Speaker: Igor Sedlár (Institute of Computer Science, Czech Academy of Sciences)
Date and Time: Thursday, April 16th 2026, 16:30-18:00
Venue: Online.
Title: Knowledge on a Budget
Abstract. In various computational systems, accessing evidence incurs time, memory or energy costs. However, standard epistemic logics usually model the acquisition of evidence as a cost-free process. In this talk, we bridge the gap between qualitative epistemic reasoning and quantitative resource constraints by introducing semiring-annotated topological spaces (seats). Building on Topological Evidence Logic (TEL), we extend the representation of evidence as open sets, adding an annotation function that maps evidence to semiring ideals, representing the resource budgets sufficient for accessing particular pieces of evidence. This framework allows us to reason not only about what is observable in principle, but also about what is affordable given a specific budget. We demonstrate that seats unify structures from diverse areas of computer science, ranging from programming semantics to database security.
We develop a family of seat-based epistemic logics with resource-indexed modalities and provide sound, strongly complete axiomatisations for these logics. Furthermore, we introduce suitable notions of bisimulation and disjoint union to delineate the expressive power of our framework. Finally, we present filtration-based decidability proofs for particular cases of the framework, namely, logics based on finite semirings and on the tropical semiring of extended natural numbers.
This is joint work with Krishna Manoorkar, Wolfgang Poiger and Ondrej Majer.