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Conference Paper

Representation Theorems and the Semantics of (Semi)Lattice-based Logics


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

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Sofronie-Stokkermans, V. (2001). Representation Theorems and the Semantics of (Semi)Lattice-based Logics. In Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logics (pp. 125-134). Los Alamitos, CA: IEEE.

Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-3238-8
This paper gives a unified presentation of various non-classical logics. We show that a general representation theorem (which has as particular instances the representation theorems as algebras of sets for Boolean algebras, distributive lattices and semilattices) allows to establish a relationship between algebraic models and Kripke-style models, and illustrate the ideas on several examples. Based on this, we present a method for automated theorem proving by resolution in such logics. Other representation theorems, as algebras of sets or as algebras of relations, as well as relational models are also mentioned.