Abstract:We introduce a logic for non distributed, deterministic Abstract State Machines with parallel function updates. Unlike other logics for ASMs which are based on dynamic logic, our logic is based on an atomic predicate for function updates and on a definedness predicate for the termination of the evaluation of transition rules. We do not assume that the transition rules of ASMs are in normal form, for example, that they concern distinct cases. Instead we allow structuring concepts of ASM rules including sequential composition and possibly recursive submachine calls. We show that several axioms that have been proposed for reasoning about ASMs are derivable in our system. We provide also an extension of the logic with explicit step information which allows to eliminate modal operators in certain cases. The main technical result is that the logic is complete for hierarchical (non-recursive) ASMs. We show that, for hierarchical ASMs, the logic is a definitional extension of first-order predicate logic.
We introduce a logic for non distributed, deterministic Abstract State Machines with parallel function updates. Unlike other logics for ASMs which are based on dynamic logic, our logic is based on an atomic predicate for function updates and on a definedness predicate for the termination of the evaluation of transition rules. We do not assume that the transition rules of ASMs are in normal form, for example, that they concern distinct cases. Instead we allow structuring concepts of ASM rules including sequential composition and possibly recursive submachine calls. We show that several axioms that have been proposed for reasoning about ASMs are derivable in our system. We provide also an extension of the logic with explicit step information which allows to eliminate modal operators in certain cases. The main technical result is that the logic is complete for hierarchical (non-recursive) ASMs. We show that, for hierarchical ASMs, the logic is a definitional extension of first-order predicate logic.
The use of designations, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Java and all Java-based marks are trademarks or registered trademarks of Sun Microsystems, Inc. in the United States and other countries. Springer-Verlag is independent of Sun Microsystems, Inc.
We explore a connection between different ways of representing information in computer science. We show that relational databases, modules, algebraic specifications and constraint systems all satisfy the same ten axioms. A commutative semigroup together with a lattice satisfying these axioms is then called an "information algebra". We show that any compact consequence operator satisfying the interpolation and the deduction property induces an information algebra. Conversely, each finitary information algebra can be obtained from a consequence operator in this way. Finally we show that arbitrary (not necessarily finitary) information algebras can be represented as some kind of abstract relational database called a tuple system. Mathematics Subject Classification (2000). Primary 03B22; Secondary 03G15 03G25 08A70 68Q99 94A99 03C95.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.