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The formal, recursive definition of DRSs and DRS-Conditions.

If are discourse referents () and () are DRS-conditions then the following is a DRS:

If is a relation symbol of arity ( ), and are some discourse referents, then is a DRS-Condition;

If and are first-order terms, then is a DRS-Condition;

If and are DRSs, then and are DRS-Conditions;

If is a DRS, then is a DRS-Condition;

Nothing is a DRS or DRS-Condition unless it can be shown to be so using clauses 1-5.

Here, first-order terms (clause 3) denote either discourse referents or constants. We sometimes refer to DRS-Conditions of the form licensed by clauses 2-3 as ``basic'' conditions, while those licensed by clauses 3-5 are called *complex* conditions. Note that, in a way, DRSs bear a lot of similarities with the first-order logic formula syntax. As in first-order logic, we have the boolean connectors (, , ) to create nested boxes and express implication, disjunction, and negation. But unlike first-order logic, we don't have explicit conjunction, and we don't have explicit quantifiers. With a formal definition of the syntax of DRSs at our disposal, we are now in a good position to define *subordination* (a relation between DRSs), which then opens the way to define accessibility.

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Aljoscha Burchardt, Stephan Walter, Alexander Koller, Michael Kohlhase, Patrick Blackburn and Johan Bos

Version 1.2.5 (20030212)