Related systems
Epistemic planning has two traditions pulling against each other. One starts from expressiveness — dynamic epistemic logic will represent anything, at the cost of the modeller hand-building event models and of undecidable plan existence. The other starts from tractability — restrict the representation until an off-the-shelf planner can be pointed at it.
Action languages sit in between: keep a semantics grounded in DEL, but let the modeller declare who observes what and derive the event models from that. delhi is in this third camp, and specifically implements mB — the branch of that lineage that swapped knowledge for belief.
Expressiveness
| Belief ≠ knowledge | Revision on contradicting evidence | Second-order false belief | False belief about who observed | Conditional B^ψ / safe □ | |
|---|---|---|---|---|---|
| DEL (Baltag–Moss–Solecki; van Ditmarsch et al.) | yes | via specific update rules | yes | yes | in extensions |
| Baltag & Smets (2006, 2008) | yes | yes — this is where it comes from | yes | — | yes, its home ground |
| mA* (Baral, Gelfond, Pontelli & Son) | limited | crude — collapses all uncertainty | no | no | no |
| mA* + higher-order observability (KR 2024) | limited | as mA* | yes | yes | no |
| mB (Buckingham thesis; KR 2021) | yes | yes, preserving other uncertainty | yes | yes (local dynamic observability) | in the models, not the language |
| mB+ / delhi | yes | yes | yes | yes | yes, as query operators |
| EFP / EFP 2.0 (Le, Fabiano, Son & Pontelli) | knowledge-oriented | — | — | — | no |
| PDKB / RP-MEP (Muise et al.) | yes (in the belief work) | bounded | to the depth bound | no | no |
Machinery
| Event models | State representation | Planner | |
|---|---|---|---|
| DEL | hand-built per problem | Kripke models | none inherent; plan existence undecidable in general |
| Baltag & Smets | action-priority update | plausibility models | none — a logic, not a planning system |
| mA* | derived from observability | Kripke models | yes, via ASP or forward search |
| mB | derived from observability | plausibility models | yes (thesis Ch. 6) |
| delhi | derived from observability | plausibility models, bitset-backed | not yet |
| EFP 2.0 | derived | possibilities / Kripke | yes, heavily optimised |
| PDKB | — | proper epistemic knowledge bases, depth-bounded | yes, compiles to classical planning |
What "mB+" means
The name is delhi's own. Buckingham's mB defines its object language with six clauses: atoms, negation, conjunction, knowledge, belief, and common knowledge. Safe belief and conditional belief are genuinely absent from it.
They are not new to the world, though — they are Baltag and Smets's operators, and mB's plausibility models already contain everything needed to evaluate them. delhi adds them to the query language rather than to the semantics, and calls the result mB+ to be clear about which parts came from where.
What else is delhi's own rather than inherited:
- The
askquery system. Patterns with a repeated hole, enumerated over modal literals — the PDKB representation used as a search space rather than a state representation. - Invariants, definitions and Horn rules as language features.
- The performance work. Hash-consed formulas, bitset models and relations, memoised entailment, canonical state keys, and contraction wired into every trace.
~Rproved sound and a congruence, with its incompleteness measured rather than assumed.
Reading the comparison honestly
Two caveats worth stating.
The planner column is where delhi is behind. EFP 2.0 and PDKB are planning systems with years of optimisation; delhi is a model checker with the pieces for a planner sitting idle. If you need plans, not answers about states, they are the mature tools today.
"Limited" for mA* is not a criticism. mA* deliberately trades expressiveness for tractability, and the trade buys real planning performance. The table records what each system chose, not how well it did it.