Commitment Space Development #
@cite{krifka-2015}
Worked examples exercising the tree-based commitment space operations from @cite{krifka-2015}. Each test uses a concrete 2-world model (rain vs no rain) and verifies specific predictions about how assertions, questions, acceptance, and rejection interact.
Key Predictions Tested #
- Assertion narrows the CG (root changes immediately)
- Questions preserve the CG (root unchanged)
- Question-then-accept = assert (same CG)
- Reject returns to pre-question state
- Questions make settled spaces unsettled; acceptance re-settles
- Bipolar questions create two continuations
- Matching tags combine assertion + question bias
Two-world model: it's raining or it's not.
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After asserting "it's raining", the root contains the rain proposition (the CG now reflects the assertion).
After assertion, the rain-world is compatible with the CG.
After assertion, the no-rain-world is NOT compatible.
Assertion preserves settledness: asserting into an empty (settled) space yields a settled space.
The speaker's commitment slate records the assertion.
The addressee's slate is unchanged (they haven't accepted yet).
After questioning "is it raining?", the root is unchanged (the CG is preserved — the question doesn't assert anything).
The question adds exactly one continuation (monopolar).
The continuation contains the questioned proposition.
Questioning makes the state unstable (there's an unresolved proposal).
Both worlds are still compatible with the CG after a question.
Accepting the question's continuation puts rain in the root (CG).
After acceptance, the space is settled again.
After acceptance, rain-world is compatible, no-rain is excluded.
Rejecting the question's continuation preserves the original root.
After rejection, the space is settled again.
After rejection, both worlds are still live (we're back to start).
The core equivalence: questioning φ and then accepting gives the same CG (root) as directly asserting φ. The two modes of updating converge on the same common ground.
The context sets are extensionally equal: same truth at every world.
Bipolar question preserves root (CG unchanged).
Bipolar question creates two continuations.
After ?rain on empty space: { root = [], continuations = [[rain]] } After ?¬rain: root stays, new continuation [¬rain] added, existing [rain] narrowed to [¬rain, rain]. By Krifka's (14): {√C} ∪ (C + S₂⊢¬rain).
Result: continuations = [[¬rain], [¬rain, rain]].
The second continuation has both rain AND ¬rain — which is contradictory (no world satisfies both). This models Krifka's observation that stacking questions can create unsatisfiable continuations.
The first continuation of the bipolar question has ¬rain. Accepting this means we commit to no rain.
Accepting the first continuation of a bipolar question yields a CG where only the no-rain world is compatible.
After asserting ¬rain over a pending rain-question, the root is narrowed to ¬rain.
The continuation is contradictory: it requires both ¬rain and rain.
The contradictory continuation has no compatible worlds.
The root has rain (from the assertion).
There is one continuation (from the question).
The continuation also has rain (the question adds rain to an already-rain root). The question is biased because it proposes what the speaker has already asserted.
Accepting the continuation of a matching tag gives the same CG as the assertion alone. The question was redundant in terms of content — its function is to seek confirmation, not new information.
A hedge modifies the JP layer (epistemic status) to weak.
"I think p" = assertion with epistemicStatus :=.weak.
The TP content (p) is unchanged; only the JP layer is modified.
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Hedging preserves content (TP is untouched by JP modification).
Hedging reduces epistemic status to weak.
Hedging does not affect commitment strength.
An oath modifies the ComP layer (commitment strength) to strong.
"I swear p" = assertion with commitmentStrength :=.strong.
The TP content (p) is unchanged; only the ComP layer is modified.
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Oaths preserve content (TP is untouched by ComP modification).
Oaths increase commitment strength to strong.
Oaths do not affect epistemic status.
JP and ComP can co-occur: hedging + oath on the same assertion.
"I think I swear p": epistemicStatus = weak, commitmentStrength = strong. "I swear I think p": same result (layers are independent).
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Order doesn't matter: hedge(oath(la)) = oath(hedge(la)).
Hedged oath is weak epistemic + strong commitment.
Both modifications preserve TP content.
Hedge data matches JP modification: All canonical hedges reduce commitment, and JP → weak is the mechanism.
Oath data matches ComP modification: All canonical oaths increase commitment, and ComP → strong is the mechanism.