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The expressive power of modal logic with inclusion atoms
Modal inclusion logic is the extension of basic modal logic with inclusion
atoms, and its semantics is defined on Kripke models with teams. A team of a
Kripke model is just a subset of its domain. In this paper we give a complete
characterisation for the expressive power of modal inclusion logic: a class of
Kripke models with teams is definable in modal inclusion logic if and only if
it is closed under k-bisimulation for some integer k, it is closed under
unions, and it has the empty team property. We also prove that the same
expressive power can be obtained by adding a single unary nonemptiness operator
to modal logic. Furthermore, we establish an exponential lower bound for the
size of the translation from modal inclusion logic to modal logic with the
nonemptiness operator.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
Logic in Opposition
It is claimed hereby that, against a current view of logic as a theory of consequence, opposition is a basic logical concept that can be used to define consequence itself. This requires some substantial changes in the underlying framework, including: a non-Fregean semantics of questions and answers, instead of the usual truth-conditional semantics; an extension of opposition as a relation between any structured objects; a definition of oppositions in terms of basic negation. Objections to this claim will be reviewed
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