Nonstandard Logics and Extensions

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• Non Standard Logics - http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm
• A comprehensive listing of flavours of non-standard logic with brief descriptions and references, compiled by Peter Suber.
• Infinitary Logic - http://plato.stanford.edu/entries/logic-infinitary/
• Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary Logic is a branch of formal logic where finitary formulae are replaced by potentially infinitary mathematical entities.
• Logic System Interrelationships - http://www.cc.utah.edu/~nahaj/logic/structures/
• Shows how a number of representative logics fit together. The interrelationships usually given as something of the form: System X is system Y plus the axiom Z. By John Halleck.
• What are Weak Arithmetics - http://www.univ-paris12.fr/lacl/jaf/html/wa.html
• Notes defining the subject. Available in HTML and PS formats.
• Computability Logic - http://en.wikipedia.org/wiki/computability_logic
• Wikipedia (free encyclopedia) article.