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We prove the Lyndon Theorem and the Łoś–Tarski Theorem for the modal \mucalculus, using automata which run on process graphs and are equivalent in expressive power to the \mucalculus.
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In this paper, we show that certain subreducts of the class of representable
relation algebras are not finitely axiomatizable. We do the same for sequential
and cylindric algebras.
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THE RANGE OF MODAL LOGIC
an essay in memory of George Gargov
Johan van Benthem
George Gargov was an active pioneer in the 'Sofia School' of modal logicians.
Starting in the 1970s, he and his colleagues expanded the scope of the subject
by introducing new modal expressive power, of various innova...
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Rohit Parikh has been one of the pioneers at the interface of modal and
dynamic logic. Bringing dynamic, processoriented concerns into modal logic
has been a major move, whose repercussions are still being felt today. In
this contribution, I consider the bridge concept of bisimulation, which ...
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We prove that there are uncountably many sets that are low for the class of
Schnorr random reals. We give a purely recursion theoretic characterization
of these sets and show that they all have Turing degree incomparable to 0'.
This contrasts with a result of Kucera and Terwijn on sets that ar...
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A positive answer to a question of M. van Lambalgen and D. Zambella
whether there exist nonrecursive sets that are low for the class of
random sets is obtained. Here a set A is low for the class RAND of
random sets if RAND = RAND^A.
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In this note we wish to draw attention to certain points of detail, concerning
the subtle differences between several possible versions of Gentzen systems and
systems of natural deduction. In notation and terminology we conform to [TS96].
Gentzen([Gen35]) introduced the calculi LJ, LK with left...
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The paper discusses the transition from informal concepts to
mathematically precise notions; examples are given, and in some
detail the case of lawless sequences, a concept of intuitionistic
mathematics, is discussed. A final section comments on philo
sophical discussions concerning intuitionist...
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We show that the $E^+$class can be decided by a liftable order, when it is
applied a posteriori. This is a surprising result, because the $E^+$class was
one of the motivations for the study of nonliftable orders. Also surprising
is the behaviour of the resolution process. Initially the variabl...
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We introduce a modal language for talking about projective planes. This
language is twosorted, containing formulas to be evaluated at points and
at lines, respectively. The language has two diamonds whose intended
accessibility relations are the two directions of the incidence relation
betwe...
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The preservation of Sahlqvist equations in completions of Boolean algebras
with operators
Steven Givant, Yde Venema
Monk [1970] extended the notion of the completion of a Boolean algebra to
Boolean algebras with operators. Under the assumption that the operators of
such an algebra A are compl...