307,391 research outputs found
A Temporal Logic for Hyperproperties
Hyperproperties, as introduced by Clarkson and Schneider, characterize the
correctness of a computer program as a condition on its set of computation
paths. Standard temporal logics can only refer to a single path at a time, and
therefore cannot express many hyperproperties of interest, including
noninterference and other important properties in security and coding theory.
In this paper, we investigate an extension of temporal logic with explicit path
variables. We show that the quantification over paths naturally subsumes other
extensions of temporal logic with operators for information flow and knowledge.
The model checking problem for temporal logic with path quantification is
decidable. For alternation depth 1, the complexity is PSPACE in the length of
the formula and NLOGSPACE in the size of the system, as for linear-time
temporal logic
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
Between quantum logic and concurrency
We start from two closure operators defined on the elements of a special kind
of partially ordered sets, called causal nets. Causal nets are used to model
histories of concurrent processes, recording occurrences of local states and of
events. If every maximal chain (line) of such a partially ordered set meets
every maximal antichain (cut), then the two closure operators coincide, and
generate a complete orthomodular lattice. In this paper we recall that, for any
closed set in this lattice, every line meets either it or its orthocomplement
in the lattice, and show that to any line, a two-valued state on the lattice
can be associated. Starting from this result, we delineate a logical language
whose formulas are interpreted over closed sets of a causal net, where every
line induces an assignment of truth values to formulas. The resulting logic is
non-classical; we show that maximal antichains in a causal net are associated
to Boolean (hence "classical") substructures of the overall quantum logic.Comment: In Proceedings QPL 2012, arXiv:1407.842
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