Updating knowledge using subsets

Larry Moss and Rohit Parikh used subset semantics to characterize a family of logics for reasoning about knowledge. An important feature of their framework is that subsets always decrease based on the assumption that knowledge always increases. We drop this assumption and modify the semantics to account for logics of knowledge that handle arbitrary changes, that is, changes that do not necessarily result in knowledge increase, such as the update of our knowledge due to an action. We present a system which is complete for subset spaces and prove its decidability.

[1]  Bernhard Heinemann.  Temporal Aspects of the Modal Logic of Subset Spaces , 1999, Theor. Comput. Sci..

[2]  Dov M. Gabbay,et al.  Products of Modal Logics, Part 1 , 1998, Log. J. IGPL.

[3]  Henrik Sahlqvist.  Completeness and Correspondence in the First and Second Order Semantics for Modal Logic , 1975 .

[4]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[5]  Marcus Kracht,et al.  Properties of independently axiomatizable bimodal logics , 1991, Journal of Symbolic Logic.

[6]  Bernhard Heinemann,et al.  A PDL-Like Logic of Knowledge Acquisition , 2007, CSR.

[7]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[8]  Wiebe van der Hoek,et al.  Dynamic Epistemic Logic and Knowledge Puzzles , 2007, ICCS.

[9]  D. Gabbay,et al.  Many-Dimensional Modal Logics: Theory and Applications , 2003 .

[10]  R. Goldblatt.  Logics of Time and Computation , 1987 .

[11]  Lawrence S. Moss,et al.  Topological Reasoning and the Logic of Knowledge , 1996, Ann. Pure Appl. Log..

[12]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[13]  Jelle Gerbrandy,et al.  Dynamic epistemic logic , 1998 .

[14]  Bernhard Heinemann,et al.  Topology and Knowledge of Multiple Agents , 2008, IBERAMIA.

[15]  Konstantinos Georgatos,et al.  Modal Logics for Topological Spaces , 2000, ArXiv.

[16]  Renate A. Schmidt,et al.  On combinations of propositional dynamic logic and doxastic modal logics , 2008, J. Log. Lang. Inf..