This book presents a pioneering investigation of the algebraic foundations of non-classical logics. Unifying paraconsistent, paracomplete, and non-alethic structures introduces Curry Systems as a versatile and unifying framework that transcends the limitations of traditional algebraization. Through the formal development of the Cn-, Pn-, Nn-, and P-algebras, as well as their first-order extensions, this book offers pre-algebraic tools for modeling contradiction, indeterminacy, and non-alethic reasoning.

Essential reading for logicians, mathematicians, philosophers of logic, and researchers in artificial intelligence, this book demonstrates how algebraic methods can rigorously capture reasoning under inconsistency and incompleteness. At once a comprehensive reference and intellectual invitation, it highlights the important role of pre-algebraic structures in the development of logical theory and intelligent systems

Shows how paraconsistent logics contributes to the development of more resilient, adaptable, and intelligent AI systems Presents an algebraic version of paraconsistent and paracomplete systems via the notion of the Curry System Presents an algebraization of paraconsistent, paracomplete and non-alethic systems

Autorentext

Jair Minoro Abe received a B.A. and M.Sc. in Pure Mathematics—University of São Paulo, Brazil. Abe also received his doctoral degree and Livre-Docente title from the same university. He acted as coordinator of the Logic Area of the Institute of Advanced Studies—University of São Paulo, Brazil (1986-2019) and Full Professor at Paulista University—Brazil. He is Senior Member of IEEE. Professor Abe is a studious of a family of Paraconsistent Annotated Logic used to solve many complex problems in engineering. He is considered one of the pioneers in this domain. He has authored/edited books on Paraconsistent and related logic published by Springer Germany and other reputed publishers. He is the recipient of many awards, including medals for his academic performance, and has received many best paper awards.

Inhalt

1.Curry Systems.- 2.C n Algebras.- 3.Heyting Algebras.- 4.P n -Algebras.- 5.N n -Algebras.- 6.Algebraization Of 1 st Order Paraconsistent Systems Cn.- 7.Algebraization of 1 st Order Paracomplete Systems Pn.- 8.Algebraization Of 1 st Order Non-Alethic Systems N n *.- 9.P Algebras & Monadic Curry Algebras Q.- 10.Alternative Algebraization of Classic Logic.- 11.Conclusion.