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Richard Wilke

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Highlights Conference 2021 Conference Abstract

Inquisitive Monadic Second-Order Logic

  • Richard Wilke

Inquisitive semantics is a branch of logic where formulae are evaluated against a set of relational structures over the same domain rather than against a single structure as in classical logics. Such a set can be viewed as an information state, where the variety in the structures encodes uncertainty of the propositions. In a logic with inquisitive semantics, not only statements about structures can be formulated but a formula can also query if the available information suffices to settle whether a proposition holds, or not. Formulae of this kind are referred to as questions. An information state settles a question if all of its structures agree on its truth. Inquisitive semantics can be applied to many different logics and in the present work we focus on inquisitive first-order logic (InqBQ) introduced by Ciardelli. A core property of this logic, called persistency, states that whenever a formula holds in an information state, it also holds in all of its refinements (i. e. its subsets). In this talk we introduce inquisitive monadic second-order logic (InqMSO) a natural extension of InqBQ which is closed under negation and therefore does not satisfy persistency. Our main goal is to understand InqFO as a fragment of InqMSO, hence we present a syntactical fragment of InqMSO which is equivalent to InqBQ. We further show that there are persistent InqMSO-formulae which are not expressible in InqBQ. This is joint work with Erich Grädel.

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CSL Conference 2020 Conference Paper

On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics

  • Matthias Hoelzel
  • Richard Wilke

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables the handling and provides a better understanding of this fragment. We also introduce inclusion-exclusion games that turn out to be precisely the corresponding model-checking games. These games are not only interesting in their own right, but they also are a key factor towards building a bridge between the semantic and syntactic fragments. On the level of logics with team semantics we additionally present restrictions of inclusion-exclusion logic to capture the union closed fragment. Moreover, we define a team based atom that when adding it to first-order logic also precisely captures the union closed fragment of existential second-order logic which answers an open question by Galliani and Hella.

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v2026.09.13