1,721,148 research outputs found
Completeness and Decidability of the Deducibility Problem for Some Classes of Formulas of Set Theory
Full text linkSome extension of results on the decidability of classes of formulas in set theory is proved. In particular some class of restricted quantified formulas is proved to be decidable also in the case in which the underlying axiomatic set theory does not contain the axiom of foundation. For all the classes considered is also studied whether or not they result to be not only decidable, but also complete and a simple decidable but not complete class of formulas is presented
Secision Procedures for Elementary Sublanguages of Set Theory XI. Unsolvability of the Decision Problem for a Restricted Subclass of the Delta_0-Formulas in Set Theory
No full text(Hybrid) automata and (stochastic) programs - The hybrid automata lattice of a stochastic program
No full textWe define a semantics for stochastic Concurrent Constraint Programming (sCCP), a stochastic process algebra, in terms of stochastic hybrid automata with piecewise deterministic continuous dynamics. To each program we associate a lattice of hybrid models, parameterized with respect to the degree of discreteness left. We study some properties of this lattice, presenting also an alternative semantics in which the degree of discreteness can be dynamically changed
Temporal Logic. From Ancient Ideas to Artificial Intelligence,by Peter Ohrstrom and Per F.V. Hasle (book review)
No full textIs Hyper-extensionality Preservable Under Deletions of Graph Elements?
Full text linkAny hereditarily finite set S can be represented as a finite pointed graph –dubbed membership graph– whose nodes denote elements of the transitive closure of {S} and whose edges model the membership relation. Membership graphs must be hyper-extensional, that is pairwise distinct nodes are not bisimilar and (uniquely) represent hereditarily finite sets.
We will see that the removal of even a single node or edge from a membership graph can cause “collapses” of different nodes and, therefore, the loss of hyper-extensionality of the graph itself. With the intent of gaining a deeper understanding on the class of hyper-extensional hereditarily finite sets, this paper investigates whether pointed hyper-extensional graphs always contain either a node or an edge whose removal does not disrupt the hyper-extensionality property
The Bernays-Schoenfinkel-Ramsey Class in Set Theory: Decidability
No full textAs proved recently. the satisfaction problem for all prenex formulae in the set-theoretic Bernays-Shonfinkel-Ramsey class is semi-decidable over von Neumann's cumulative hierarchy. Here that semi-decidability result is strengthened into a decidability result for the same collection of formulae
Expressing Infinity without Foundation
Full text linkThe axiom of infinity can be expressed by stating the existence of sets satisfying a formula which involves restricted universal quantifiers only, even if the axiom of foundation is not assumed
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