## Abstract

Spatial constraint systems (scs) are semantic structures for reasoning about spatial and epistemic information in concurrent systems. We develop the theory of scs to reason about the distributed information of potentially infinite groups. We characterize the notion of distributed information of a group of agents as the infimum of the set of join-preserving functions that represent the spaces of the agents in the group. We provide an alternative characterization of this notion as the greatest family of join-preserving functions that satisfy certain basic properties. For completely distributive lattices, we establish that the distributed information of c amongst a group is the greatest lower bound of all possible combinations of information in the spaces of the agents in the group that derive c. We show compositionality results for these characterizations and conditions under which information that can be obtained by an infinite group can also be obtained by a finite group. Finally, we provide an application to mathematical morphology where dilations, one of its fundamental operations, define an scs on a powerset lattice. We show that distributed information represents a particular dilation in such scs.

Original language | English (US) |
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Article number | 100674 |

Journal | Journal of Logical and Algebraic Methods in Programming |

Volume | 121 |

DOIs | |

State | Published - Jun 1 2021 |

### Bibliographical note

Funding Information:This work has been partially supported by the ECOS-NORD project FACTS ( C19M03 ).

Publisher Copyright:

© 2021 Elsevier Inc.

## Keywords

- Algebraic modeling
- Distributed knowledge
- Infinitely many agents
- Mathematical morphology
- Reasoning about groups
- Reasoning about space