Almost APAL

Hans Van Ditmarsch, Mo Liu, Louwe B. Kuijer, Igor Sedlar

Research output: Contribution to journalArticleAcademicpeer-review


Arbitrary public announcement logic (APAL) is a logic of change of knowledge with modalities representing quantification over announcements. We present two rather different versions of APAL wherein this quantification is restricted to formulas only containing a subset of all propositional variables: SAPAL and SCAPAL. Such restrictions are relevant in principle for the specification of multi-agent system dynamics. We also present another version of APAL, quantifying over all announcements implied by or implying a given formula: IPAL. We then determine the relative expressivity of all these logics and APAL. We also present complete axiomatizations of SAPAL and SCAPAL and show undecidability of satisfiability for all logics involved, by arguments nearly identical to those for APAL. We show that the IPAL quantifier, motivated by the satisfaction clause for substructural implication, yields a new substructural dynamic consequence relation.
Original languageEnglish
Pages (from-to)1350-1378
Number of pages29
JournalJournal of Logic and Computation
Issue number6
Publication statusPublished - Sept 2023


  • APAL
  • expressivity
  • quantification over announcements
  • substructural logic


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