Common Knowledge Always, Forever

AI 总结

• There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e
• g
• , modelling evidence, degrees of belief, and self-reference
• We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model prop…
• The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property

内容摘录

There has been an increasing interest in topological semantics for epistemic logic, which has been shown to be useful for, e.g., modelling evidence, degrees of belief, and self-reference. We introduce a polytopological PDL capable of expressing common knowledge and various generalizations and show it has the finite model property over closure spaces but not over Cantor derivative spaces. The latter is shown by embedding a version of linear temporal logic with `past', which does not have the finite model property.