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Hybridization of Institutions
"... Abstract. Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for nami ..."
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Abstract. Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to ‘universalize ’ the hybridization idea. Following the lines of [16], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institutionindependent level. The method extends arbitrary institutions with Kripke semantics (for multimodalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL) determines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features. 1
The Complexity of Satisfiability for Fragments of Hybrid Logic  Part II
, 2010
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On the hybrid extension of CTL and CTL+
, 2009
"... The paper studies the expressivity, relative succinctness and complexity of satisfiability for hybrid extensions of the branchingtime logics CTL and CTL + by variables. Previous complexity results show that only fragments with one variable do have elementary complexity. It is shown that H 1 CTL + a ..."
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The paper studies the expressivity, relative succinctness and complexity of satisfiability for hybrid extensions of the branchingtime logics CTL and CTL + by variables. Previous complexity results show that only fragments with one variable do have elementary complexity. It is shown that H 1 CTL + and H 1 CTL, the hybrid extensions with one variable of CTL + and CTL, respectively, are expressively equivalent but H 1 CTL + is exponentially more succinct than H 1 CTL. On the other hand, HCTL +, the hybrid extension of CTL with arbitrarily many variables does not capture CTL ∗, as it even cannot express the simple CTL ∗ property EGFp. The satisfiability problem for H 1 CTL + is complete for triply exponential time, this remains true for quite weak fragments and quite strong extensions of the logic.