Logic & Formal Reasoning


In Memoriam Alain Colmerauer: 1941-2017

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Alain Colmerauer, a French computer scientist and a father of the logic programming language Prolog, passed away on May 15 at the age of 76. He earned a degree in computer science from the Institut polytechnique de Grenoble (Grenoble Institute of Technology) in 1963, and a doctorate in the discipline in 1967 from the École nationale supérieure d'informatique et de mathématiques appliquées de Grenoble, which is part of the Institut. He was promoted in 1979 to Professeur 1ère classe (Full Professor), and in 1988 to Professeur classe exceptionnelle (University Professor). From 1993 to 1995, he was Head of the Laboratoire d'Informatique de Marseille (LIM), a joint laboratory of the Centre National de la Recherche Scientifique, the University de Provence and the University de la Mediterranee.


Goedel's Incompleteness Theorem and the Emergence of AI

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Some leading scientists like Sir Roger Penrose even argue that Goedel showed with his Incompleteness Theorem that today's computers can never reach human level intelligence or consciousness, that humans will always be smarter than current computers or any computer algorithm can ever be and that computers will never in the true sense of the word "understand" anything like higher level mathematics, especially not mathematics that deals with trans-finite sets and numbers. Many famous mathematicians (and physicists) created fascinating new theories and discovered deep and far reaching mathematical results. He proved this by using his famous "diagonal" construction (see pic below) that showed that any supposedly complete enumerated list of irrational or real numbers R will always miss some irrational numbers, thereby proving that a complete enumeration of the real numbers by the natural numbers is impossible. Cantor has actually shown that there are even an infinite number of ever bigger infinities by showing that the set of all subsets of any given infinite set is always substantially bigger (cannot be put into a 1-1 relation) than the set itself.


Innovative mathematical model that simulates How the Mind Works

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This model allows quantifying --in precise way-- any fact, matter, phenomenon or thing, which has some relevance for the human being. In short, it is possible to quantify -- with mathematical precision-- any problem raised. In practical terms, the model offers an efficient universal methodology --which represents a drastic reduction in time and money-- for the application and development of all those tools or systems oriented to facilitate decision making (Systems of Support to Decisions or DSS, Games Theory, Decision Theory, Complex System, Expert Systems, etc.).The scope of this model is determined by its universal condition, charact…


Interview with Alan Robinson, inventor of resolution logic

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A. Robinson), English literature (Mark Halpern), Classics (C. A. R. Hoare), Physics (E.W. APP I never programmed in assembler until I was in my fifties, which was after Algol 60, Pop-2, APL, Lisp, Prolog, Fortran, Cobol, Basic, C, and C . I remember once at Donald [Michie]'s house in Dick Place a conversation with Christopher Strachey in which the subject was the alleged benefit of Latin and Greek for mastery of English. Because of the wonderful plasticity of the developing brain, early life is an excellent time for this sort of preparation.


Peter Suber, "Glossary of First-Order Logic"

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Predicate logic in which predicates take other predicates as arguments and quantifiers bind predicate variables. Standard predicate logic excludes empty domains and defines logical validity accordingly, i.e. Predicate logic in which predicates take other predicates as arguments and quantifiers bind predicate variables. Standard predicate logic excludes empty domains and defines logical validity accordingly, i.e.


Peter Suber, "Propositional Logic Terms and Symbols"

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To indicate that a compound is to be taken as a whole or single statement, we put it in parentheses. For example, p q is a compound. Its negation is (p q). If we wanted to say that either the whole latter statement was true, or that s t was true, we would write, [(p q)·(q r)] (s t).


Inductive Logic Programming

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Presently successful applications areas for ILP systems include the learning of structure-activity rules for drug design, finite-element mesh analysis design rules, primary-secondary prediction of protein structure and fault diagnosis rules for satellites.



Would YOU take fashion advice from a robot?

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Scientists have created a mathematical model that can give people fashion tips by analysing the latest season trends. Scientists have created a computer that can give people fashion tips by analysing the latest season trends. The system can then predict how fashionable a person looks, and more importantly, give fashion advice to users. The latest to be rolled out in the US is the MemoryMirror that uses augmented reality to show how clothes will fit, and lets shoppers change outfits with the swipe of a hand.