Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Logical Analysis of Dynamic Dependence   Many forms of dependence manifest themselves over time, with behavior of
variables in dynamical systems as a paradigmatic example. This paper studies
temporal dependence in dynamical systems from a logical perspective, by
extending a minimal modal base logic of static functional dependencies. We
define a logic for dynamical systems with single time steps, provide a complete
axiomatic proof calculus, and show the decidability of the satisfiability
problem for a substantial fragment. The system comes in two guises: modal and
first-order, that naturally complement each other. Next, we consider a timed
semantics for our logic, as an intermediate between state spaces and temporal
universes for the unfoldings of a dynamical system. We prove completeness and
decidability by combining techniques from dynamic-epistemic logic and modal
logic of functional dependencies with complex terms for objects. Also, we
extend these results to the timed logic with functional symbols and term
identity. Finally, we conclude with a brief outlook on how the system proposed
here connects with richer temporal logics of system behavior, and with dynamic
topological logic.

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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg