How to optimize proof-search in modal logics: new methods of proving redundancy criteria for sequent calculi

Authors:
Andrei Voronkov
Affiliations:
Univ. of Manchester, Manchester, U.K.
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2001

Citing 13
Cited 7

Automated deduction in nonclassical logics

Automated deduction in nonclassical logics
A proof-search method for the first order logic

COLOG-88 Proceedings of the international conference on Computer logic
SAT-Based Decision Procedures for Classical Modal Logics

Journal of Automated Reasoning
Equality Elimination for the Tableau Method

DISCO '96 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Logics Workbench 1.0

TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
FaCT and DLP

TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
A Terminological Knowledge Representation System with Complete Inference Algorithms

PDK '91 Proceedings of the International Workshop on Processing Declarative Knowledge
Theorem Proving in Non-Standard Logics Based on the Inverse Method

CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
A Resolution Theorem Prover for Intuitonistic Logic

CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Building Decision Procedures for Modal Logics from Propositional Decision Procedure - The Case Study of Modal K

CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
SPASS & FLOTTER Version 0.42

CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Reasoning in expressive description logics

Handbook of automated reasoning
On evaluating decision procedures for modal logic

IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1

The Inverse Method Implements the Automata Approach for Modal Satisfiability

IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
From tableaux to automata for description logics

Fundamenta Informaticae
Automata can show PSpace results for description logics

Information and Computation
Automated reasoning in modal and description logics via SAT encoding: the case study of KmALC-satisfiability

Journal of Artificial Intelligence Research
One-pass tableaux for computation tree logic

LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
A practical automata-based technique for reasoning in expressive description logics

IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
From Tableaux to Automata for Description Logics

Fundamenta Informaticae - The 1st International Workshop on Knowledge Representation and Approximate Reasoning (KR&AR)

Quantified Score

Hi-index	0.02

Visualization

Abstract

We present a bottom-up decision procedure for propositional modal logic K based on the inverse method. The procedure is based on the “inverted” version of a sequent calculus. To restrict the search space, we prove a number of redundancy criteria for derivations in the sequent calculus. We introduce a new technique of proving redundancy criteria, based on the analysis of tableau-based derivations in K. Moreover, another new technique is based on so-called traces. A new search with a strong notion of subsumption. This technique is based on so-called traces. A new formalization of the inverse method in the form of a path calculus considerably simplifies all proofs as compared to the previously published presentations of the inverse method. Experimental results demonstrate that our method is competitive with many state-of-the-art implementations of K.