Project: Foundations, Modeling and Automation of Reasoning
Description: Logic is the science and art of reasoning. It
is a way of symbolic processing of information, aiming to get explicit pieces
of information which before were implicit. While a science, it has a proper
methodology, which investigates expressions of reasoning inside organized linguistic
contexts. While an art, it aims to model formal systems representing as faithfully
as it is possible reasoning forms which weren’t caught yet in a satisfactory
way. The study, knowledge and research in Logic reveal very important tools
for a cognitive evolution of every human being which wants to be really free,
not conditioned by fear and by harmful beliefs spread by media of most societies
nowadays such as from the past. Such cognitive evolution guides us to clarity
of thinking, which becomes possible the practice of getting free from what is
false for each one, what is essential for an increasing intimate contact with
own Truth. The inner clarity is a gate for all authentic Philosophy, which conducts
us to a never ending travel for meeting the Whole. Logic is connected in a close
way with three great knowledge branches: Mathematics, Informatics and Philosophy.
Many of the founders of modern Computer Science were logicians. Symbolic Artificial
Intelligence is based on Logic, as one of its main pillars. All Mathematics
uses, in its linguistic expression, concepts of Logic, hence it is not possible
to understand Mathematics (which includes foundations of Computer Science) seriously
without knowing Logic, at least its elementary bases. The three lines of this
project – Foundations, Modeling and Automation – are not separate
and independent subjects, but they have a strong connection. Foundations aim
to clarify, elucidate and expand some aspects of Logic which lack a better insight,
such as relationship among the diverse logical systems, translations between
them, general proofs of soundness and completeness, general concepts of semantics
of logical systems, and other similar subjects. Modeling concerns to construction
of logical systems filling certain requirements, motivated in many cases by
questions of Knowledge Representation and Foundations of Mathematics. In this
research line we have been working for many years with systems aiming to formalize
common sense reasoning. Automation aims to specify and construct automated systems
for performing inference, in many levels of generality, related to logics considered
relevant for many applications.
References:
“Introduction to Logic”, by Irving M. Copi and Carl Cohen, Prentice
Hall.
“Logic”, by John Nolt, Dennis Rohatyn and Achille Varzi, McGraw?Hill
“Logics”, by John Nolt, Wadsworth Publishing.
“A Course in Mathematical Logic”, by J. L. Bell & M. Machover,
North-Holland.
“A Mathematical Introduction to Logic”, by Herbert B. Enderton,
Academic Press.
“Logic for Applications”, by Anil Nerode & Richard A. Shore,
Springer.
“Elements of Set Theory”, by Herbert B. Enderton, Academic Press.
“Axiomatic Set Theory”, by Patrick Suppes, Dover.
“A Logical Approach to Discrete Math”, by David Gries & Fred
B. Schneider, Springer.
“Automated Theorem Proving – A Logical Basis”, by Donald
W. Loveland.
“Symbolic Logic and Mechanical Theorem Proving”, Chin-Liang Chang
& Richard Char-Tung Lee, Academic Press.
“First-Order Logic and Automated Theorem Proving”, by Melvin
Fitting, Springer.
“First-Order Logic”, by Raymond M. Smullyan, Dover.
“Computability and Logic”, by George S. Boolos and Richard C.
Jeffrey, Cambridge University Press.
“Ensaio sobre os Fundamentos da Lógica”, by Newton C.
A. da Costa, Hucitec.
“Philosophy of Logics”, by Susan Haack, Cambridge University
Press.
“Readings in Nonmonotonic Reasoning”, edited by Matthew L. Ginsberg,
Morgan Kaufmann Publishers.
