Modeling concurrency with partial orders
International Journal of Parallel Programming
Modeling concurrency with geometry
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Event structures and trace monoids
Theoretical Computer Science
A logical study of distributed transition systems
Information and Computation
Undecidability of partial order logics
Information Processing Letters
Modal logic
Linear Time Temporal Logics over Mazurkiewicz Traces
MFCS '96 Proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science
LTL Is Expressively Complete for Mazurkiewicz Traces
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Petri Nets, Event Structures and Domains
Proceedings of the International Sympoisum on Semantics of Concurrent Computation
Linear Time, Branching Time and Partial Order in Logics and Models for Concurrency, School/Workshop
An expressively complete linear time temporal logic for Mazurkiewicz traces
Information and Computation - Special issue: LICS'97
A practical decision method for propositional dynamic logic (Preliminary Report)
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Transition and cancellation in concurrency and branching time
Mathematical Structures in Computer Science
Higher dimensional automata revisited
Mathematical Structures in Computer Science
Deciding Global Partial-Order Properties
Formal Methods in System Design
On the expressiveness of higher dimensional automata
Theoretical Computer Science - Expressiveness in concurrency
From local to global temporal logics over Mazurkiewicz traces
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
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Higher dimensional automata (HDAs) are a model of concurrency that can express most of the traditional partial order models like Mazurkiewicz traces, pomsets, event structures, or Petri nets. Modal logics, interpreted over Kripke structures, are the logics for reasoning about sequential behavior and interleaved concurrency. Modal logic is a well behaved subset of first-order logic; many variants of modal logic are decidable. However, there are no modal-like logics for the more expressive HDA models. In this paper we introduce and investigate a modal logic over HDAs which incorporates two modalities for reasoning about "during" and "after". We prove that this general higher dimensional modal logic (HDML) is decidable and we define a complete axiomatic system for it. We also show how, when the HDA model is restricted to Kripke structures, a syntactic restriction of HDML becomes the standard modal logic. Then we isolate the class of HDAs that encode Mazurkiewicz traces and show how HDML can be restricted to LTrL (the linear time temporal logic over Mazurkiewicz traces).