In Gerla (1987), G. Gerla introduced the so-called transformational semantics for predicate modal logic and considered in particular semantic frame- works given by a classical model endowed with a group of automorphisms, where a boxed formula is true iff it holds invariantly (i.e. it remains true whenever an automorphism is applied to the individuals it is talking about). With this interpreta- tion, de dicto modalities collapse, but de re modalities remain quite informative. We handle the axiomatization problem of such modal structures, by employing classic model-theoretic tools (iterated ultrapowers and double chains).

The Invariance Modality / S. Ghilardi (OUTSTANDING CONTRIBUTIONS TO LOGIC). - In: V.A. Yankov on Non-Classical Logics, History and Philosophy of Mathematics / [a cura di] A. Citkin, I.M. Vandoulakis. - [s.l] : Springer, 2022 Nov. - ISBN 978-3-031-06842-3. - pp. 165-175 [10.1007/978-3-031-06843-0_6]

### The Invariance Modality

#### Abstract

In Gerla (1987), G. Gerla introduced the so-called transformational semantics for predicate modal logic and considered in particular semantic frame- works given by a classical model endowed with a group of automorphisms, where a boxed formula is true iff it holds invariantly (i.e. it remains true whenever an automorphism is applied to the individuals it is talking about). With this interpreta- tion, de dicto modalities collapse, but de re modalities remain quite informative. We handle the axiomatization problem of such modal structures, by employing classic model-theoretic tools (iterated ultrapowers and double chains).
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Quantified modal logic; Presheaf semantics; Invariance modality; Ultrapowers
Settore MAT/01 - Logica Matematica
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