Hennessy-Milner and Van Benthem for Instantial Neighbourhood Logic

Groot, Jim de

doi:10.1007/s11225-021-09975-w

Stud Logica

2022

DOI: 10.1007/s11225-021-09975-w

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Hennessy-Milner and Van Benthem for Instantial Neighbourhood Logic

Jim de Groot

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Cited by 2 publications

References 34 publications

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A correspondence theorem for interpretability logic with respect to Verbrugge semantics

Horvat,

Perkov

2024

Logic Journal of the IGPL

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Interpretability logic is a modal logic that can be used to describe relative interpretability between extensions of a given first-order arithmetical theory. Verbrugge semantics is a generalization of the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. The Van Benthem Correspondence Theorem establishes modal logic as the bisimulation invariant fragment of first-order logic. In this paper we show that a special type of bisimulations, the so-called w-bisimulations, enable an analogue of the Van Benthem Theorem for interpretability logic w.r.t. Verbrugge semantics.

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A correspondence theorem for interpretability logic with respect to Verbrugge semantics

Horvat,

Perkov

2024

Logic Journal of the IGPL

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Non-distributive positive logic as a fragment of first-order logic over semilattices

Groot

2023

Journal of Logic and Computation

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We characterize non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations because they relate pairs of states from one model to single states from another. En route to this result, we use a more traditional notion of simulations and prove a Hennessy–Milner-style theorem for it, using an analogue of modal saturation called meet-compactness.

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Hennessy-Milner and Van Benthem for Instantial Neighbourhood Logic

Cited by 2 publications

References 34 publications

A correspondence theorem for interpretability logic with respect to Verbrugge semantics

A correspondence theorem for interpretability logic with respect to Verbrugge semantics

Non-distributive positive logic as a fragment of first-order logic over semilattices

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