Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras

7 pages•Published: July 28, 2014

Abstract

We show how to implement an effective decision procedure to check if a propositional Basic Logic formula is a tautology. For a formula with $n$ variables, the procedure consists of a translation, depending on $n$, from Basic Logic to the language of Satisfiability Modulo Theories SMT-LIB2 using the theory of quantifier free linear real arithmetic. Many efficient SMT-solvers exist to decide formulas in the SMT-LIB2 language. We also study finitely generated varieties of Basic Logic (BL-)algebras and give a description of the lattice of these varieties. Extensions to finitely generated varieties of Generalized BL-algebras are discussed, and a simple connection between finite GBL-algebras and finite closure algebras is noted.

Keyphrases: basic logic, decision procedure, gbl algebras, lattice of varieties

In: Nikolaos Galatos, Alexander Kurz and Constantine Tsinakis (editors). TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, vol 25, pages 113-119.

Links:	https://easychair.org/publications/paper/dxv
	https://doi.org/10.29007/nptc

BibTeX entry

@inproceedings{TACL2013:Basic_Logic_SMT_solvers,
  author    = {Peter Jipsen},
  title     = {Basic Logic, SMT solvers and finitely generated varieties of GBL-algebras},
  booktitle = {TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic},
  editor    = {Nikolaos Galatos and Alexander Kurz and Constantine Tsinakis},
  series    = {EPiC Series in Computing},
  volume    = {25},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/dxv},
  doi       = {10.29007/nptc},
  pages     = {113-119},
  year      = {2014}}

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