Proof systems for lattice theory

Author:

NEGRI SARA,VON PLATO JAN

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.

Publisher

Cambridge University Press (CUP)

Subject

Computer Science Applications,Mathematics (miscellaneous)

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The intensional side of algebraic-topological representation theorems;Synthese;2017-02-14

2. Logic of approximate entailment in quasimetric spaces;International Journal of Approximate Reasoning;2015-09

3. Proof analysis in intermediate logics;Archive for Mathematical Logic;2011-11-20

4. Combinatorial analysis of proofs in projective and affine geometry;Annals of Pure and Applied Logic;2010-11

5. A solution of the uniform word problem for ortholattices;Mathematical Structures in Computer Science;2010-05-27

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