📄 Context Dynamics

Summary

The paper asks how an assertion changes the shared information in a conversation, assuming the speakers jointly know a compositional semantics. The orthodox Stalnakerian answer, called here Standard Updating, holds that for every world belonging to the context set, exactly one compositional context interprets the assertion, so the assertion expresses exactly one proposition there. The update works by diagonalization: a world is removed when the proposition expressed there is false there. Caie argues that this picture cannot account, in a principled way, for some natural discourses. These involve configurational predicates such as 'pair of socks'. He proposes Disjunctive Updating as a generalization. Several compositional contexts may interpret an assertion at a world, and a world is removed only when the disjunction of all propositions expressed there fails at that world. A companion principle, Contextual Pruning, lets earlier assertions narrow the contexts available for later ones. Together these predict the problematic update patterns. The account also offers a non-expressivist reading of formalisms proposed by Barker and MacFarlane.

Key points

• The paper distinguishes two notions of context. Compositional contexts are parameter sequences (following Kaplan 1989) that fix the values of indexicals, demonstratives and gradable adjectives. Context sets are the worlds compatible with what all participants presuppose (following Stalnaker 1978).
• Standard Updating requires a unique interpreting context per world and updates by diagonalization.
• The counterexamples are two discourses, Tim Likes Matching and Tim Dislikes Mixed, which are built around the configurational predicate 'pair of socks'.
• Disjunctive Updating allows one-to-many interpretation. Contextual Pruning makes the propositions a sentence expresses depend systematically on what earlier assertions in the same discourse expressed.
• The account is compared with Barker 2002 and 2013, MacFarlane 2020 and King 2021. King's view also allows multiple interpretations but sometimes updates conjunctively. Whether Disjunctive Updating can cover those conjunctive cases is left open.

Interesting ideas

• I1. Instead of committing to one reading of a vague or context-dependent expression, keep the full set of admissible readings and discard a possibility only if none of them holds; this avoids premature, arbitrary disambiguation.
• I2. Contextual Pruning means each assertion both adds information and shrinks the pool of interpretations allowed for later sentences, so discourse history steers interpretation.
• I3. Keep the semantic parameters that interpret a sentence separate from the shared information state that the sentence modifies, because they play different roles.
• I4. Treat an assertion as eliminating possibilities from a set of candidate worlds, so that a conclusion counts as established only when all surviving worlds agree.
• I5. Short, carefully built discourses around a single tricky predicate can show where a theory fails.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (world): Predicates like "pair", "tall" or "near" could carry a set of candidate interpretations in the world of the text, and a state would be ruled out only when every candidate contradicts it.
• I2 (frames): Frame building could keep a per-discourse register of admissible senses or parameters that earlier sentences progressively narrow, giving an explainable trace of why a later word got its reading.
• I3 (world): The world model could store interpretation settings (comparison classes, standards for gradable adjectives) apart from entity states, so that each can be updated and inspected on its own.
• I4 (answer): Readers answering fable or test questions could return "yes", "no" or "undetermined" depending on whether all remaining world variants agree, with the eliminated variants serving as the explanation.
• I5 (learn): Evaluation suites could include minimal discourse pairs with configurational predicates as negative controls, checking that the system's updates change correctly when the preceding sentence changes.