Logics Admitting Final Semantics

  title={Logics Admitting Final Semantics},
  author={Alexander Kurz},
  • A. Kurz
  • Published in FoSSaCS 8 April 2002
  • Computer Science
A logic for coalgebras is said to admit final semantics iff-- up to some technical requirements--all definable classes contain a fully abstract final coalgebra. It is shown that a logic admits final semantics iff the formulas of the logic are preserved under coproducts (disjoint unions) and quotients (homomorphicimages). 

Coalgebraic Modal Logic in CoCasl

COCASL is extended by full coalgebraic modal logic based on predicate liftings for functors and becomes a modern modal language that covers a wide range of Kripke and non-Kripke semantics of modal logics via the coal algebraic interpretation.

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It is shown that the well-known coalgebraic modal logic can be expressed in CoCasl, and sufficient criteria for the existence of cofree models is presented, also for several variants of nested cofree and free specifications.

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An analysis of the existing proof systems for dynamic epistemic logic from the viewpoint of proof-theoretic semantics, and a generalisation of Belnap’s cut elimination metatheorem for display calculi and a revised version of the display-style calculus D.EAK are provided.

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  • H. Tews
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  • 2002
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Algebraic-coalgebraic specification in CoCasl



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  • A. Kurz
  • Computer Science, Mathematics
  • 1998

Modal Rules are Co-Implications

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  • G. Rosu
  • Mathematics
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  • 2001

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  • L. Moss
  • Mathematics
    Ann. Pure Appl. Log.
  • 1999

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  • B. Jacobs
  • Mathematics
    RAIRO Theor. Informatics Appl.
  • 2001
This paper gives a semantical underpinning for a many- sorted modal logic associated with certain dynamical systems, like tran- sition systems, automata or classes in object-oriented languages, as coalgebras of so-called polynomial func- tors, built up from constants and identities, using products, coproducts and powersets.

Universal coalgebra: a theory of systems