Systematic software development using VDM
Systematic software development using VDM
Computational aspects of three-valued logic
Proc. of the 8th international conference on Automated deduction
Theoretical Computer Science
Readings in nonmonotonic reasoning
On interpretation of inconsistent theories
Information Sciences: an International Journal
Information and Computation
Bilattices and the semantics of logic programming
Journal of Logic Programming
Natural 3-valued logic—characterization and proof theory
Journal of Symbolic Logic
Kleene's three valued logics and their children
Fundamenta Informaticae
The semantic foundations of logic: predicate logic
The semantic foundations of logic: predicate logic
Sequent formalizations of three-valued logic
Partiality, modality, and nonmonotonicity
Artificial Intelligence
Basic proof theory (2nd ed.)
Canonical Propositional Gentzen-Type Systems
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Automated deduction for many-valued logics
Handbook of automated reasoning
Coherent integration of databases by abductive logic programming
Journal of Artificial Intelligence Research
Kripke semantics for basic sequent systems
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
| Hi-index | 0.00 |
A classical Gentzen-type system is one which employs two-sided sequents, together with structural and logical rules of a certain characteristic form. A decent Gentzen-type system should allow for direct proofs, which means that it should admit some useful forms of cut elimination and the subformula property. In this survey we explain the main difficulty in developing classical Gentzen-type systems with these properties for many-valued logics. We then illustrate with numerous examples the various possible ways of overcoming this difficulty, and the strong connection between semantic completeness and cut-elimination in each case. Our examples include practically all 3- valued and 4-valued logics, as well as Gödel finite-valued logics and some well-known infinite-valued logics.