Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Model checking
Semiring-based constraint logic programming: syntax and semantics
ACM Transactions on Programming Languages and Systems (TOPLAS)
Soft Constraint Logic Programming and Generalized Shortest Path Problems
Journal of Heuristics
A Modal Mu-Calculus for Durational Transition Systems
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Quantitative Analysis and Model Checking
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
A modal logic for mobile agents
ACM Transactions on Computational Logic (TOCL)
Multi-valued symbolic model-checking
ACM Transactions on Software Engineering and Methodology (TOSEM)
Quantitative μ-calculus and CTL defined over constraint semirings
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
A Temporal Logic for Stochastic Multi-Agent Systems
PRIMA '08 Proceedings of the 11th Pacific Rim International Conference on Multi-Agents: Intelligent Agents and Multi-Agent Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Knowledge-Based Policy Conflict Analysis in Mobile Social Networks
Wireless Personal Communications: An International Journal
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Model checking and temporal logics are boolean. The answer to the model checking question does a system satisfy a property? is either true or false, and properties expressed in temporal logics are defined over boolean propositions. While this classic approach is enough to specify and verify boolean temporal properties, it does not allow to reason about quantitative aspects of systems. Some quantitative extensions of temporal logics has been already proposed, especially in the context of probabilistic systems. They allow to answer questions like with which probability does a system satisfy a property? We present a generalization of two well-known temporal logics: CTL and the @m-calculus. Both extensions are defined over c-semirings, an algebraic structure that captures many problems and that has been proposed as a general framework for soft constraint satisfaction problems (CSP). Basically, a c-semiring consists of a domain, an additive operation and a multiplicative operation, which satisfy some properties. We present the semantics of the extended logics over transition systems, where a formula is interpreted as a mapping from the set of states to the domain of the c-semiring, and show that the usual connection between CTL and @m-calculus does not hold in general. In addition, we reason about the feasibility of computing the logics and illustrate some applications of our framework, including boolean model checking.