Independence-friendly logic without Henkin quantification

Fausto Barbero, Lauri Hella, Raine Rönnholm

Tutkimustuotos: ArtikkeliScientificvertaisarvioitu

2 Lataukset (Pure)

Abstrakti

We analyze the expressive resources of IF logic that do not stem from Henkin (partially-ordered) quantification. When one restricts attention to regular IF sentences, this amounts to the study of the fragment of IF logic which is individuated by the game-theoretical property of action recall (AR). We prove that the fragment of prenex AR sentences can express all existential second-order properties. We then show that the same can be achieved in the non-prenex fragment of AR, by using “signalling by disjunction” instead of Henkin or signalling patterns. We also study irregular IF logic (in which requantification of variables is allowed) and analyze its correspondence to regular IF logic. By using new methods, we prove that the game-theoretical property of knowledge memory is a first-order syntactical constraint also for irregular sentences, and we identify another new first-order fragment. Finally we discover that irregular prefixes behave quite differently in finite and infinite models. In particular, we show that, over infinite structures, every irregular prefix is equivalent to a regular one; and we present an irregular prefix which is second order on finite models but collapses to a first-order prefix on infinite models.

AlkuperäiskieliEnglanti
JulkaisuArchive for Mathematical Logic
DOI - pysyväislinkit
TilaJulkaistu - 16 kesäk. 2021
OKM-julkaisutyyppiA1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Julkaisufoorumi-taso

  • Jufo-taso 1

!!ASJC Scopus subject areas

  • Philosophy
  • Logic

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