Representation Theorems and Theorem Proving in Non-Classical Logics

Authors:
Viorica Sofronie-Stokkermans
Affiliations:
-
Venue:
ISMVL '99 Proceedings of the Twenty Ninth IEEE International Symposium on Multiple-Valued Logic
Year:
1999

Citing 0
Cited 4

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

CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Automated deduction for many-valued logics

Handbook of automated reasoning
Representation theorems and the semantics of non-classical logics, and applications to automated theorem proving

Beyond two
Resolution-based decision procedures for the universal theory of some classes of distributive lattices with operators

Journal of Symbolic Computation

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Abstract

In this paper we present a method for automated theorem proving in non-classical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestley-style representation for distributive lattices with operators in order to define a class of Kripke-style models with respect to which the logic is sound and complete. If this class of Kripke-style models is elementary, it can then be used for a translation to clause form; satisfiability of the resulting clauses can be checked by resolution. We illustrate the ideas by several examples.