de.mpg.escidoc.pubman.appbase.FacesBean
English
 
Help Guide Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Conference Paper

On the Universal Theory of Varieties of Distributive Lattices with Operators: Some Decidability and Complexity Results

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45516

Sofronie-Stokkermans,  Viorica
Automation of Logic, MPI for Informatics, Max Planck Society;
Programming Logics, MPI for Informatics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available
Citation

Sofronie-Stokkermans, V. (1999). On the Universal Theory of Varieties of Distributive Lattices with Operators: Some Decidability and Complexity Results. In H. Ganzinger (Ed.), Proceedings of the 16th International Conference on Automated Deduction (CADE-16) (pp. 157-171). Berlin, Germany: Springer.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-367B-0
Abstract
In this paper we give a method for automated theorem proving in the universal theory of certain varieties of distributive lattices with well-behaved operators. For this purpose, we use extensions of Priestley's representation theorem for distributive lattices. We first establish a link between satisfiability of universal sentences with respect to varieties of distributive lattices with operators and satisfiability with respect to certain classes of relational structures. We then use these results for giving a method for translation to clause form of universal sentences in such varieties, and obtain decidability and complexity results for the universal theory of some such varieties. The advantage is that we avoid the explicit use of the full algebraic structure of such lattices, instead using sets endowed with a reflexive and transitive relation and with additional functions and relations. We first studied this type of relationships in the context of finitely-valued logics and then extended the ideas to more general non-classical logics. This paper shows that the idea is much more general. In particular, the method presented here subsumes both existing methods for translating modal logics to classical logic and methods for automated theorem proving in finitely-valued logics based on distributive lattices with operators.