Multi-valued logics, automata, simulations, and games

Orna Kupferman*, Yoad Lustig

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Multi-valued systems are systems in which the atomic propositions and the transitions are not Boolean and can take values from some set. Latticed systems, in which the elements in the set are partially ordered, are useful in abstraction, query checking, and reasoning about multiple view-points. For example, abstraction involves systems in which an atomic proposition can take values from {true, unknown, false}, and these values can be partially ordered according to a "being more true" order (true ≤ unknown ≤ false) or according to a "being more informative" order (true ≤ unknown and false ≤ unknown). For Boolean temporal logics, researchers have developed a rich and beautiful theory that is based on viewing formulas as descriptors of languages of infinite words or trees. This includes a relation between temporal-logic formulas and automata on infinite objects, a theory of simulation relation between systems, a theory of two-player games, and a study of the relations among these notions. The theory is very useful in practice, and is the key to almost all algorithms and tools we see today in verification.

Original languageAmerican English
Title of host publicationVerification, Model Checking, and Abstract Interpretation - 9th International Conference, VMCAI 2008, Proceedings
Number of pages1
StatePublished - 2008
Event9th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2008 - San Francisco, CA, United States
Duration: 7 Jan 20089 Jan 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4905 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th International Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI 2008
Country/TerritoryUnited States
CitySan Francisco, CA


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