Quantales and Temporal Logics
B. Möller, P. Höfner, G. Struth
2006-06
in: Universität Augsburg
Technical Report, Institute of Computer Science, University of Augsburg, June 2006
Abstract:
We provide an algebraic semantics for the temporal logic CTL
* and
simplify it for its sublogics CTL and LTL. We abstractly represent
state and path formulas over transition systems in Boolean left
quantales. These are complete lattices with an operation of
multiplication that is completely disjunctive in its left argument
and isotone in its right argument. On these quantales, the semantics
of CTL
* formulas can be encoded via finite and infinite iteration
operators, the CTL and LTL operators can be related to domain operators.
This yields interesting new connections between representations as known from
the modal μ-calculus and Kleene/ω-algebraic ones.
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