241-245; Marcin Wiśniewski, Ocena zdolności kredytowej gminy (rec. Teresa L u b i ń s k a), s. 245-24