Call for Papers
Special Issue of Studia Logica
on Abstract Algebraic Logic
Guest editors: Josep Maria Font and Ramon Jansana (University of Barcelona)
The discipline of Abstract Algebraic Logic can be described as Algebraic Logic for the XXIst century. It gathers all mathematical studies of the process of algebraization of logic in its most abstract and general aspects. In particular it provides frameworks where statements such as "This class of algebras is the algebraic counterpart of that logic" or "A logic satisfies (some form of) the interpolation theorem if and only if its algebraic counterpart satisfies (some form of) amalgamation" become meaningful; then one may be able to prove them in total generality, or one may investigate their scope, or prove them after adding some restrictions, etc.
The term appeared for the first time in Volume II of Henkin-Monk- Tarski's "Cylindric Algebras" (1985), referring to the algebraization of first-order logics, but after the Workshop on Abstract Algebraic Logic (Barcelona, 1997) it has been widely adopted to denote all the ramifications in the studies of sentential-like logics that have flourished following Blok, Pigozzi and Czelakowski's pioneering works in the 1980's. Abstract Algebraic Logic has been considered as the natural evolution of the traditional works in Algebraic Logic in the style of Rasiowa, Sikorski, Wójcicki, etc., and integrates the theory of logical matrices into a more general framework.
The 2010 version of the Mathematics Subject Classification incorporates Abstract Algebraic Logic as entry 03G27, a fact that witnesses the well-delimited, qualitatively distinctive character of this discipline and its quantitative growth. In the Unilog'2010 Congress (Estoril, April 2010) a Special Session has been devoted to this discipline, and all contributors have been invited to submit a paper for this Special Issue. Besides, all active researchers in the field are encouraged to submit.
Topics that can fit this Special Issue include, but are not limited to, the following ones:
- Studies of the Leibniz hierarchy, the Frege hierarchy and their refinements, and relations between them.
- Usage of abstract algebraic logic tools in an essential way to study a specific logic (for instance, to determine its algebraic counterpart, to place it in the above mentioned hierachies, or to obtain some of its metalogical properties).
- Lattice-theoretic and category-theoretic approaches to representability and equivalence of logical systems.
- Use of algebraic tools to study aspects of the interplay between sentential logics and Gentzen systems, hypersequent systems and other kinds of calculi and logical formalisms.
- Formulation of abstract versions of well-known algebraic procedures such as completions, representation theory and duality.
- Studies of the algebraization process for logics where order, besides equality, is the main relation to be considered in the algebraic counterparts.
- Extensions to other frameworks, in particular to those motivated by applications to computer science, such as the theory of institutions, behavioural logics, combining logics, etc.
- Study of algebra-based semantics of first-order logics.
Submissions (in the form of a PDF file) should reach the guest editors by e-mail (to jmfont@ub.edu) not later than 1 December 2010.
last modfied 3.05.2010; designer and webmaster: Krzysztof Pszczola
