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Proof systems for lattice theory

Published online by Cambridge University Press:  05 August 2004

SARA NEGRI  and
JAN VON PLATO
SARA NEGRI
Affiliation:
Department of Philosophy, PL 9, 00014 University of Helsinki, Finland Email: sara.negri@helsinki.fi
JAN VON PLATO
Affiliation:
Department of Philosophy, PL 9, 00014 University of Helsinki, Finland Email: jan.vonplato@helsinki.fi
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Abstract

A formulation of lattice theory as a system of rules added to sequent calculus is given. The analysis of proofs for the contraction-free calculus of classical predicate logic known as G3c extends to derivations with the mathematical rules of lattice theory. It is shown that minimal derivations of quantifier-free sequents enjoy a subterm property: all terms in such derivations are terms in the endsequent.

An alternative formulation of lattice theory as a system of rules in natural deduction style is given, both with explicit meet and join constructions and as a relational theory with existence axioms. A subterm property for the latter extends the standard decidable classes of quantificational formulas of pure predicate calculus to lattice theory.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 14 , Issue 4 , August 2004 , pp. 507 - 526
Copyright
2004 Cambridge University Press

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