TL;DR
This paper investigates contact posets, demonstrating their embeddability into Boolean posets with overlap contact relations, and explores their algebraic properties and applications to event structures in computer science.
Contribution
It introduces the embedding of contact posets into Boolean posets and analyzes their algebraic properties like superamalgamation and Fraïssé limits, with applications to event structures.
Findings
Contact posets can be embedded into Boolean posets with overlap contact relations.
Contact posets and contact semilattices possess superamalgamation property.
Results have applications to event structures with binary conflict in computer science.
Abstract
We study contact posets and show that every contact poset can be embedded into a Boolean poset with overlap contact relation. Contact posets and (nonadditive) contact semilattices have the superamalgamation property, Fra\"\i ss\'e limits and model completion. Some results apply to event structures with binary conflict, as introduced in computer science.
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Taxonomy
TopicsLogic, Reasoning, and Knowledge · Formal Methods in Verification · Logic, programming, and type systems