ABSTRACT ALGEBRAIC LOGIC
A Treasure Chest^®

This page contains references and links to papers in the general field of Abstract Algebraic Logic (AAL) and papers that have had a significant influence in the development of that field.

AAL is a subfield of Mathematical Logic. Its origins may be traced back in the late 70's and early 80's work of the Polish School of Logic, but its maturity as a field on its own became apparent with the publication of the work of Blok and Pigozzi on "Algebraizable Logics". This seminal paper is widely acknowledged to be the "founding manifesto of AAL". AAL has been developing following three distinct but parallel and cross-fertilizing directions.

• In one, the abstract process by which a class of algebras is associated to a logical system in a specific class is studied. This is the direction that provides the field's distinct flavor.
  
• In the second, the classes of algebras that are canonically associated with the logical systems via the aforementioned abstract process are studied from the algebraic point of view. Universal Algebraic techniques are ordinarily used, that provide the flavor in this category.
  
• In the third direction, the relation between algebraic properties of the algebraic counterpart of the logic under study and metalogical properties of the logical system itself are at the focus of investigation. The ability to study logical systems via algebraic means and vice-versa is one of the motivating factors for the development of AAL. As a result, this direction lies at the heart of the field and may be taken as its main raison d'être.
  

• Encyclopedia of Mathematics: Algebraic Logic
• Stanford Encyclopedia of Philosophy: Propositional Consequence Relations and Algebraic Logic
• Wikipedia: Abstract Algebraic Logic
• Wikipedia: Leibniz Operator
  

This page contains references and links to papers that either belong to AAL proper or have had a significant impact in the development of this field. Its purpose is to provide a quick reference resource for people that are working in the field, but most importantly an enticement and a resource for people that are studying the field. The hope is that they will find the papers included in this small treasure chest interesting enough to start a wider search of the relevant bibliography and, maybe even decide to contribute themselves to the field.

I will make an effort to follow a taxonomy both according to year and according to author.

As with any other selection process, the choice of papers for inclusion is a highly subjective task and reflects my own view of the field. I would be glad to receive suggestions and comments as far as something that should be included and is not or something that is included and should not. Any advice will be greatly appreciated and given careful consideration but may not be followed. I would also be very grateful if any authors some of whose papers are listed without a pdf link would offer to send a pdf reprint to me for inclusion in this treasure chest.

© Last updated: October 17, 2010. George Voutsadakis^®