This discipline 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 "A logic satisfies (some form of) the interpolation theorem if and only if the class of its algebraic counterparts 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", referring to the algebraization of first-order logics, but after the Workshop on Abstract Algebraic Logic (Barcelona, 1997) it has been 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 will incorporate Abstract Algebraic Logic as entry 03G27, which witnesses the well-delimited, qualitatively distinctive character of this discipline and its quantitative growth.

Topics that can fit this Special Session include, but are not limited to, the following ones:

  • Studies of the Leibniz hierarchy, the Frege hierarchy and their refinements, and relations between them.
  • 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.
  • Study 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 motivated by applications to computer science, such as institutions, behavioural logics, secrecy logic, etc.
  • Study of algebra-based semantics of first-order logics.
Abstract Algebraic Logic

Special Session

Organized by Josep Maria Font

and Ramon Jansana

University of Barcelona, Spain

Accepted contributed talks

1. Félix Bou, Research Institute in Artificial Intelligence, Bellaterra and Umberto Rivieccio, Università di Genova
"Implicative Bilattices"

2. Carlos Caleiro and Ricardo Gonçalves, Instituto Superior Técnico, Lisboa
"Behavioral algebraization of logics I"

3. Petr Cintula, Academy of Sciences of the Czech Rrepublic and Carles Noguera, Research Institute in Artificial Intelligence, Bellaterra
"A general approach to non-classical first-order logics"

4. Janusz Czelakowski, Opole University, Poland
"Some Structural Theorems on Congruence-Modular Quasivarieties of Algebras"

5. Lisa Fulford and Alessandra Palmigiano, Universiteit van Amsterdam
"Modular canonicity for bi-implicative algebras"

6. Nikolaos Galatos,University of Denver and José Gil-Férez, Japan Advanced Institute of Science and Technology
"The Isomorphism Problem for modules over quantaloids, Part I"

7. Àngel Gil, Universitat Pompeu Fabra, Barcelona
"On Hilbertizable Gentzen systems associated with finite valued logics"

8. José Gil-Férez, Japan Advanced Institute of Science and Technology and Nikolaos Galatos, University of Denver
"The Isomorphism Problem for modules over quantaloids, Part II "

9. Ricardo Gonçalves and Carlos Caleiro, Instituto Superior Técnico, Lisboa
"Behavioral algebraization of logics II"

10. Ramon Jansana,Universitat de Barcelona
"Equationally orderable quasivarieties and sequent calculi"

11. Tomasz Kowalski, Università di Cagliari, Francesco Paoli, Università di Cagliari and Matthew Spinks, La Trobe University
"Quasi-subtractive varieties"

12. Manuel A. Martins, Universidade de Aveiro
"Abstract Algebraic Logic approach to Algebraic Specification"

13. Michal l. Stronkowski,Warsaw University of Technology
"Finite axiomatizability theorems and sub-technology"