ACG

Flat modal fixpoint logics

Modal fixpoint logics constitute a research field of considerable interest, not only because of its many applications in computer science, but also because of its rich mathematical theory, which features connections with fields as diverse as lattice theory, automata theory, and universal coalgebra.

In this talk I discuss so-called flat fixpoint logics. These arise by adding fixpoint connectives to a basic (poly-)modal languages. The semantics of these fixpoint connectives is defined using a least (or greatest) fixpoint of some modal formula. Examples of such logics, that are all included in the alternation-free fragment of the modal mu-calculus, are LTL and CTL.

After providing the basic definitions I will first discuss the question when such fixpoint connectives are constructive, that is, the fixpoint is approximated in finitely many rounds. I will then turn to the main topic of the talk: the axiomatics of flat modal fixpoint logics. I will present a general completeness theorem, and give a sketch of the proof.

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Published: di 16 maart 2004
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In presentations.

There is a long tradition in theoretical computer science connecting logic and automata theory. As a paradigmatic example we mention the link between the modal mu-calculus and parity automata on graphs. Much of this work has a strong coalgebraic flavour, but to our knowledge this perspective has never been made …
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Automata and Fixed Point Logics for Coalgebras

Published: di 24 februari 2004
By Yde Venema (ILLC at UvA)

In presentations.

There is a long tradition in theoretical computer science connecting logic and automata theory. As a paradigmatic example we mention the link between the modal mu-calculus and parity automata on graphs. Much of this work has a strong coalgebraic flavour, but to our knowledge this perspective has never been made …
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Published: di 01 juli 2003
By Yde Venema (ILLC at UvA)

In presentations.

Nowadays there is an enormous and at times bewildering variety of modal and other non-classical logics. Nevertheless, it still makes sense to speak of `modal logic' as such since there is a well-developed mathematical theory which emphasizes the unity of the field. This theory is supported by a number of …
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