TY - CHAP
T1 - Knowledge and simplicial complexes
AU - van Ditmarsch, Hans
AU - Goubault, Éric
AU - Ledent, Jérémy
AU - Rajsbaum, Sergio
PY - 2022/5/5
Y1 - 2022/5/5
N2 - Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and also dynamics in the shape of simplicial action models. We give a survey on how to interpret all such notions on simplicial complexes, building upon the foundations laid in Goubault et al. (Inf Comput 278:104597, 2021).
AB - Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can define: knowledge, belief, bisimulation, the group notions of mutual, distributed and common knowledge, and also dynamics in the shape of simplicial action models. We give a survey on how to interpret all such notions on simplicial complexes, building upon the foundations laid in Goubault et al. (Inf Comput 278:104597, 2021).
KW - bisimulation
KW - epistemic models
KW - knowledge and belief
KW - logical tools
KW - simplicial complexes
UR - https://arxiv.org/abs/2002.08863
U2 - 10.1007/978-3-030-75267-5_1
DO - 10.1007/978-3-030-75267-5_1
M3 - Chapter
SN - 9783030752668
VL - 143
T3 - Philosophical Studies Series
SP - 1
EP - 50
BT - Philosophy of Computing
PB - Springer
CY - Cham, Switzerland
ER -