Institutions: abstract model theory for specification and programming
Journal of the ACM (JACM)
Nondeterminism in algebraic specifications and algebraic programs
Nondeterminism in algebraic specifications and algebraic programs
A complete calculus for the multialgebraic and functional semantics of nondeterminism
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algebraic approaches to nondeterminism—an overview
ACM Computing Surveys (CSUR)
Rasiowa-Sikorski deduction systems in computer science applications
Theoretical Computer Science
Rasiowa-Sikorski Deduction Systems: A Handy Tool for Computer Science Logics
WADT '98 Selected papers from the 13th International Workshop on Recent Trends in Algebraic Development Techniques
Multialgebras, Power Algebras and Complete Calculi of Identities and Inclusions
Selected papers from the 10th Workshop on Specification of Abstract Data Types Joint with the 5th COMPASS Workshop on Recent Trends in Data Type Specification
Modeling Partiality by Nondeterminism
ISAS-SCI '01 Proceedings of the World Multiconference on Systemics, Cybernetics and Informatics: Information Systems Development-Volume I - Volume I
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We develop a quantifier-free logic for deriving consequences of multialgebraic theories. Multialgebras are used as models for nondeterminism in the context of algebraic specifications. They are many sorted algebras with set-valued operations. Formulae are sequents over atoms allowing one to state set-inclusion or identity of 1-element sets (determinacy). We introduce a sound and weakly complete Rasiowa-Sikorski (R-S) logic for proving multialgebraic tautologies. We then extend this system for proving consequences of specifications based on translation of finite theories into logical formulae. Finally, we show how such a translation may be avoided--introduction of the specific cut rules leads to a sound and strongly complete Gentzen system for proving directly consequences of specifications. Besides giving examples of the general techniques of R-S and the specific cut rules, we improve the earlier logics for multialgebras by providing means to handle empty carriers (as well as empty result-sets) without the use of quantifiers, and to derive consequences of theories without translation into another format and without using general cut.