Almost APAL

0557952 - ÚI 2024 RIV GB eng J - Journal Article
van Ditmarsch, H. - Liu, M. - Kuijer, L. B. - Sedlár, Igor
Almost APAL.
Journal of Logic and Computation. Roč. 33, č. 6 (2023), s. 1350-1378. ISSN 0955-792X. E-ISSN 1465-363X
Institutional support: RVO:67985807
Keywords : APAL * quantification over announcements * substructural logic * expressivity
OECD category: Pure mathematics
Impact factor: 0.7, year: 2022
Method of publishing: Open access
http://dx.doi.org/10.1093/logcom/exac012

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.
Permanent Link: http://hdl.handle.net/11104/0331834