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On modal logics of linear inequalities
 Proc. AiML 2010
, 2010
"... We consider probabilistic modal logic, graded modal logic and stochastic modal logic, where linear inequalities may be used to express numerical constraints between quantities. For each of the logics, we construct a cutfree sequent calculus and show soundness with respect to a natural class of mode ..."
Abstract

Cited by 4 (1 self)
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We consider probabilistic modal logic, graded modal logic and stochastic modal logic, where linear inequalities may be used to express numerical constraints between quantities. For each of the logics, we construct a cutfree sequent calculus and show soundness with respect to a natural class of models. The completeness of the associated sequent calculi is then established with the help of coalgebraic semantics which gives completeness over a (typically much smaller) class of models. With respect to either semantics, it follows that the satisfiability problem of each of these logics is decidable in polynomial space. Keywords: Probabilistic modal logic, graded modal logic, linear inequalities
Flat Coalgebraic Fixed Point Logics
"... Abstract. Fixed point logics are widely used in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the µcalculus and its relatives. However, popular fixed point logics tend to trade expressivity for simplicity and readability, and ..."
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Abstract. Fixed point logics are widely used in computer science, in particular in artificial intelligence and concurrency. The most expressive logics of this type are the µcalculus and its relatives. However, popular fixed point logics tend to trade expressivity for simplicity and readability, and in fact often live within the single variable fragment of the µcalculus. The family of such flat fixed point logics includes, e.g., CTL, the ∗nestingfree fragment of PDL, and the logic of common knowledge. Here, we extend this notion to the generic semantic framework of coalgebraic logic, thus covering a wide range of logics beyond the standard µcalculus including, e.g., flat fragments of the graded µcalculus and the alternatingtime µcalculus (such as ATL), as well as probabilistic and monotone fixed point logics. Our main results are completeness of the KozenPark axiomatization and a timedout tableaux method that matches EXPTIME upper bounds inherited from the coalgebraic µcalculus but avoids using automata. 1